Supporting Early Numeracy - nlpslearns.sd68.bc.ca · 2 SUPPORTING EARLY NUMERACY Connecting Assessment and Instruction When used at the end of kindergarten or early in grade one,

B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) I

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Supporting Early NumeracyBC Early Numeracy Project (K-1)

Ministry of Education



Ministry of Education

S U P P O R T I N G E A R L Y N U M E R A C Yii

N AT I O N A L L I B R A RY O F C A N A D I A N C ATA L O G U I N G I N P U B L I C AT I O N D ATAMain entry under title:Supporting early numeracy : BC Early Numeracy Project (K-1)

“Developed by the British Columbia Early NumeracyProject to complement Assessing early numeracy.”—Introd.

ISBN 0-7726-5134-5

1. Arithmetic - Study and teaching (Elementary) -British Columbia. 2.Arithmetic - Study and teaching(Preschool) - British Columbia. I. British Columbia.Ministry of Education. II. British Columbia. EarlyNumeracy Project. III. Title: Assessing early numeracy.

QA135.6.S96 2004 372.7’2044 C2004-960017-6

© 2003 Ministry of Education, Province of British Columbia.

C O P Y R I G H T N OT I C E

No part of this document may be reproduced in any form or by any means,including electronic storage, reproduction, execution or transmissionwithout the prior written consent of the Province.

P R O P R I E TA RY N OT I C E

This document contains information that is proprietary and confidential to theProvince. Any reproduction, disclosure or other use of this document is expresslyprohibited except as the Province may authorize in writing.

Permission to copy and use this publication in part, or in its entirety, for non-profiteducational purposes within British Columbia and the Yukon, is granted to all staffof BC school board trustees, including teachers and administrators; organizationscomprising the Educational Advisory Council as identified by Ministerial Order; andother parties providing direct or indirect education programs to entitled students asidentified by the School Act.

B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) iii

Table of ContentsTable of Contents

Introduction . . . 1

Introducing Supporting Early Numeracy . . . 1

Connecting Assessment and Instruction . . . 2

Using Assessment Results to Inform Instruction . . . 4

Fostering Numeracy Development . . . 5

Framework for Number Development . . . 7

Numeracy Experiences in K-1 Classrooms . . . 10

Quick Tour of This Resource . . . 13

Small-Group Intervention . . . 15

Surprise Box . . . 15

Focused Instruction for the Classroom . . . 27

Estimation . . . 27

Pattern . . . 47

Counting and Numeral Recognition . . . 59

Visual-Spatial Pattern Recognition . . . 78

Math Playground . . . 91

Masters

Master 1: Sorting Boards . . . 101

Master 2: Two-column Bar Graph . . . 102

Master 3: Comparison Strips . . . 103

Master 4: Ladybug Mat . . . 104

Master 5: Ten-frame Mat . . . 105

Master 6: Dice Game Record Sheet . . . 106

S U P P O R T I N G E A R L Y N U M E R A C Yiv

Master 7: Dice Pattern Cards . . . 107

Master 8: Numeral Cards 0–9 . . . 108

Master 9: 100 Chart . . . 109

Master 10: Number Lines . . . 110

Master 11: Record Sheet 1 . . . 111

Master 12: Record Sheet 2 . . . 112

Master 13: 5-Way Sorting Mat . . . 113

Master 14: 100 Chart Grid . . . 114

Master 15: Coin Cut-outs . . . 115

Master 16: Dice Mat . . . 116

Master 17: Domino Mat . . . 117

Master 18: Dot Pattern Cards . . . 118

Master 19a: Domino Cards . . . 119

Master 19b: Domino Cards . . . 120

Master 20: Ten-frame Cards . . . 121

Master 21: Ladybug Cards . . . 122

Master 22: Ten-frame Mats . . . 123

Master 23: Double Ten-frame Cards . . . 124

Master 24: Pattern Cards . . . 125

Master 25: Pattern Game Board . . . 126

Master 26: Small 100 Charts . . . 127

Master 27: Geoboards . . . 128

Master 28: Bingo Cards . . . 129

Master 29: Cover the Blocks 1 . . . 130



Master 32: Cover and Copy . . . 133

Master 33: Pattern Block Challenge . . . 134

Master 34: Combinations 1 . . . 135

B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) v



Master 37: How Many Triangles? 1 . . . 138





Master 42: Tangram Matching . . . 143

Master 43: Tangram Cover-up 1 . . . 144







Master 50: Surprise Box Record Sheet . . . 151

Master 51: Large Triangles for Triangle Challenge . . . 152

Master 52: Squared Paper . . . 153

Master 53: Triangle Paper . . . 154

Master 54: Assessment Class Compilation . . . 155

B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 1

Introduction

“There is a bigchange for mein terms ofhow I assess.… a lot of kidsjust aren’t ableto share theirthinking in awritten formator even inpictorial form. ”

Introduction

Introducing Supporting Early Numeracy

Supporting Early Numeracy was developed by the British Columbia

Early Numeracy Project to complement Assessing Early Numeracy.

● Assessing Early Numeracy helps teachers determine which

children would benefit from support in grade one and identifies

the aspects on which to focus.

● Supporting Early Numeracy is an instructional resource to

support grade one students who are at risk of falling behind

because they lack basic numeracy concepts, skills and attitudes.

Children who would benefit from using these materials include

those who:

– need explicit and structured support

– hesitate to ask for assistance

– avoid taking risks

– do not demonstrate growth or progress over time

– might respond to an alternative approach

Supporting Early Numeracy provides teaching suggestions to follow

up the K-1 assessment. An overall focus of the resource is to develop

positive math attitudes or dispositions. The content focuses on

number sense (Estimation, pages 27–46; Pattern, pages 47–58;

Counting and Numeral Recognition, pages 59–77) and spatial

thinking (Visual-Spatial Pattern Recognition, pages 78–90; Math

Playground, pages 91–100).

S U P P O R T I N G E A R L Y N U M E R A C Y2

Connecting Assessment and Instruction

When used at the end of kindergarten or early in grade one, the K-1

Early Numeracy Assessment can help you determine which

students might benefit most from the activities in this resource.

Once you have completed the assessment, the Learner Profiles

you compile provide an overview of each child’s strengths and

weaknesses. This information can be used to determine

appropriate follow-up instruction for individuals, small groups

or the whole class.

Supporting Early Numeracy was informed by the Framework

for Number Development described on pages 7 to 9.

The developmental progression (Emergent,

Early, Developing, Expanding and Established)

is noted in the directions for each activity (with the exception of

those in Surprise Box and Math Playground). These levels are

approximate and are meant to be used only as a guideline.

❍ ❍ ❍ ❍ ❍


Counting, Visual- MathEstimation Pattern Numerals Spatial Playground

1 Mathematical Awareness

2 Recognizing Dot Patterns

3 Matching Numerals and Sets

4 Ordering Numerals 0-9

5 Counting Forward

6 Counting Backwards

7 Estimate and Check

8 Invariance and Counting On

9 Build and Change

10 Pattern Items

11 Problem Solving

12 Squares Puzzle

13 Reading Numerals

14 Printing Numerals

15 Coin Sets •

16 Cube Building •

17 100 Chart •

• optional items

Table 1: Linking Assessing Early Numeracy withSupporting Early Numeracy

The following table shows how Supporting Early Numeracy

connects to the different assessment items in Assessing Early

Numeracy. A dark screen indicates a major relationship, a light

screen indicates a minor relationship, and no screen indicates

no relationship.


Using Assessment Results to Inform

Instruction

S U P P O R T I N G E A R LY N U M E R AC Y

Supporting Early Numeracy offers instructional suggestions for

follow-up to the assessment:

S M A L L - G R O U P I N T E RV E N T I O N

You may find children who struggled with most or all of the items

on the assessment. These children likely would benefit most from

additional support working in a small-group setting outside the

classroom to build or consolidate kindergarten-level early numeracy

skills. The section designed with these children in mind is Surprise

Box, a small-group intervention program for children at risk.

F O C U S E D I N S T RU C T I O N F O R T H E C L A S S R O O M

Some children perform strongly on some assessment items and

struggle with others. The chart on page 31 can help to determine

which parts of this resource to use for working on specific concepts

and skills. The Focused Instruction for the Classroom section

contains skill-specific activities that are designed to be used in

small groups (or with the whole class if appropriate).

W E B S I T E R E S O U R C E S

The Ministry of Education website (http://www.bced.gov.bc.ca/

primary_program/) also provides access to Math for Families –

Supporting Numeracy at Home, which provides suggestions for

ways that families can continue to support children’s numeracy

development through at home activities. Please encourage parents

to use the ideas in Math for Families – Supporting Numeracy at

Home on the website. You are also invited to duplicate the parts you

would like to share with families in newsletters, conferences or

family mathematics sessions.


Fostering Numeracy Development

Supporting Early Numeracy balances spatial and number content to

encourage alternative paths to success. The lessons and activities

described in this resource develop numeracy skills in ways that are

active and fun.

● Number sense involves number skills, number concepts and a

positive mathematical disposition.

● Spatial activities involving hands-on experiences provide the

sensory input that helps to develop mental imagery.

● Attitude is key. Children who see themselves as capable math

thinkers and problem solvers are on the road to mathematical

success.

● The focus is on meaning, with skills used in context. The more

connections children can make, the better.

● Visual cues and formats support learning.

● Building mental imagery expands children’s ability to think in

flexible ways.

● Bridges are built to new learning by first reviewing what the children

know and then connecting their knowledge to new goals.

● Emphasis is gradually put on making written records of the

activities that can be used for reinforcement in the classroom

and at home.



Framework for Number Development

K

Grade 1

Grade 2

Grade 3

Table 2: Typical Number Concept DevelopmentPatterns for K-3

In Assessing Early Numeracy a research-based developmental

scheme is used as a frame of reference to consider children’s

understanding of number. This frame of reference is not tied to ages

or grades. Rather, it highlights growth in number reasoning and

understanding. Table 2 includes a graphic representation of the

scheme’s levels. This graphic is included with the activity directions

in Supporting Early Numeracy to provide you with “at a glance”

information about each activity’s level.

❍ ❍ ❍ ❍ ❍

Emergent Early Developing Expanding Established

K

Grade 1

Grade 2

Grade 3

The following framework for the development of number is based

on extensive research. This framework is concerned first with the

underlying conceptual development that provides the foundation

for children’s understanding of number. Though the rate and nature

of growth in number understanding varies for every child, growth

generally follows the described sequence from emergent to

established number.

The following chart summarizes the characteristics of the develop-

mental scheme. These stages or levels of understanding are perhaps

the most important aspect of a child’s grasp of number, and have

important implications for the development of early numeracy.


Emergent Number

Children at this stage rely on

visual perception to make

estimates. They are starting to

use the language of quantity

but are not yet counting

systematically (e.g., they can

tell you which of two piles

contains more by “eyeballing”

them and seeing that one is

bigger, but they can’t count

the groups).

Children’s thinking at this pre-

counting stage typically

demonstrates:

● reliance on intuitive

reasoning

● unsystematic means of

counting (e.g., 1, 2, 3, 5,

8, 9…)

● visual-spatial strengths,

with perception used as

the basis for judgments

● multisensory

dependence (i.e., need

to see, hear, feel/touch)

● the ability to recognize

visual-spatial groupings

(e.g., dice patterns)

without counting

Early Number

Once children have

established a reliable one-to-

one counting scheme, they are

able to work systematically

with quantities of gradually

increasing size. At this stage,

for example, given an

established set of 10, when 2

more are added, they will

count from 1 to 12.

Children’s thinking at this

stage typically demonstrates:

● a systematic counting

chain to at least 10

● counting by 1s from 1.

This is called “Count All.”

● one-to-one

correspondence at least

for small quantities

● dependence on the use

of materials to support

thinking

● an ordinal view of

number (e.g., 3 means

number 3 in the row)

● a lack of invariance or

conservation of

number; perception still

dominates

Framework for the Development of Number

SNAPSHOT

CHILDREN’STHINKING


Expanding Number

Counting is no longer limited to

1s. Children can use mental chunks

as part of the quantifying process

(e.g., asked for the sum of 5+6, they

will use the known fact of 5+5 and

add 1 more to 10). This is the

early basis of place value reasoning

and multiplicative thinking.

Children’s thinking at this stage

typically demonstrates:

● a preference for using mental

reasoning, drawing on known

facts and relationships

● an ability to think in chunks

rather than counting by 1s

(shifting to many-to-one

correspondence)

● a grasp of place value, which

extends their number range

● an understanding of

reversibility and part-whole

thinking

Developing Number

Children are now able to

mentally represent a quantity

and count on or back (e.g., given

an established set of 10, when 2

more are added, they will count

11, 12). Children at this stage

conceptualize 10 as a unit and

group and count objects in

10s, but often revert to counting

by 1s.



● reliance on counting by 1s

including counting on or

back from a starting set

(e.g., 5+3…5…6, 7, 8)

● the ability to count on or

back with tally (double

count—e.g., put out

fingers to show 1, 2, 3 but

count on 12, 13, 14)

● a cardinal view of number:

- inclusion relation

(e.g., sees 3 as part of 5)

- conservation of

number

● the ability to mentally

represent number

● reliance on fingers,

touching or head nods to

support counting

Established Number

This stage represents a shift from

additive thinking to multiplicative

reasoning. Children have moved from

relying on counting by 1s to relying

on more powerful groupings and

relationships (e.g., asked for the sum

of 27 and 35, they can mentally

decompose the numbers into 10s and

1s and recompose the groupings).



● efficient use of facts,

relationships, strategies

● extensive mental

representation

● the ability to keep track of

several operations at once

● fully operational grouping

structures—i.e., can

meaningfully shift place values;

rename metric measures (e.g.,

2␣ m = 200 cm); and recognize

equivalent fractional parts (e.g.,

2 whole pies = 4 half pies)


Numeracy Experiences in K-1 Classrooms

A rich mathematical environment is important for all kindergarten

children. Children benefit from early exposure to a wide range of

mathematical concepts, skills and attitudes, and the opportunity to

learn from these experiences. The following list provides examples

of kindergarten experiences typical of a rich mathematical

environment. The Integrated Resource Package (IRP) was used as

the starting point for this list; however, some elaboration has been

provided on particular aspects. It is important to keep in mind that

this list involves exposure or “the opportunity to learn” in

kindergarten. It is not a list of expectations for all children.

In order for this assessment to be fair, it is important that

kindergarten children have had the opportunity to learn the

concepts and skills assessed. The following overview describes

learning opportunities that kindergarten students might experience

as part of a rich mathematical literacy program.

N U M B E R C O N C E P T S A N D O PE R AT I O N S

● using a wide variety of concrete, hands-on manipulatives for

counting

● comparing more or less

● counting and comparing how many students are here today

(number of boys/girls/in all)

● ordering/sequencing sets, pictures and numbers from least to

greatest

● counting forward and backwards to and from 20

● using counting rhymes and finger play

● estimating and checking guesses for objects, actions, times, and

so on

● counting beyond 20—people, things, actions, days (e.g.,

celebrate the 100th day of school)

● solving problems involving joining, separating, grouping and

sharing, drawn from real-life situations

● being exposed to numbers from 0 to 100, including the use of

number lines and 100 charts

● using calendar activities to count forward and backwards to

specific days or events (e.g., someone’s birthday)


● recognizing, identifying and printing numerals from 1 to 10

(minimum)

● matching objects and numerals to 10 (minimum)

● using numbers on the computer keyboard

● counting by 2s, 5s and 10s and connecting counting to the

number line and 100 chart using colour coding

● grouping using counting sticks or straws and bundling quantities

by 2s, 5s, 10s and 100s

● cutting snacks (e.g., apples) into equal parts to share

● understanding half as part of a whole

● playing games using dice and playing cards to reinforce increase/

decrease skills (e.g., Box Cars and One-Eyed Jacks)

● being exposed to part/whole relationships (e.g., using two-sided

counters: 3 red, 2 white, 5 in all)

P AT T E R N S

● creating, identifying, reproducing and extending patterns using a

variety of hands-on manipulatives (e.g., Unifix cubes, pattern

blocks, buttons)

● creating, identifying, reproducing and extending patterns using

different body actions (e.g., clapping, snapping, stomping,

patting) and pictures or diagrams

● using words to describe the pattern (e.g., red, red, blue, red, red,

blue or a, a, b, a, a, b)

● being exposed to and experiencing patterns using the Calendar

● looking for patterns on the 100 chart

● experiencing dot patterns through the use of dice and dominoes

games

● identifying patterns in the environment or surroundings

M E A S U R E M E N T

● experiencing non-standard units (e.g., estimate and check how

many paper clips or Unifix cubes are needed to make the length

of the chalk brush)

● ordering objects by size, length, height and/or weight; identifying

which object is bigger/smaller, longer/shorter, taller/shorter,

heavier/lighter

● reading the thermometer and identifying the temperature through

daily calendar activities; using the terms hotter, colder or warmer


● being exposed to units of time through daily calendar activities

(e.g., days of the week/times of the day/seasons)

● being exposed to the names and values of different Canadian

coins (penny, nickel, dime, quarter, loonie, toonie) through

informal activities (e.g., set up a store or restaurant with a cash

register)

● comparing different-size containers on the water table; using the

terms empty, full, half-full

S H A PE S

● recognizing, identifying and creating basic shapes (square, circle,

triangle, rectangle, oval, diamond)

● making body shapes in the gym

● identifying basic shapes in the environment or in their

surroundings (e.g., going on a Shape Walk to identify shapes: tires

are circles; the door is a rectangle; and so on)

● sorting and classifying objects by shapes

● tracing and drawing different shapes

● patterning with shapes (e.g., using pattern blocks: diamond,

square; diamond, square)

● experimenting and constructing using foam or wooden blocks

V I S UA L - S PAT I A L

● being exposed to tangram shapes, geometric puzzles.

● using tangram or pattern block pieces to re-create a picture or

build on top of a picture

● using geoboards and geobands

● being exposed to dice and domino patterns

● being exposed to simple symmetry using mirrors and pattern

blocks

S TAT I S T I C S A N D P R O B A B I L I T Y / D ATA A N A LY S I S

● collecting, organizing and comparing data using appropriate

language (e.g., more/less)

● conducting surveys (e.g., surveying their classmates)

● graphing information and interpreting data

● using many different types of graphs to record information in a

variety of ways


● being exposed to concepts such as always, sometimes, and never

● being exposed to probability through dice activities (e.g., Box

Cars) and other fun, hands-on activities (e.g., How many red

candies do you think are in this box?)

Quick Tour of This Resource

Supporting Early Numeracy is divided into two sections:

● Small-Group Intervention

● Focused Instruction for the Classroom

The blackline masters for both sections are located on pages 101–151.

S M A L L - G R O U P I N T E RV E N T I O N

Surprise Box—an instructional sequence for working with at-risk

grade one children in a small-group setting outside of the

classroom. The Surprise Box resource is designed to develop

positive attitudes and kindergarten-level concepts and skills in a

supportive environment.


Surprise Box Part 4Surprise Box Part 4

W H AT D O YO U N E E D ?

● Two-Column Bar Graph (Master 2)

● Comparison Strips (Master 3)

● Numeral Cards for 7 and 8 (Master 8; use

only if child is secure in recognizing

numerals up to 6)

W H A T ’ S I N T H E B O X ?

● Each box contains up to 15 Unifix cubes of

two colours (e.g., 7+8 or 6+9).

● Have extra cubes available for patterning,

but put the same number back in the boxes.

W H AT D O YO U D O ?

● Count objects as they come out of the boxes

and go back into the boxes.

● Count backwards as you return one cube at

a time to the box (e.g., “3 red cubes, 2 red

cubes, 1 red cube, 0 red cubes. All the red

ones are in the box—3, 2, 1, 0. Now let’s do

our blue cubes—4 in all, and so on.”) Use

subsets of one colour at a time, increasing

the number gradually.

● Sort and count, using comparative language.

● Work on recognizing parts of a set and the

whole set (e.g., 3 red, 5 blue, 8 cubes in all).

● Work on creating and reading patterns,

making sounds and actions to match.

L A N G UAG E TO M O D E L A N D E N C O U R AG E

● part/whole language (e.g., some, all, none)

● the language of addition and subtraction

(when items are put into and taken out of

the boxes)

● pattern words (e.g., repeat, same, change,

different)

P R O C E S S E S T O M O D E L A N D E N C O U R AG E

● representing patterns and collections in

various ways

D I S P O S I T I O N S TO E N C O U R A G E

● positive attitude: Patterning is fun; I can

continue patterns; I can count and compare

groups.




● part/whole mat, such as Ladybug Mat

(Master 4)

● 10-Frame Mats (Master 5)

● dice

● Dice Game Record Sheet (Master 6)


● Each box has up to 20 objects, 6 round

counters as one set, 10 and 4 as the others.


● Count to 20 for all objects in the box; count

back from 10 using subsets.

● Name parts and wholes for sets to 6 using

part/whole mats.

● Make sets of 10 on 10-frames, matching to

fingers.

● Part/Whole Game:

5 little ants in all.

Some are hiding under the rock.

4 are on the rock.

How many are hidden?

Let’s check:

4 on the rock.

1 under the rock.

5 in all.

This time 2 are on the rock….

L A N G UA G E TO M O D E L A N D E N C O U R A G E

● words for pulling apart and putting back

together (e.g., separate, join, subtract, add)

● names for numbers, naming parts of wholes

(e.g., 4 and 2 is a name for 6; 3 and 3 is

another name for 6)

P R O C E S S E S TO M O D E L A N D E N C O U R A G E

● building sets of 10

● recognizing numerals

● printing numerals

● using number rhymes to remember numerals

D I S P O S I T I O N S T O E N C O U R AG E

● positive self-concept: I can take sets apart and

rejoin them; I can name parts and wholes.



Find and Read Two-Digit NumbersFind and Read Two-Digit Numbers

Math Focus: Two-Digit Numbers❍ ● ● ❍ ❍


◗ wall-size 100 Chart

◗ wall calendar

◗ individual sets of Numeral Cards 0-9 (Master 8)

W H AT A R E YO U L O O K I N G F O R ?

Can the children:

◗ count to 100?

◗ give the number that comes after, to 100?

◗ give the number that comes before, to 100?

◗ give the number that comes between two

other two-digit numbers?

◗ find given two-digit numbers on the 100

chart and number line?

◗ print or use cards to show given two-digit-

numbers?

◗ find two-digit numbers on the calendar, 100

chart or number line?

◗ recognize and name numerals to 100?

The ability to recognize and read two-digit

numbers can support children’s early

understanding of place value. Similarly,

knowing that 12 is “twelve” in the counting

sequence precedes recognizing 12 as 10 and 2.

W H AT M I G H T YO U T RY ?

◗ Introduce the 100 chart (the wall chart may

already have been noticed). Focus on the 10s

column, and count together. Ask the children

what patterns they can see on the chart. Ask

them to show the patterns they see. Do this

on a regular basis. Your most adept math

students will find patterns that the other

children will gradually be able to see.

◗ Practise counting daily on the wall 100 chart.

◗ On the calendar, focus on reading 20 to 31.

Then look at the 100 chart and practise

reading 20 to 100.

◗ Play I Spy: “Can you find 75? What row will it

be in on the 100 chart? Point to it.” Model

analytical thinking, and have the children

explain how they knew where the numbers

would be found.

◗ Use individual numeral cards to show two-

digit numbers. Point to 36, for example, on

the number line, and ask the students to

make that number with their cards. At first

this will be a simple matching task. Later, try

it from memory.

◗ Continue to work with extending the children’s

counting chains up to 100. Emphasize the

decade shifts with your expression. Build

rhythm into the counting. Connect this

counting to the Estimation work.

◗ Connect this counting to work the children

are doing in the Visual-Spatial section,

particularly with 10-frames.

◗ Practise naming the number before, after or

between, using the 100 chart and number

line as a reference at first, then working

toward doing it with eyes closed. Different

children will develop the mental imagery at

different times.


Teen NumbersTeen Numbers

Math Focus: Teen Numbers


◗ number line

◗ 100 Chart

◗ baggies and small counters

◗ Unifix cubes

◗ dimes and pennies


Can the children:

◗ count verbally from 1 into the 20s or 30s?

◗ give the next number when given a teen

number?

◗ give the number that comes before when

given a teen number?

◗ describe 14 as 10 and 4 when given a 10 and

1s model?

◗ find teen numbers in a random collection of

numerals?

◗ read teen numbers accurately and match

them to the 100 chart?

The teen numbers can be challenging for young

children because of their conflicting number

names (i.e., seventeen suggests 7teen and is

often written as 71). There are also auditory

challenges due to the similar sounding number

names of teens with multiples of 10 (i.e., thirty

sounds like thirteen and can cause confusion if

not addressed).


◗ Ensure the students have a grasp of number

above 20 for counting, reading and even writing

before going back and re-emphasizing teens.

◗ Ensure the students are familiar with the 100

chart before focusing on teens, so they can

place them within the counting framework.

◗ Clearly articulate and focus on the verbal

difference between teens and the decades

(i.e., 30, 40, 50). This is especially important

for ESL students.

◗ Use the number line and 100 chart to show

13 vs. 30, 15 vs. 50, and so on.

◗ Introduce a new way to read the teen numbers

by building up from 10, saying 10 and 1, 11 in

all; 10 and 2, 12 in all; 10 and 3, and so on.

Sometimes this verbal pattern can help to

establish both the correct printing pattern for

teens and an intuitive understanding of the

place value that underlies our system.

◗ Bag and label sets of 10 so that you can practise

counting together 10 and 1, 10 and 2, and so on.

◗ Provide Unifix cubes for building 5s in one

colour. Use these to build 10-sticks in two

colours. Use the 10-sticks with 1s to build

teen numbers.

◗ Introduce the dime as 10 cents, and use

dimes and pennies to practise teens. (This is

useful even for children who don’t count on.

Familiarity will help connect the conceptual

and procedural when it makes sense.)

❍ ● ● ❍ ❍

F O C U S E D I N S T RU C T I O N F O R T H E C L A S S R O O M

This section includes two sets of structured activities and three

“idea files” that can all be used in small groups (or whole groups as

appropriate). The five skill-specific sections include:

● Estimation—a collection of structured activities that help

children learn a variety of strategies to assist with estimation and

recognize when it is appropriate to estimate.

● Pattern—a sequence of patterning activities that moves from

simple hands-on, active pattern tasks to more complex number

patterns. This section combines number concepts and spatial

thinking.

● Counting and Numeral Recognition—an idea file for children

who need more time and systematic reinforcement to reach

proficiency in counting and numeral recognition.

● Visual-Spatial Pattern Recognition—a sequential set of five-

minute teacher-led activities aimed at developing mental

imagery to support number sense.

● Math Playground—a resource file of hands-on spatial

explorations for independent centre work, either in the

classroom or for small-group work outside the classroom.


Small-Group InterventionSmall-Group Intervention

Children who struggle with learning have few opportunities to feel

successful and safe working at their level of understanding. This

small-group intervention strategy provides a chance for these

children to shine. It is designed to be active and fun and to provide

something special for the at-risk student. Most importantly, it is

designed to build in success through careful sequencing of key

numeracy concepts and skills.

Surprise Box

Surprise Box is an activity that children can look forward to—

coming to the resource room to get their shoebox of surprises,

opening it and sorting the objects in it, then working with the

teacher to use the contents of the box. The teacher changes the

contents on a regular basis so there is an element of surprise. The

materials used can be any kind of small objects good for counting,

sorting, comparing and manipulating: Unifix cubes, pennies,

wrapped candies, buttons, shells and ribbons. Finding things that

are not usually found in the classroom adds to the “special” aspect.

Be creative!

Surprise Box activities let children practise:

● counting forward and backwards

● counting and building sets of objects

● multiple counting

● counting on

● visual-spatial quantifying

● matching and sorting

● comparing and ordering


● interrelating concrete, verbal and symbolic

● recognizing a quantity despite perceptual changes (invariance)

● recognizing parts of wholes (e.g., seeing 3 as part of 5 without

having to recount from 1)


● increasing and decreasing

● combining and separating sets

● seeing different ways to name the parts of a whole

● problem solving through modeling and recording

The numeracy intervention sessions should develop the following:

● active engagement

● numeracy concepts and skills

● vocabulary/language

● time on task

● organizational skills

● thinking and reasoning

● positive dispositions

● confidence

Using the Surprise Box Small-Group

Intervention Resource

The Surprise Box resource is divided into seven parts. Each part will

take approximately a week. By changing the objects in the boxes,

you can repeat the same focus over several days as necessary.

Repeating tasks over a series of days and with a variety of materials

provides a chance for children to become secure in their

understanding of concepts and to become competent and

confident with the skills involved. Move on to the next part only

when students have a firm grasp of the content goals.

P A R T S O F T H E R E S O U R C E

The Surprise Box activity is intended to be the first part of a 25-to-

30-minute intervention session. Each session includes three

elements:

Su r p r i s e B o x ( 1 0 - 1 5 m i n u t e s )

The children arrive and immediately get their personal “Surprise

Box.” Have each child decorate a shoebox on the first day. Fill them

with “surprises” every week (or more often). The starting set of

surprises might include three ribbons, five buttons and two of


something else (different items for each child). Have the children

take their boxes and lay the contents out on the rug or table, sorting

the materials any way they like. Ask them to count, compare, order,

describe, build and change, or pattern in progressively more

complex ways each day and week, always with the intent of

developing key number concepts connected with counting skills

and organizational strategies. As you work through the lessons,

gradually increase the number of objects and sets as well as the

complexity of ideas and language.

Sp e c i a l Sk i l l ( 5 - 1 0 m i n u t e s )

Depending on the needs of your group, choose a focus from the

skill-specific sections of the Supporting Early Numeracy resource.

For example, you may choose to focus on Estimation or Counting or

to use the Visual-Spatial sequence to build systematic patterns for

number.

W i n d - u p E x p l o r a t i o n ( 5 - 1 0 m i n u t e s )

For a fun and active wind-up, choose one of the Math Playground

activities for the children to use independently while you record

progress, informally assess or make notes for the next session.

S U R P R I S E B OX F O R M AT

Each of the seven parts of the Surprise Box resource includes the

following headings:

● What do you need?

● What’s in the box?

● What do you do?

Parts 2 through 6 also offer suggestions for:

● language to model and encourage

● processes to model and encourage

● dispositions to encourage



Day 1 Welcome and decorate

boxes.


● shoeboxes, one per child

● paper, stickers, glitter, paint, feathers or

other materials to decorate the boxes

● glue, felts, scissors, tape


This is a day to get to know the children and to

provide them with their boxes and decorating

materials, such as stickers, pictures, felts and

glitter. They can add things to the outside of the

boxes as they go along. They change the

outside, but you change the surprises inside.

Before the children leave, build some

excitement for the next session by having them

predict what might be in the boxes and how

many items there might be. On a chart or

chalkboard, record at least one idea from each

child. Read the list together before the children

return to their classes.

Day 2 Introduce the format

for using the Surprise Boxes.


● Before the children arrive on Day 2, put a

starting set of objects into each box. Make

each box the same to begin (e.g., 3 ribbons,

5 buttons, 2 stickers).

W H AT ’ S I N T H E B OX ?

● Three types of objects in groups of 2, 3 and 5,

for a total of 10.

● Aim for variety and novelty in your choice of

objects.


● Have the children find their boxes, empty out

the contents carefully and sort the contents

in some way (children’s choice).

● Ask questions to elicit sorting concepts and

vocabulary. Build on the children’s language,

connecting to more accurate labels and

reinforcing sorting vocabulary.

“How have you sorted the things in your

Surprise Box? Can you explain it to me?”

(Accept anything the students do, and

describe it in your language.)

“Jan has (model how to move as you

count so that the organization is clear) 1,

2, 3 ribbons (move and count), 1, 2, 3, 4, 5

buttons, 1, 2 stickers.”

“How many do you think she has in all?”

(Hear ideas, then count to check.)

“Do the groups of surprises have the same

number of objects? How many do you

think you have in all?”

“Matt’s things are grouped by colour. Let’s

count his groupings. Do you think he will

have the same number in all? How do you

know?”

● Repeat for each child. Look for positives to

highlight (e.g., creative sortings, verbal

descriptions, careful counting, reasonable

estimating, organized groupings).


● Explain the format for putting the objects

away:

“How many here? Let’s count as we put

them away…1, 2, 3.” (In Part 4, students

begin to count backwards as they put the

materials away.)

Day 3 Use the basic format as

above, but with the following

changes:


● Objects as described above.


● Alter each child’s box so the subsets are

different but the total is still 10.


● Greet the children as they come in and

ensure they follow the previous day’s

routine.

● Discuss same and different in comparison to

the previous session’s collections. Use more

and most as you discuss the box contents

(e.g., more stickers, more than the number

of ribbons, “Which has more?” “Which has

the most?”)

● Help the children recognize that it is

sometimes hard to remember from day to

day. You want them to realize that it can help

to write down amounts. This can be an

introduction to using numerals and making

a permanent record. Model the use of

numerals from this point on.

“Which row has the most?”

“How many are red? Let’s count.”

“What about the rest? What do you have

the most of today?”

“Is that different from yesterday?”

“How many __ do you have today?”

“Can you put your groups in order from

the least to the greatest number of

things?”

Day 4

If you need another day to establish the routine,

repeat the previous day’s plan. If the children

are ready, continue on to Part 2, using the

established format.




● Sorting Boards (enlarge Master 1)


● Everyone’s boxes hold the same: three types

of objects, groups of 2, 3 and 5 objects.


S o r t i n g

● Encourage the children to sort the objects in

their box any way they like.

“How did you sort your objects? John

sorted his by ___ (e.g., shape, colour).”

Name the characteristic.

● Gradually introduce the students to sorting

boards, or different ways to separate their

materials. (See Master 1.)

C o m p a r i n g

● Ask: “What is the same about the things in

this group? What is different about these two

groups?”

“Let’s match or count to find which

groups have the same amount (have the

same/equal, have more/fewer, have the

most/least).”

“Let’s count to see how many we have

altogether.”

C o u n t i n g

“Can you count your group of ___?” (sets

to 10)

“How many in this part? That part? In all?”

“Count to find which group has one

more/one less.”

L A N G UA G E TO M O D E L A N D E N C O U R A G E

● the language of sorting processes, categories

and characteristics (e.g., sort, organize, same,

different, group by colour, by shape, by size)

● the language of comparison (e.g., bigger/

biggest, more/most, fewer/fewest)

● counting words to 10


● helpful ways to organize materials

● moving and counting vs. pointing and counting

to ensure clarity of what has been counted


● positive self-concept: I can do it; I am smart;

I can learn it.

● positive view of math: This is fun; this is

something I enjoy doing.

Good thinking!That is a differentidea for sorting!

How manybuttons do wehave altogether?

Let’s count as weput them back inour boxes!




● Numeral Cards to match to groupings

(Master 8)

● Sorting Boards for sorting (Master 1)

● Dice Pattern Cards to connect to quantities

(Master 7)


● Each child’s box holds different numbers of

objects, total to 10, three types maximum.


Build on what you introduced the first week by

adding the following:

S o r t i n g

● Use the sorting boards to sort materials. This

is a pre-bar graph activity—encourage the

children to sort in rows, one object per box,

then ask comparison questions (e.g., more/

less, in all). This helps children start to line

up objects for one-to-one comparisons.

Comment on how rows make comparing

easy.

● Ask: “Can you use the sorting board to

separate your groups?”

C o m p a r i n g a n d c o u n t i n g s e t s t o 1 0

● Continue counting and comparing, finding

parts and finding the whole or total.

● Compare different collections, different ways

to get 10 in all.

● As appropriate, introduce numeral cards to

6, practise reading numerals, and match

numerals to sets. (Adjust to correspond to

the child’s progress in reading numerals.)

● As appropriate, introduce dice pattern cards:

match objects to dice patterns and to

numerals.

L A N G UAG E TO M O D E L A N D E N C O U R A G E

● full sentences

● reinforce number names, part/whole

language and comparative language (e.g.,

more/less, most/least)


● naming, counting, comparing

D I S P O S I T I O N S T O E N C O U R A G E

● curiosity: I wonder what is in here; I wonder

how many.

● independence




● Two-Column Bar Graph (Master 2)

● Comparison Strips (Master 3)

● Numeral Cards for 7 and 8 (Master 8; use

only if child is secure in recognizing

numerals up to 6)


● Each box contains up to 15 Unifix cubes of

two colours (e.g., 7+8 or 6+9).

● Have extra cubes available for patterning,

but put the same number back in the boxes.


● Count objects as they come out of the boxes

and go back into the boxes.

● Count backwards as you return one cube at

a time to the box (e.g., “3 red cubes, 2 red

cubes, 1 red cube, 0 red cubes. All the red

ones are in the box—3, 2, 1, 0. Now let’s do

our blue cubes—4 in all, and so on.”) Use

subsets of one colour at a time, increasing

the number gradually.

● Sort and count, using comparative language.

● Work on recognizing parts of a set and the

whole set (e.g., 3 red, 5 blue, 8 cubes in all).

● Work on creating and reading patterns,

making sounds and actions to match.


● part/whole language (e.g., some, all, none)

● the language of addition and subtraction

(when items are put into and taken out of

the boxes)

● pattern words (e.g., repeat, same, change,

different)


● representing patterns and collections in

various ways


● positive attitude: Patterning is fun; I can

continue patterns; I can count and compare

groups.




● part/whole mat, such as Ladybug Mat

(Master 4)


● dice

● Dice Game Record Sheet (Master 6)


● Each box has up to 20 objects, 6 round

counters as one set, 10 and 4 as the others.


● Count to 20 for all objects in the box; count

back from 10 using subsets.

● Name parts and wholes for sets to 6 using

part/whole mats.

● Make sets of 10 on 10-frames, matching to

fingers.

● Part/Whole Game:

5 little ants in all.

Some are hiding under the rock.

4 are on the rock.

How many are hidden?

Let’s check:

4 on the rock.

1 under the rock.

5 in all.

This time 2 are on the rock….

L A N G UA G E TO M O D E L A N D E N C O U R AG E

● words for pulling apart and putting back

together (e.g., separate, join, subtract, add)

● names for numbers, naming parts of wholes

(e.g., 4 and 2 is a name for 6; 3 and 3 is

another name for 6)


● building sets of 10



● using number rhymes to remember numerals

D I S P O S I T I O N S T O E N C O U R A G E

● positive self-concept: I can take sets apart and

rejoin them; I can name parts and wholes.




● Dice Pattern Cards (Master 7)


● Numeral Cards 0-9 (Master 8)


● Each box has a total of 20 objects.

● Make one subset something fun and silly, a

real surprise (perhaps something edible).


● Follow the previous format, making

adjustments to suit the pace of your group.

● Order (multiple comparisons); organize box

subsets from least to greatest.

● Order numeral cards (to highest number

introduced).

● Work on recognizing one more/one less,

finding subsets. (e.g., I have 5; Who has one

more than 5?)

● Play Build and Change game for recognizing

increase/decrease, decompose/recompose.

● Build and Change game:

Show me 5.

Now change it to 3.

What did you do?

Now change it to 6.

What did you do?

What do you have to do to change it to 4? 5?

2? (Use dice or numeral cards to show

change.)


● the language of order (e.g., more/most,

higher/highest, in order)


● matching, comparing, ordering, counting,

increasing and decreasing


● rolling dice


● positive self-concept: I can count; I can

understand more and less; I can graph

numbers.




● All materials used to date (e.g., counters,

numeral cards, 10-frames)

● Master 50 to record results (Surprise Box

Record Sheet).


● Each box contains up to 25 objects that are

suitable for patterning (e.g., buttons, shells,

macaroni).


Over the next few days, students can use

independent tasks from the Pattern section

while you assess the following and record the

results on the record sheet:

● Counts sets to ___.

● Counts backwards from ___.

● Recognizes numerals to ___.

● Compares and orders sets to ___.

● Matches numerals and sets to ___.

● Compares sets to ___.

● Compares numerals to ___.

● Orders sets and numerals to ___.

● Builds and changes to ___.

● Counts on verbally (e.g., start at 6) to ___.

● Counts on with materials (e.g., sees 3 as part

of 5 and counts on to 3 to make 5) to ___.

● Recognizes parts and wholes to ___.

● Decomposes/recomposes (names for

numbers) to ___.

● Finds a missing part to ___.



Focused Instruction forthe ClassroomFocused Instruction forthe Classroom

The Learner Profiles you compiled when you completed the Early

Numeracy Assessment indicate each child’s strengths and

weaknesses. This section of the resource is intended to help you

target specific areas where children need extra instruction. The

activities in this section can be used in small groups or with the

whole class. The section is divided into five parts:

● Estimation—a collection of structured activities that help

children recognize when it is appropriate to estimate and learn a

variety of strategies to assist with estimation.

● Pattern—a sequence of patterning activities that moves from

simple hands-on, active pattern tasks to more complex number

patterns. This section combines number concepts and spatial

thinking.

● Counting and Numeral Recognition—an idea file for children

who need more time and systematic reinforcement to reach

proficiency in counting and numeral recognition.

● Visual-Spatial Pattern Recognition—a sequential set of five-

minute teacher-led activities aimed at developing mental

imagery to support number sense.

● Math Playground—a resource file of hands-on spatial

explorations for independent centre work, either in the

classroom or for small-group work outside the classroom.

Estimation

A B O U T T H E E S T I M AT I O N A C T I V I T I E S

In this section the term estimation is broadly interpreted to include

estimating, predicting and checking. Estimation is a sense-making

process rather than discrete skills arranged developmentally.

Throughout the development of number sense, children need to

have experiences that require them to estimate increasingly greater

amounts in a variety of contexts. Developing the ability to make

reasonable estimates depends on:


● the extent of the child’s meaningful number range

● their inclination to use what they know to figure out a reasonable

estimate

● their ability to use both numerical and spatial information in the

process

● their personal store of relevant benchmarks, which involves both

experience and memory (e.g., I am 110cm tall, so you must be

about ___)

● their willingness to risk an incorrect answer

● their experience with the estimation process and with strategies

for refining estimates

W h y a r e e s t i m a t i o n s k i l l s i m p o r t a n t ?

Estimation is an important process for helping children make sense

of number. The process encourages children to create a personal

frame of reference that can be used in similar situations in the

future. Children need to experience estimation activities in a variety

of situations throughout the early years so that:

● their estimates become more refined

● they learn when it is appropriate to estimate

● they learn a variety of strategies to assist with estimation

C O N N E C T I O N TO T H E K - 1 E A R LY N U M E R A C Y A S S E S S M E N T

The estimation activities in this section are appropriate for all

children, especially those who lack confidence or competence with

number. This section is especially valuable for students who had

difficulty with the following items in the Early Numeracy

Assessment:

Item 2—Recognizing Dot Patterns

Item 5—Counting Forward

Item 6—Counting Back

Item 7—Estimate and Check

Item 8—Counting on and Invariance of Number

Item 9—Build and Change

Item 11—Problem Solving


U S I N G T H E E S T I M AT I O N A C T I V I T I E S

This section includes 10 activities that use a variety of strategies to

help children refine their ability to estimate. The strategies may be

used in any order you prefer, but if the student’s sense of number is

at a very early level, you may wish to introduce the set comparison

strategy first. The estimation strategies include:

● set comparisons

● number comparisons

● spatial clues

● samplings

● finding differences

Each of the 10 activities include the following:


● What are you looking for?

● What do you do?

● How might you adapt this activity?

● How might you extend this activity?

At the end of each activity description, ideas are provided for

adapting and extending the activity to meet the needs of a diverse

group of learners. The activities can be adapted and extended in

several ways by changing the collections. You can do this by:

● changing the quantity in the collections

● changing the complexity of the collections

● varying the materials or level of representation of the collection

Also, at the end of the set of 10 activities, there is a Quick Tasks

section that gives further ideas for incorporating these strategies

into the classroom routine.

G u i d e l i n e s f o r t e a c h i n g e s t i m a t i o n

● Choose relevant, varied and motivating contexts.

● Encourage children to take risks.

● Limit quantities to within the reach of the estimators. (i.e.,

Children who count to only 5 or 10 will not be able to make a

reasonable estimate of 50. To them, 50 looks like a million.)

● Make constant use of reference points (e.g., “There are 5 in here.


Can that help us figure out how many are in the bigger pile?”

“John has 8. Do we have more or less?”

● Focus on improving estimates, not on right or wrong. Look at the

range where most of the estimates fall, not at the “way out there”

estimates. Emphasize reasonable estimates. Encourage children

to ask: “Does this make sense?”

● Provide opportunities to revise estimates based on new

information. Recognize good thinking for using that new

information.

● Focus on developing estimation skill in a range of contexts (e.g.,

height, number, area). Remember that appropriate estimates

always depend on the context.

C o l l e c t i o n s ( l e v e l s o f r e p re s e n t a t i o n )

The collections of items provided for estimating need to include:

● a variety of concrete, pictorial and symbolic items

● items that are sometimes arranged randomly and other times in

order

● both two- and three-dimensional collections

The activities described in this section should be repeated with

different types of collections, which may alter the difficulty of the

estimation activity. Types of collections may include:

● like objects/people

● like objects of different sizes

● unlike objects

● items presented on an overhead

● pictures of collections

● items in containers (e.g., jelly beans in a jar)

● items in existing groupings (e.g., pages in a book)

R e c o rd i n g

As soon as the children are able to identify specific numerals, they

can use numeral cards to record their estimates or say them orally.

Their inability to write numerals should not prevent children from

engaging in estimation activities. Once children learn to print

numerals, recording should be an integral part of the activities.


Estimation Activities

Activity Stage/Level Math Focus Page

Musical Chairs Set Comparisons 32

Make a Graph Set Comparisons 33

One for Me? Number Comparisons 34

How Much Time? Number Comparisons 36

Taking Up Space Spatial Clues 37

How Many Beans, Jack? Spatial Clues 38

Let Me Guess Samplings 40

Estimate Before You Eat Samplings 42

Targets Finding Differences 44

How Long Is It? Finding Differences 45

Quick Tasks 46

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● ● ● ❍ ❍

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● ● ● ❍ ❍


Musical ChairsMusical Chairs

Math Focus: Set Comparisons


● a collection of chairs or mats for the children

to sit on


Can the children:

● understand the language used?

● willingly make a guess?

● make an estimate without being concerned

about being correct?

● give reasonable answers to questions within

their range of number understanding?

● independently answer the questions?

● estimate without counting the collections

from 1?

● use spatial clues to estimate?

● share their thinking about the estimates?


● Set up more/less/the same number of chairs

as there are children.

● Introduce the term estimate to mean making

a good guess or prediction.

● Ask a variety of questions to compare the

quantity of the collection to the quantity of

children.

“Do we have enough chairs for everyone?”

“Do we have too many chairs for everyone?”

“Will there be somebody who does not get a

chair?”

● ● ● ❍ ❍

“Why do you think there are enough/too

many?”

“Do we have more or less chairs than

children? Do we have the the same number

of chairs as children?”

● Have the children sit on chairs.

● Encourage the children to make concluding

statements. Emphasize matching to check

predictions.

“We had less/more chairs than children.”

“We had less/more children than chairs.”

“We had just enough chairs for everyone.”

“We had the same number of chairs as

children.”

“There are some chairs/children left over.”

“There are not enough chairs/children.”

H OW M I G H T YO U A D A P T T H I S A C T I V I T Y ?

● Reduce the size of the group and work with

small groups (e.g., four children) if children

have difficulty with understanding number

to 5.

H OW M I G H T YO U E X T E N D T H I S A C T I V I T Y ?

● Use name cards for the students and picture

cards of hats. Spread each group out

separately. Ask if there are enough “hats” for

all of the names.


Make a GraphMake a Graph

Math Focus: Set Comparisons● ● ● ❍ ❍


● two collections of items with different

quantities (e.g., plastic spiders and snakes)

● graphing floor mat with two columns of

eight boxes for sorting


Can the children:





from 1?




● Show the two collections to the children.

● Ask the children to estimate/predict which

collection has more, which has less or

whether the sets are the same. Ask the

children to explain their predictions.

● Discuss different ideas for deciding which

collection has more/less/the same (e.g.,

separating and sorting sets, organizing sets

in a line or in groups of 2).

● After the discussion ask the children to

estimate and predict again.

● Focus on matching as a way to check and

compare. Have children put the items on a

graphing mat and match them one-to-one.

The items can be placed on the mat in pairs

to highlight the matching.

● Compare the collections by asking these

questions:

“Do we have more spiders or snakes?”

“How many more/less do we have?”

“How do you know there are more/less?”

● Help children make concluding statements.

“We had less/more spiders than snakes.”

“It is easier to see how many more/less we

have when we match them and put them on

a graphing mat.”


● Use real people for the two sets (e.g., male

and female students, 5- and 6-year-olds).

After estimating, match the students in lines

by putting one child from each group side by

side.


● Place two sets of items on the overhead

projector for estimating. Then place a two-

column bar graph (Master 2) on the overhead

to do the matching.


One for Me?One for Me?

Math Focus: Number Comparisons


● a collection of items to distribute (e.g.,

lollipops)

● chart paper and markers

● individual Number Lines (Master 10)

● math journals and pencils


Can the children:







from 1?



● record their thinking?


● Ask a variety of questions to compare the

quantity of the collection to the quantity of

children. Start the discussion with

comparative terms (e.g., more, less) and

then discuss numbers.

“Do we have enough lollipops for everyone?

What can we do to find out?”

“Why do you think there are enough/too

many?”

● ● ● ❍ ❍

“Will there be somebody who does not get a

lollipop? What can we do to find out?”

● Discuss the strategy of matching the two sets.

● Ask the children to estimate and state the

number of lollipops. Record these numbers

on a chart.

● Pick a child to distribute the lollipops to the

others, and help the children make

concluding statements. Discuss matching as

a way of checking predictions.

● Have the group count children and lollipops.

Discuss counting as a way of checking

predictions.

“We had less/more lollipops than children.”

“We had less/more children than lollipops.”

“We had just enough lollipops for everyone.”

“There are ___ lollipops/children left over.”

“There are ___ more lollipops/children.”

“There are ___ lollipops, and there are ____

children.”

“___ (number of lollipops) is more/less than

___ (number of children).”

● Compare the actual number to the estimates.

Use a number line and locate both numbers

for the comparison. It is important to focus

on the reasonableness of the answers rather

than the correctness.

● Have the students record their thinking in

their math journals.


H OW M I G H T YO U A D A P T T H I S AC T I V I T Y ?

● Work with a smaller group of students and

use a collection of items that the children

can physically put on (e.g., hats or old

shirts). If the children are not yet able to

print numerals, they can make their

estimates, choose the corresponding

numeral card and place it in front of them.

When the actual number is determined, they

can then choose that numeral card and

compare the two numbers. Have them find

the numbers on a number line to help with

the comparison. Dot pattern cards can also

be used instead of numeral cards.

H OW M I G H T YO U E X T E N D T H I S AC T I V I T Y ?

● Use pairs of items for estimating (e.g.,

mittens). Lead the students to discuss how

the number of students relates to the pairs

of mittens rather than to the total number

of mittens.

● Use a collection of items for estimating that

have several pieces per person (e.g., a table

place setting with plate, cup, fork, knife and

spoon).


How Much Time?

Math Focus: Number Comparisons



● percussion instrument (e.g., drum or triangle)

● Record Sheet 1 (Master 11) and/or journal


Can the children:








● use references (e.g., benchmarks, visual

patterns, samplings) to estimate?




● Have the children perform a number of

activities (e.g., walk across the classroom, tie

shoes, walk across the gym, walk to the

playground and back, print their name).

● Time each activity by counting beats on the

percussion instrument.

● Ask the children to estimate the number of

beats before each activity and record their

estimates on the chart.

● Have the children predict which activities

will need the fewest beats and which will

need the most.

● Check by comparing the actual to the estimates.

Focus on the reasonableness of the answers.

● Compare the number of beats for different

activities. Put the activities in order from

shortest to longest amount of time.

“Which took the longest/shortest amount

of time?”

“Are there any activities which took the same

amount of time?”

“Can you think of another activity which

might take the same amount of time as one

of the activities we already did?”

● Have the students test their predictions and

compare the results.

● Ask the students to record their thinking in

their math journals.


● Choose activities that are quick, active and

easily manageable by the children (e.g., 10

jumping jacks). Predict and compare after

each activity.


● Time the activity with a stopwatch. Estimate

the amount of time it takes to perform in

seconds/minutes.

● Ask the students to suggest three new activities.

Estimate the amount of time each activity

will take and rank the activities from shortest

to longest amount of time before starting.

Have the children do the activities and

compare their estimates to the actual times.

❍ ● ● ● ❍


Taking Up SpaceTaking Up Space

Math Focus: Spatial Clues


● a collection of macaroni



Can the children:










● Place 2 pieces of macaroni in front of each

child.

● Look at the space that the macaroni pieces

take up (spatial clue).

● Ask the children to draw in their math

journals the smallest rectangle that they

think would hold 10 pieces of macaroni.

● Test with macaroni.

● Draw a rectangle around the 10 pieces of

macaroni.

● Compare the two rectangles.

● Discuss how looking at the space taken up

by two pieces can help estimate the space

needed for 10 pieces.


● Have the students place 2 pencils end to end.

Ask them to draw a line that they think would

be 4 pencils long. Test with the pencils and

discuss the results.


● Place 2 pattern blocks so that they touch

each other on one side. Ask the children to

draw the smallest square that would hold 10

pieces. Have them test with the pattern

blocks and draw the square around the

blocks. Compare the two squares.

● Choose a different pattern block and repeat

the activity.

“Are there other ways to orient the pieces to

make a smaller square?”

● ● ● ❍ ❍


How Many Beans, Jack?How Many Beans, Jack?

Math Focus: Spatial Clues


● a collection of beans

● a copy of Jack and the Beanstalk

● individual chalk boards or math journals

and pencils



Can the children:












● Read Jack and the Beanstalk aloud. Remind

the children that Jack received only a few

beans for the cow.

“How many beans do you think Jack would

have if he had received a whole handful

instead of just a few?”

● Have the children record their estimates on

their chalk boards and then say “1, 2, 3 show

me.”

● The teacher can take a range of estimates by

asking someone to share their estimates.

“Does anyone have a number larger than

what (the first student) said?”

● Find the largest estimate in the class, and

then ask if anyone has a smaller estimate

than the first estimate shared.

● Discuss the range of estimates made by the

children.

“How many beans do you think you can

hold in a handful?”

● Have the children record their estimates.

“How did you make your estimate?”

“What were you thinking?”

“Did anyone do it a different way?”

● Have the children work in pairs to take

handfuls of beans and then compare their

estimates and actual counts.


● Show a handful of beans to the class for five

seconds, and then ask the students to

estimate how many beans.

● Do the activity in small groups with adult

direction, using extra-large lima beans.


● Pour out a collection of beans that fills a jar.

● Use a 500ml scoop instead of handfuls and

estimate the total number of beans as well as

the number of scoops needed to refill the jar.

Fill the scoop with beans, and have the

students revise their estimates.

● ● ● ❍ ❍


“Are there enough beans to fill the scoop

again?”

● Count the beans in the scoop. Have the

students revise their estimates of the total

number of beans.


Let Me GuessLet Me Guess

Math Focus: Samplings● ● ● ❍ ❍


● a collection of similar counters (e.g., bugs,

dinosaurs)—total number should be a

multiple of 5

● Five-Way Sorting Mats (Master 13)

● overhead projector

● overhead copy of a Five-Way Sorting Mat

(Master 13)



Can the children:










● Pour out the collection of items on the

overhead projector. (Use a collection size

appropriate for the counting abilities of the

group.)

● Give the students five seconds to estimate

how many objects. Ask them to record their

estimates.

● Ask for a volunteer to state his or her estimate.

“Who has a lower guess?”

● Keep asking until you get the lowest guess.

Repeat to find the highest guess.

● State the range of guesses (e.g., the range is

20 to 100).

● Next, show the sorting mat on the overhead.

Count the five sections.

● Ask a child to put the items from the

collection on the mat. Then ask:

“How many mats do we need altogether so

that all the items are on a mat?”

“How many items are there in the collection?”

● Discuss and record the revised estimates.

● Begin to match the items on the mat with the

children.

“How many groups of 5s do we have so far?”

“How many more groups of 5s do we need?”

● When about half of the collection has been

placed on the mats, have the children

estimate again how many mats are needed

and the total of the collection. Compare all

their estimates.

● Finish matching the objects on the mats and

then count the number of mats.

● Count the total number of items by 5s.

● Compare the estimates to the actual numbers.

● Discuss how the set of 5 on the mat helped to

estimate the total collection.

● Repeat the activity with partners or in small

groups using a variety of materials. Have the

students place the objects on their own

sorting mats.



● Use mats that have only two sections and

use groupings of two to help estimate the

number of the objects.


● Show a 10-frame for 5 or a domino pattern for

5. Then show a collection of coloured disks.

“How many groups of 5?”

“How many altogether?”

● Use mats with 10 sections. Increase the size

of the collection.

“How many groups of 10?”

“How many altogether?”


Estimate Before You EatEstimate Before You Eat

Math Focus: Samplings● ● ● ❍ ❍


● a collection of coloured candies

● small paper cups for counting sets of 10

● a copy of More m & m’s Math by Barbieri

McGrath (optional)

● Record Sheet 2 (Master 12)

● index cards

● crayons to match the candy colours


Can the children:









● Fill the cups with 10 candies of different

colours before starting the activity. The total

number of candies and cups needed will

vary, depending on the size of the collection

the children are able to work with.

● Make colour cards for each candy colour.

Print the colour word on an index card with

the matching crayon colour.

● If you have the book, read the first 12 pages

of More m & m’s Math as motivation.

● Explain that the children are going to use

cups with groups of 10 candies in each to

help them sort the candy.

● Distribute the cups so that each child has a

cup of multicoloured candies.

● Have the students estimate the total number

of candies (some may immediately see how

to figure out the actual number based on

counting by 10s).

● Ask the children to sort their set of candies by

colour. Have each child place his or her

candies near the appropriate colour cards.

● Discuss which colour appears to have the

most or the least.

“Are there any colours which have the same

amount?”

● Then focus on one colour at a time. Ask the

children to estimate how many candies there

are. Have them record their estimates for

each colour on their record sheets, or record

them on a large chart.

● Ask the children to estimate how many

counting cups with 10 candies would be

needed for that colour.

● To check, have the children put 10 candies of

one colour in a cup. Keep filling the cups

with groups of 10. Discuss and record how

many cups of candies and how many

remaining candies. Have the students

determine the totals for the different colours.

Discuss and record the actual number, and

compare to the estimates on the recording

sheets or chart.


● Compare and discuss the results for all the

colours.

● Count the total number of candies by 10s

and 1s. Compare to the original estimates.

● At the end of the activity, let the students eat

one candy of each colour.


● Use only two different colours of candies.

● Place a smaller number of candies in the

cups (e.g., groups of 2s or 5s).

● Use buckets and coloured balls (or other

large containers and objects) for the activity.


● Record each colour with tallies on the record

sheet.

● Create a bar graph for each colour to record

the results.


TargetsTargets

Math Focus: Finding Differences● ● ● ❍ ❍



● Number Lines (Master 10)

● math journal and pencils


Can the children:





from 1?







● Shuffle the cards and turn over the top card.

● Mark this number on the number line. It is

the target number.

● Have each child pick a card from the pack

and show it to the group.

● Ask the children to predict whose number is

closest to the target number. Encourage the

children to think about where his or her

number is on the number line.

“Whose numbers are close to the target?”

“Whose numbers are farther away?”

“Roughly how much would you have to add

(or subtract) to your number to get to the

target number?”

“Is the target number closer to 0 or to 10 (or

100)?”

● Check and mark each number on the number

line using visual clues (such as circling). Com-

pare the differences between the estimates

and the targets.

“How many places away from each other are

the numbers?”

● Have the children state whether their number

or the target number is closer to 0 or 10.

● Assign students to groups of four and have

them repeat the activity in the small groups.

They can record their predictions on their

own number lines and record their thinking

in their math journals.


● Use dot pattern cards (Master 18) instead of

numeral cards. Before having the students

pick a card, order the dot pattern cards from

the smallest to the largest. Pick the target

card, and ask the children to help find it in

the ordered cards. Place it below the ordered

lines. Have the children pick dot pattern

cards and predict whose is closest or farthest

away. Ask them to place the cards under the

ordered cards in the correct location, and

discuss the predictions.


● Use a number line higher than 10, or use a

100 chart.


How Long Is It?How Long Is It?

Math Focus: Finding Differences


● items to be measured (e.g., tracings of the

children’s feet)

● non-standard units of different sizes (e.g.,

paper clips, toothpicks, Unifix cubes)

● paper and pencils

● scissors

● Record Sheet 2 (Master 12)

● math journals

● calculators


Can the children:








● Show the children how to measure objects

by placing units end to end.

● Have the children work in pairs to trace

around one foot and then cut out the

footprints.

● Each pair of students chooses a unit for

measuring and records it on the record sheet

under the heading “What is it?”

● Have the students estimate and record how

many of the unit will be needed to measure

the length of their own footprint.

● ● ● ❍ ❍

● Now have the students use the unit to

measure the footprint.

● Record the actual number of units it takes.

● Repeat the activity with other units. Then

compare the results of the units.

“Which units gave the lowest number? The

highest number? Why?”

● Compare the actual measurements to the

estimates by calculating the differences on a

calculator.

● Have the students record their thinking and

the calculations in their math journals.


● Make several copies of your own footprint,

and use a variety of units to measure it. Do

many examples together as a class before

assigning partners.


● Ask the students to find out a way to see who

has the largest foot in the class and who has

the smallest. “How will you estimate?”


Quick TasksQuick Tasks

● Have the students look at a piece of wrapping

paper with repeating pictures of the same

object, and ask them to estimate how many.

● Hold a small collection in your hand, and ask

the children to estimate how many there are.

● At the beginning of the week, fill a jar with a

collection of objects (e.g., jelly beans), and

leave it in the math centre. Over the week,

have the students record their estimates and

strategies. Determine the actual number at

the end of the week. Change the items weekly.

● Leave sets of pictures in the math centre

(e.g., paper dolls and hats, houses and doors,

frogs and lily pads). Ask the children to

predict whether there are enough of one

item to match the other item. Have the

students record more/less/the same.

● Ask the children to estimate how much

money is in a coin purse or a piggy bank. Use

one type of coin or many types of coins.

● If the class is having a party, show the

children party items (e.g., hats, plates,

spoons), and have them estimate and then

check whether there are enough.

● Estimate how many words are on a page.

● Estimate how many books are on a shelf.

● Show a collection of objects. Have the

students estimate within a given range.

● Show a collection of objects in a square on

the overhead. Show for 10 seconds, and have

the students estimate. Organize the guesses

from least to greatest.


The Pattern Activities include

the following:



● What do you do?

● How might you adapt

this activity?

● How might you extend

this activity?

Pattern

A B O U T T H E P AT T E R N A C T I V I T I E S

The Pattern section is a sequence of activities that moves from simple

hands-on, active pattern tasks to more complex number patterns.

Each of the tasks can be used as often as necessary. Many of the

required materials can be stored with directions in a zip-lock bag.

W h y a r e p a t t e r n s k i l l s i m p o r t a n t ?

Patterns are everywhere. As children become aware of patterns in a

variety of contexts, they learn to use analytical skills. They also learn

to look for similarities and differences that can help them to make

sense of the world. For young children, working with visual,

auditory, tactile, concrete and verbal patterns provides the intuitive

foundation for working with symbolic patterns, such as our base

10 number system. Regardless of when you use these lessons, be

sure to model and highlight patterns in everything you do in class

(e.g., borders around class charts, newsletters going home, covers

for journals, stickers on the weather graph).

C O N N E C T I O N TO T H E K - 1 E A R LYN U M E R AC Y A S S E S S M E N T

Children who are just beginning to reflect and analyze situations

before responding would benefit from practice with the analytical

skills developed in this section. The Pattern section

is especially valuable for children who had difficulty with the

pattern task (Item 10) in the K-1 Early Numeracy Assessment.

U S I N G T H E P AT T E R N A C T I V I T I E S

Nine pattern tasks are included here, and each can be used as often

as you see fit. Having the children record the patterns can extend

the difficulty of any one task.


Pattern Activities


People Patterns and Action Recognizing Patterns 49

Patterns

Linking Pattern Trains Making Patterns with Objects 50

What’s My Pattern? #1 Object and Size Patterns 51

Keep the Pattern Going! Extending Patterns 52

A Pattern to Follow Creating and Extending Patterns 53

Checkerboard Patterns Creating and Extending Patterns 54

What’s My Pattern? #2 Size and Shape Patterns 55

100 Chart Patterns Number Patterns 56

Guess My Pattern Mathematical Thinking Strategies 57

Action Pattern Quick Tasks 58

Number Pattern Quick Tasks 58

● ● ❍ ❍ ❍

● ● ❍ ❍ ❍

● ● ❍ ❍ ❍

❍ ● ● ❍ ❍

❍ ● ● ● ❍

❍ ● ● ● ❍

❍ ● ● ● ●

❍ ● ● ● ❍

❍ ● ● ● ❍


People Patterns and Action PatternsPeople Patterns and Action Patterns

Math Focus: Recognizing Patterns● ● ❍ ❍ ❍


No special materials are required, but pattern

cards or pattern picture cards may be used to

adapt the activity.


Can the children:

● join in the activity?

● predict or tell what comes next in a pattern?

● create their own pattern for others to follow?


● Have the children sit or stand in a circle so they

can watch as the pattern emerges. Start with a

simple pattern (e.g., stand, sit, stand, sit).

● Assign positions to the first few children to

establish the pattern. Say the pattern aloud

as the children move to their positions.

● Encourage the children to predict the

positions as soon as they recognize the

pattern.


● Repeat as needed, with the teacher or all

students saying the pattern aloud while the

students make the appropriate action

(especially for language minority children).

● If a child seems to know the next action, ask

them: “What comes next?” This will alert the

other children to think about what they

will do.


● As children become more familiar with

patterns, change the complexity:

- Expand the pattern to three components

(e.g., stand up, stand on knees, sit cross-

legged; or stand up, stand up, sit down).

- Use action patterns (e.g., clap, snap, clap,

snap). Begin the pattern, and encourage

the children to join in when they feel they

know the pattern.

- Extend these to verbal patterns, using

words related to the motions, letters (e.g.,

ABAB) or silly sounds (e.g., boink, ding).

- Use picture cards so the children can create

their own patterns (e.g., clap, snap, pat).

● Make books with action pictures (e.g., clap,

snap, pat) for a variety of patterns. Have the

children read through them, doing the

actions and extending the patterns.


Linking Pattern TrainsLinking Pattern Trains

Math Focus: Making Patterns with Objects


● Unifix cubes (each student will need five

each of two colours)

● repeat this activity with a variety of materials


Can the children:

● make a pattern that continues?

● explain their pattern using descriptive words

or letters?

● predict what comes next in their pattern? In

someone else’s pattern?

● extend a modeled pattern?

● create their own pattern with their own

materials?

● recognize what it is that keeps repeating?


● Have all or some students say their patterns

out loud as they point to the cubes.

● Ask: “How can we make the pattern longer?

What would come next?”

● Work with a pattern, such as AB, using

actions to establish the pattern.

● Show students your AB pattern (red, blue,

red, blue...).

● Have students make their own AB pattern

(do this for AAB, ABB, AABB, ABC...).

● Make sure the children discuss what they did

with the others.


● Use a smaller number of cubes, 3 of each

colour.

● Have the students use the same colours you

do and copy your pattern.

● Say the colours out loud while they are

making their pattern.

● Use actions for their patterns. (They may

need more active practice.)


● Increase the complexity of the pattern.

● Put a pile of blocks on the carpet, and ask:

“Can you make our action pattern using

Unifix cubes?”

● Say the patterns using alphabet letters (e.g.,

ABABAB...).

● To provide variety and allow for additional

levels of complexity, supply pattern blocks in

place of the Unifix cubes.

● Using collections (containers of materials

such as paper clips, bread tags, buttons or

money) is the most challenging. (See next

activity for ideas.)

● Have the children create patterns using

manipulatives of only one colour. This will

force them to think about ways to make

patterns that do not rely on colour.

● Record the patterns using drawings to

provide challenge for all pattern activities.

● ● ❍ ❍ ❍


What’s My Pattern? #1What’s My Pattern? #1

Math Focus: Object and Size Patterns


● “Pattern Baggies” with materials of different

colours and sizes appropriate for patterning

(e.g., rocks, keys, shells, buttons, coloured

pasta or cereal)


Can the children:

● recognize what feature is creating the

pattern (e.g., size, colour)?

● extend a modeled pattern?

● create their own patterns rather than use the

objects randomly?

● reproduce the patterns in their math journals?


● Create a pattern, using size as the pattern

feature.

● “Read” the pattern with the children and

ask: “Is this a pattern? How do you know?”

● Have the children take turns adding on a

next piece.

● Talk about what actions might represent

each piece and do the actions.

● Give the children their own “Pattern Baggie”

and ask them to create a size pattern.

● After a few minutes, visit each pattern and

ask questions about each. (e.g., “Is this a

pattern? How do you know? What would

come next? How do you know?”)

● ● ❍ ❍ ❍

H OW M I G H T YO U A D A P T O R E X T E N D T H I SAC T I V I T Y ?

● Take a pattern walk in the school, and look

for patterns.

● Ask the children to look for patterns at home

and report on what they find. Have them

reproduce the patterns on paper.

● Take a long, narrow piece of newsprint, and

ask: “How could we show Davinder’s pattern

on this paper?” Encourage the children to

experiment. Share and discuss.

● Change back to a colour pattern, and see if

the children can identify what type of pattern

you have.

● Use a jewelry box with lots of costume

jewelry, some with patterns and some

without. Have the children separate

patterned from non-patterned.

● Make a pattern necklace using coloured

cereal or pasta and string.

“What do you notice about these materials?”

(e.g., colour, size, shape)

“How could we make a pattern necklace?

Make yourself a pattern necklace.”

“‘Read’ your necklace. Is this a pattern? Why

or why not?”


Keep the Pattern Going!Keep the Pattern Going!

Math Focus: Extending Patterns


● Pattern Cards (use Master 24 to make cards

with a variety of patterns and empty spaces

at the ends)

● long, blank pieces of newsprint

● wrapping paper with repeating patterns


Can the children:

● relate the abstract picture to real materials?

● recognize the pattern?

● extend the pattern using real materials?

● verbalize what they are doing?


● Take out a set of cards you have made with

different patterns and empty spaces at the

end of the cards.

● “Read” the card with the children. When you

get to the end, ask:

“What would come next? How do you know?

Next? Next?”

● Give each child a different card.

“Can you keep the pattern going using the

materials on the table?”

● Have each student “read” their card while

others determine whether they kept the

pattern going.

H OW M I G H T YO U A D A P T O R E X T E N D T H I SA C T I V I T Y ?

● Bring in patterned wrapping paper. Discuss

how to extend the pattern and keep it going.

● Cut strips of patterned wrapping paper into

small pieces. Ask the children to find the

other piece(s) that extend their pattern and

glue it/them onto a long strip of newsprint.

● Invite the children to look at home for

patterned paper and materials and bring

them to school. Create a class “Patterns from

Home” book.

❍ ● ● ❍ ❍


A Pattern To FollowA Pattern To Follow

Math Focus: Creating and Extending Patterns


● Pattern Game Boards (Master 25)

● blocks or tiles


Can the children:

● create a pattern that “travels” horizontally

and vertically?

● recognize someone else’s pattern?

● extend the pattern?



Model the game for the class. The teacher

(Partner 1) creates a pattern on the game board

with blocks or tiles. Partner 2 watches. About

halfway through, Partner 1 stops building the

pattern, and Partner 2 continues it. Switch at

the end so that Partner 2 creates a pattern and

Partner 1 gets to finish it.

How might you adapt or extend thisactivity?● Place this activity in a math centre for the

children to use during free time.

● Invite the children to make up other game

boards and travelling patterns.

❍ ● ● ● ❍


Checkerboard PatternsCheckerboard Patterns

Math Focus: Creating and Extending Patterns❍ ● ● ● ❍


● a real checkerboard

● 100 Chart Grids (Master 14)


Can the children:

● create a pattern in a row or column?

● “see” the repeating feature of the columns or

rows?



● Show a real checkerboard to the group, and

ask what they notice (i.e., black-red pattern

alternates up and down and across).

● Experiment with tiles to create checkerboard

patterns.

● Record a checkerboard pattern on a 100

chart grid.

How might you adapt or extend thisactivity?● Use the 100 chart grid to record a pattern

made with tiles, or experiment with making

tile patterns right on the 100 chart grid.


What’s My Pattern? #2What’s My Pattern? #2

Math Focus: Size and Shape Patterns


● attribute blocks in baggies (a few sets, if

possible)


Can the children:

● see the various orientations possible and

how they can create patterns?


● Present a problem: choose one shape only

and make a pattern.

“How can you create a pattern using only

one shape?”

● When someone discovers the orientation of

the shapes as a pattern, comment on their

discovery and “read” their pattern together.

● Ask: “Is there another way of doing it?” (e.g.,

using thickness or size)

How might you adapt or extendthis activity?● Have the children sort the attribute blocks

by size and shape. Ask them which sets

could be used to “tile” an area (i.e., to

completely cover it, with no space showing

between blocks). Use this activity as an

introduction to tessellations, and place it in

the math centre. Encourage the children to

discover many designs.

❍ ● ● ● ●

● Use sets of dominoes in baggies. Do the

children see relationships and patterns

within the dominoes?

● Experiment with making domino patterns.

Discuss what the children discover and any

insights they uncover.

● Extend the work with domino patterns into

noticing patterns about numbers.

“Look at all the dominoes with blank spaces.

What happens when you add a zero to a

number?”

“Do this a few times. Is there a pattern?”

● If the children are ready, extend the activity

by asking them what happens when they add

one to a number, and so on.


100 Chart Patterns100 Chart Patterns

Math Focus: Number Patterns


● 100 Charts (Master 9)

● overhead projector

● transparency of 100 Chart (Master 9)

● overhead pens

● 100 Charts, cut apart (Master 9)


Can the children:

● find patterns on the 100 chart when

identified? Independently?

● put the 100 chart together?

● share their thinking about how they put the

100 chart together?


● Give each child a 100 chart.

● Assign tasks (e.g., Circle all the numbers that

end in 0 or 5 or…).

● Ask the children to see if they can find any

other patterns.

● Encourage the children to share their

discoveries.

● Put a transparency of the 100 chart on the

overhead, and ask the students to tell you

about it.

● Record their observations on a sheet of chart

paper.

● Have the students colour in some of the

patterns that are brought up in the

discussion.

❍ ● ● ● ❍

“What do you notice about the numbers in

the last column?”

“Where are all of the numbers with a 3 in the

1s place? Where are all the 0s? How many 0s

are there?”

● After the class has talked about the 100 chart

and has identified various patterns, divide

the students into pairs or small groups and

give each group a 100 chart that has been cut

apart. (Or have the students cut the charts.)

● Challenge the teams to reassemble their

charts without looking at a completed chart.

● Discuss how the students reassembled their

charts. What strategies did they use?

● Encourage the children to share their thinking.


● Cut apart less of the 100 chart (i.e., to 20, 25,

50, depending on the level).


● To make this activity more challenging,

colour in a pattern on the 100 chart

transparency. Ask the students to guess what

rule was used to colour in that pattern.


Guess My PatternGuess My Pattern

Math Focus: Mathematical Thinking Strategies


● 100 Charts (Master 9)

● individual chalk boards

● pencil or chalk and eraser

● overhead projector and pens

● transparency of 100 Chart (Master 9)


Can the children:

● share their thinking in a clear and articulate

manner?

● come up with more than one answer?

● see relationships between numbers?

● create their own patterns?


● Colour in a pattern on the 100 chart (e.g., 11,

22, 33, 44, 55, 66, 77, 88, 99).

● Ask the students to describe the pattern.

“What might the rule be?”

● As the children suggest rules, ask them to

share their thinking strategies.

“How did you come up with that rule?”

“How did you figure that out?”

“Are there any other rules?”

“Has anyone else come up with a different

answer?” Discuss their suggestions.

● Encourage students to come up with various

answers (e.g., multiple of 11, skip counting

by 11, add 11, no difference in digits).

● Colour in another pattern on the 100 chart

and ask the students to guess what the

pattern is and what the rule might be. Ask

them to share their responses and thinking

strategies.

● Record some number patterns on the

overhead (e.g., 4, 8, 12, 16), and ask the

students to predict which three numbers

would come next.

● Have the students share their thoughts on

what they think the pattern might be.

Encourage them to come up with more than

one answer.


● Use very simple patterns (e.g., 5, 10, 15, 20 or

10, 20, 30, 40).

● Include fewer numbers in the pattern, and

keep the numbers and pattern simple.


● Give students patterns that involve more

than one step or operation (e.g., 4, 3, 6, 5, 8, 7,

10...).

● Encourage the children to come up with their

own challenging patterns and have the

others guess what the pattern is.

❍ ● ● ● ❍


Number Pattern Quick Tasks

Action Pattern Quick TasksAction Pattern Quick Tasks

Action patterning channels a child’s natural

need to move into constructive activities.

Patterning activities can be used often

throughout the day—during circle time, while

waiting in line, for getting students’ attention

after transitions or as part of music and PE

lessons.

● Have the children watch for patterns

everywhere they go for a day.

● Choose stories and songs with patterns.

● Have a “Pattern Day” when everyone tries to

wear something that has a pattern.

● Give each child a clipboard for “Pattern

Discoveries” to record what they find.

Number Pattern Quick Tasks

● Whenever you have a few minutes, ask for

volunteers to come up to the 100 chart and

use a pointer to share any patterns or

interesting facts they notice about the 100

chart.

● Play Guess My Number: describe a number

on the 100 chart, and ask the students to

guess the number. (e.g., My number has a 2

in the 10s place, is an even number, is in the

same column as 13.)

● Place the cut up 100 chart pieces in zip-lock

bags, and leave them in the math centre for

the children to play with whenever they have

extra time.

● Give a short pattern, and ask the students to

fill in the next three numbers. (This can be

done whenever you have two minutes.)

● Discuss the types of number patterns found

in a storybook.


Counting and Numeral Recognition

A B O U T T H E C O U N T I N G A N D N U M E R A LR E C O G N I T I O N A C T I V I T I E S

This part of the resource is designed to provide focused practice in

specific counting and numeral recognition skills for children who

need more time and systematic reinforcement. Making connections

between words and symbols, number names and numerals is a skill

that requires varying degrees of practice for different children. The

activities in this section provide practice opportunities to

supplement the contextualized counting practice in your regular

mathematics program. Look for natural ways to incorporate these

skills into your daily routine.

W h y a re c o u n t i n g s k i l l s i m p o r t a n t ?

Verbal counting patterns are essential to systematic, accurate

counting. Similarly, learning automatic associations between

number words and numerals is a building block for future work.

When counting and numeral skills are automatic, children are able

to use them as reliable tools to support their growing

understanding of our number system. Fluency in counting and

numeral recognition frees up short-term memory, allowing children

to focus on important conceptual goals instead of struggling to

retrieve relatively low-level associations. This section uses multi-

sensory activities to provide the visual, verbal and kinesthetic

involvement children need to commit these skills to memory.


This section is a valuable resource for children who had difficulty

with the following tasks on the Early Numeracy Assessment:

Item 5—Verbal Counting Forward

Item 6—Verbal Counting Back

Item 9—Build and Change

Item 13—Reading Numerals

Item 15 (optional)—Building Coin Sets

Item 17 (optional)—100 Chart


The following assessment items also connect to these activities,

although more loosely:

Item 1—Number Awareness


Item 7—Estimate and Check

Item 14—Numeral Printing

U S I N G T H E C O U N T I N G A N D N U M E R A LR E C O G N I T I O N A C T I V I T I E S

The quick and easy-to-use activities in this section are organized by

specific skill areas. They are meant to supplement your existing

math program by allowing you to zero in on a skill. This is a useful

section to include when shaping an intervention program for small

groups. The key is to use the skills as often as possible to begin, then

reinforce occasionally. Most sections involve creating a chart or

visual to remind students what they have learned (and show you

what needs to be reinforced). These visual aids help to connect

verbal learning with visual-spatial information.

There are 14 Counting and Numeral Recognition activities in this

section, and each includes the following headings:



● What might you try?

Prepare or collect the following materials ahead of time:

● Large numeral cards on stiff card for group work. Laminate if

possible. Enlarge Master 8 or hand print.

● Individual sets of numeral cards printed on stiff card for easy

handling and durability. Use Master 8 or hand print. One set per

student.

● 100 Chart. Large and clear reference chart for the wall. Can be

constructed by enlarging Master 9, cutting and pasting. Laminate

if possible.

● Number Line. Good-sized reference chart for the wall, 0 to 50

minimum, with 10s highlighted. Can be constructed by enlarging

Master 9, cutting and pasting. Laminate if possible. Extend as the

term progresses.


● Calendar. Good-sized reference chart for the wall, with easy to

read numerals.

● Flip-card holders and strip cards. Use a strip of stiff card 8cm x

40cm. Cover the strip with 8cm x 8cm cards that can flip up to

show one number at a time. Tape the top edge of each card

securely to the strip so the flip chart is durable. Make different

number sequence cards to use under the flip cards. (It works best

to hand print these to ensure the size is right.)


Counting and Numeral Recognition Activities


Verbal Counting Verbal Counting 63

Counting Objects Counting Objects 64

Reading Numerals Reading Numerals 65

Matching Numerals and Sets Matching Numerals and Sets 66

Ordering Ordering 67

One Greater Number One Greater 68

One Less Number One Less 69

Counting On Counting On 70

Counting to 100 Counting to 100 71

Find and Read Two-Digit Numbers Two-Digit Numbers 72

Teen Numbers Teen Numbers 73

Counting by 10s Counting by 10s 75



● ● ❍ ❍ ❍

● ● ❍ ❍ ❍

● ● ❍ ❍ ❍

● ● ❍ ❍ ❍

● ● ❍ ❍ ❍

● ● ❍ ❍ ❍

● ● ❍ ❍ ❍

● ● ❍ ❍ ❍

❍ ● ● ❍ ❍

❍ ● ● ❍ ❍

❍ ● ● ❍ ❍

❍ ● ● ❍ ❍

❍ ● ● ❍ ❍

❍ ● ● ❍ ❍


Verbal CountingVerbal Counting

Math Focus: Verbal Counting


No special materials are required for these ideas.


Can the children:

● count consistently to 10 minimum?

● count by 1s to 30 minimum? (may need

teens or transition help)


● Connect rhythm, action, tone and pacing

with the count so that children have many

ways to internalize the pattern.

● Focus on bridges between decades to over-

learn those transitions. Use rhythm, tone,

volume and actions to do this.

● Have any children made the connection

between verbal counting and the number

line or 100 chart? Watch for that awareness

to emerge.

● Establish the forward count to 10 verbal

pattern through many and varied methods

throughout the day (e.g., Calendar, books,

steps, objects, fingers).

● Use a rhythm with the count, either 2s or 5s.

Use tone to build up to 10.

● Choose a motor pattern to associate with

counting by 1s. Make it simple, as you will

use it often. Use a build-up to another action

for reaching 10 and, later, multiples of 10.

(e.g., finger-climbing up to a clap over the

head for 10).

● ● ❍ ❍ ❍

● Count aloud while doing actions to 10

minimum (e.g., steps, jumps, claps, taps,

snaps). Build in a rhythm in 2s or 5s.

● Play Guess my Count: have one child clap up

to 10 times while the others, eyes closed,

count the claps.

● Count around the circle and at 10 (and

multiples thereof), everyone claps. Use the

motor, rhythm and tone patterns with the

count.

● Extend the verbal counting chain as you

walk, clap or do rhythmic movements.


Counting ObjectsCounting Objects

Math Focus: Counting Objects


● Unifix cubes

● small objects for counting

● 10-holder egg cartons (cut off the last pair of

holders in an egg carton)

● 10-Frame Cards (Master 20)


● large Numeral Cards 0-9 (enlarge Master 8

onto stiff card and laminate, if possible)

● individual sets of Numeral Cards 0-9

(Master 8)


Can the children:

● count up to 10 objects accurately using a

move-and-count strategy (rather than

random pointing)?

What might you try?● Count sets to 5 using Unifix cubes on fingers.

(Drop cubes, count on ground, move

around, count again…still 5?)

● Use 10-holder egg cartons for students to

build and count. To begin, work left to right,

top to bottom until students have

established the patterns. You want a stable

and reliable visual image before looking at

other ways to build numbers in the frame.

● Introduce 10-frame cards for students to

match and build. As appropriate, match to

numeral cards.

● Use Master 5 to make 10-frame mats. Practise

building sets up to 10 and back down using

the left to right, top to bottom pattern.

● Continue counting sets to 10 to establish the

counting pattern and the connection to the

number words. Use “move and count” and

visual organization of groupings of 2s, 3s, 4s

or 5s rather than random piles.

● Gradually introduce the rest of the numerals,

one per day as appropriate, so that students

can name them on sight. Use the association

games as described in the previous sections.

Integrate these counting and naming skills into

as many real-life situations as possible.

● ● ❍ ❍ ❍


Reading NumeralsReading Numerals

Math Focus: Reading Numerals


● counters

● large Numeral Cards 0-9 (enlarge Master 8)

● poster board, newspapers, scissors and glue


Can the children:

● recognize numerals to 5 by saying the

number and showing that number of fingers

or counters?

● show the appropriate numeral card when

given a number verbally?


● Work on recognizing 1 and 2: Introduce the

two numerals, playing a game of showing

with fingers.

● Once 1 and 2 are solid, gradually build

recognition to 5.

● Have the children trace their fingers over

numerals, in the air and on the floor in the

patterns of each numeral to help internalize

the shapes.

● Ask the children to find all the 3s (or 2s or 4s)

in a set of magnetic numerals.

● Have the children make numeral posters:

Search in newspapers for specific numerals

and glue all different fonts and sizes of that

number on their poster.

● In the computer lab, experiment with

different fonts. Print out a variety in at least

24 point. Have the children cut out and sort

the numerals and then glue them into

number books.

● Have the children place the numeral cards

around the room and play I Spy. Ask them to

point to the numeral when they hear the

number name.

● ● ❍ ❍ ❍


Matching Numerals and SetsMatching Numerals and Sets

Math Focus: Matching Numerals and Sets● ● ❍ ❍ ❍



● dice

● blocks for building


Can the children:

● build the set, when given the number name?

● label the set, when given the number name?


● Practise finding numerals on a chart or in a

card pile.

● Practise calling out number names while

rolling numeral dice.

● Practise finding numeral cards while rolling

dot dice.

● Play I Spy, where the children count objects

(e.g., doors) and show numeral cards to

match.

● Play Build and Label with numerals:

Say 5, have the child build 5 and show the

5 card.

Show the 3 card, have the child build 3 and

say 3.

Clap 2 times, have the child build 2 and

show the 2 card.

Any number of matching games fit this skills set.


OrderingOrdering

Math Focus: Ordering


● like objects in a range of sizes and lengths

(e.g., ribbon, pencils, nesting cups)

● bead strips

● Unifix cubes


● flip-card holders and strip cards

(instructions can be found on page 61)

● wall-size number line


Can the children:

● order materials from least to greatest?


● Order numerals to 10.

● Order many types of materials by length

(e.g., ribbon, pencils), by area (e.g., lids,

pieces of card), by volume (e.g., nesting

shapes) so that students connect the

concept of ordering with the ordering of

number specifically.

● Use bead strips cut in lengths from 1 to 10.

● Use ribbon lengths with differences of 2cm

or 3cm each, so that comparisons are clear.

● Build linking stairs to 10. Mix up, then reorder.

● Connect numeral cards to ordered materials

where the number differences are clear (e.g.,

Unifix cubes).

● Focus on comparing, ordering, one more

than, one less than.

● Have the children order numeral cards.

● Create a flip chart counting card (see

instructions on page 61). Have the children

try to predict what is hidden under a flap. Ask

one child to lift one cover while the others try

to name one more (right side) and one less

(left side).

● Show the children a starting number of 0 or

1. Ask, “Where’s 2? What’s next? What’s here?

Find 4,” and so on.

● Change the hidden number sequence as

appropriate by substituting the number strip

(e.g., 1-5, 0-4, 2-6, 5-9).

● Work with two counting strips beside each

other (two strips of five, 1 to 5 and 6 to 10) to

practise one more/one less to 10.

● If the children haven’t noticed it, introduce

the number line. Integrate extended

counting practice into the routine, using the

line as a reference point.

● ● ❍ ❍ ❍


One GreaterOne Greater

Math Focus: Number One Greater● ● ❍ ❍ ❍


● Unifix cubes


● paper plate

● small counters


Can the children:

● identify the number one greater, one more

than, or next to 10?


● Build linking stairs together, modeling one

more than each time. Mix up the stairs, and

have the students reorder them by length

and number. Count them together.

● Show the children how to use cards to label

each step. This way, the children will be able

to match and order the cards independently

in the future.

● Focus on ordering to 5, then to 10 (or as

appropriate). Add 0 after 1 to 10 are

established.

● Play Pass the Plate: Pass a paper plate around

the circle. Have each child add one counter

as everyone counts the number on the plate.

When the leader claps, the child with the

plate leads a count of the objects, moving

each piece to show it has been counted.


One LessOne Less

Math Focus: Number One Less


● paper plate

● small counters

● card stock and crayons

● flip-card holder and strip cards (instructions

can be found on page 61)


Can the children:

● identify the number that comes before, or is

one less?

What might you try?● Use the same procedure as in One Greater

(p. 69), working backwards. Ensure the

forward counting sequence is solid before

reversing.

● For Pass the Plate, when the leader claps,

have the children count, then start working

backwards. You may need to count to check

after each move.

● “5, 6, 7, clap. Jon, how many are on the plate?

7. Now we go backwards. If you take one off

the plate, how many will there be? Do it,

then let’s count and check.”

● Have the students each draw a bus (or ferry

or hot air balloon) on a card. Using counters

to represent the passengers on the bus (draw

the driver), go for a drive.

● “At the first stop, 3 people get on. At the next

stop, 1 person gets off. How many now? Now

3 more get on. How many now? (Jazz it up!)

● ● ❍ ❍ ❍

● Work backwards with the flip-card holders

and counting strips. Have the children

predict the number that is hidden, then

check by lifting the flap.


Counting OnCounting On

Math Focus: Counting On


● bags

● dice

● blocks or other counters

● 10-frames (made from egg cartons, or 10-

Frame Mats—Master 5)

● wall-size number line

● pennies

● flip-card holder and strip cards (instructions

can be found on page 61)


Can the children:

● count on from 5, up to 15?

● given a bag with up to 10 objects in it, count

on 2 or 3 more objects as you add them in?

The ability to keep a double count (adding 1, 2,

3 but saying 6, 7, 8) requires considerable skill

and is an important developmental milestone.

It shows that the child has moved beyond one-

to-one correspondence and can grasp the part/

whole relationship of number (i.e., that 5 is a

part of 8 and that counting on from 5 will name

the other part).

W H A T M I G H T Y O U T R Y ?

● Provide lots of opportunities to build a set,

cover it and add 1, 2 or 3. If the student is

unsure of how many are hidden, show them,

count to check, cover and continue. (“Boy, I

can’t fool you!”)

● Discuss the different ways to keep a tally of

the count (e.g., fingers, keeping a beat or

rhythm, pointing to each block).

● Roll a die, have the children build that number

with counters and put them in a bag. Establish

how many are in the bag, then record by

showing a numeral card or printing to keep

track of the bag contents. Roll again, build,

then count on to the bag contents as you add

in the roll number. “Five here now…6, 7, 8.”

Predict how many: “Who thinks 8?” Open the

bag to check. Work up from 2 rolls to 3, 4 or 5

in a row before checking. Children can play

this game in pairs and do their own recording.

● “Five in a bag—now how many?” (Count on

from 5.) Practise with many different starting

quantities, ensuring the children are clear on

what is actually in the bag to start. (Eventu-

ally you can pretend what is in the bag.)

● Count on from 5 using fingers 5…6, 7, 8.

Practise showing 6-to-10 fingers, starting

with the hand as 5.

● Use the 10-frames as mats or holders. Work

with the idea of starting with 5 or 10 and

adding on.

● Practise starting at different places on the

number line, flip charts or counting charts

and counting on.

● Use sets of pennies. Put them in the bank and

keep track by counting on. If children are

familiar with dimes and pennies, count on

from a dime or two dimes.

● ● ❍ ❍ ❍


Counting to 100Counting to 100

Math Focus: Counting to 100


● 100 Chart (enlarge Master 9)

● adding machine tape

● old calendar


Can the children:

● count to 100 by 1s?

● count on from a starting number?

● name the number that comes before, after

and in between?


● Use activities in the Estimation section for

practice in counting to 100.

● Read number lines, count on calculators,

turn pages in a book and read the number-

ing, read the calendar, and so on. Any

context children see and are familiar with is

a good one for focusing on number to 100.

● Enlarge Master 9, colour the 10s column, cut

the decade strips, and give out the strips for

the children to help you make a number line.

Glue the strips onto adding machine tape to

make a number line to 100. Compare the new

number line to the wall chart.

● Demonstrate that a calendar is a number line

cut and stacked. Cut up a calendar page, and

glue the parts onto a number line.

❍ ● ● ❍ ❍


Find and Read Two-Digit NumbersFind and Read Two-Digit Numbers

Math Focus: Two-Digit Numbers❍ ● ● ❍ ❍


● wall-size 100 Chart

● wall calendar

● individual sets of Numeral Cards 0-9 (Master 8)


Can the children:

● count to 100?

● give the number that comes after, to 100?

● give the number that comes before, to 100?

● give the number that comes between two

other two-digit numbers?

● find given two-digit numbers on the 100

chart and number line?

● print or use cards to show given two-digit-

numbers?

● find two-digit numbers on the calendar, 100

chart or number line?

● recognize and name numerals to 100?

The ability to recognize and read two-digit

numbers can support children’s early

understanding of place value. Similarly,

knowing that 12 is “twelve” in the counting

sequence precedes recognizing 12 as 10 and 2.


● Introduce the 100 chart (the wall chart may

already have been noticed). Focus on the 10s

column, and count together. Ask the children

what patterns they can see on the chart. Ask

them to show the patterns they see. Do this

on a regular basis. Your most adept math

students will find patterns that the other

children will gradually be able to see.

● Practise counting daily on the wall 100 chart.

● On the calendar, focus on reading 20 to 31.

Then look at the 100 chart and practise

reading 20 to 100.

● Play I Spy: “Can you find 75? What row will it

be in on the 100 chart? Point to it.” Model

analytical thinking, and have the children

explain how they knew where the numbers

would be found.

● Use individual numeral cards to show two-

digit numbers. Point to 36, for example, on

the number line, and ask the students to

make that number with their cards. At first

this will be a simple matching task. Later, try

it from memory.

● Continue to work with extending the children’s

counting chains up to 100. Emphasize the

decade shifts with your expression. Build

rhythm into the counting. Connect this

counting to the Estimation work.

● Connect this counting to work the children

are doing in the Visual-Spatial section,

particularly with 10-frames.

● Practise naming the number before, after or

between, using the 100 chart and number

line as a reference at first, then working

toward doing it with eyes closed. Different

children will develop the mental imagery at

different times.


Teen NumbersTeen Numbers

Math Focus: Teen Numbers


● number line

● 100 Chart

● baggies and small counters

● Unifix cubes

● dimes and pennies


Can the children:

● count verbally from 1 into the 20s or 30s?

● give the next number when given a teen

number?

● give the number that comes before when

given a teen number?

● describe 14 as 10 and 4 when given a 10 and

1s model?

● find teen numbers in a random collection of

numerals?

● read teen numbers accurately and match

them to the 100 chart?

The teen numbers can be challenging for young

children because of their conflicting number

names (i.e., seventeen suggests 7teen and is

often written as 71). There are also auditory

challenges due to the similar sounding number

names of teens with multiples of 10 (i.e., thirty

sounds like thirteen and can cause confusion if

not addressed).


● Ensure the students have a grasp of number

above 20 for counting, reading and even writing

before going back and re-emphasizing teens.

● Ensure the students are familiar with the 100

chart before focusing on teens, so they can

place them within the counting framework.

● Clearly articulate and focus on the verbal

difference between teens and the decades

(i.e., 30, 40, 50). This is especially important

for ESL students.

● Use the number line and 100 chart to show

13 vs. 30, 15 vs. 50, and so on.

● Introduce a new way to read the teen numbers

by building up from 10, saying 10 and 1, 11 in

all; 10 and 2, 12 in all; 10 and 3, and so on.

Sometimes this verbal pattern can help to

establish both the correct printing pattern for

teens and an intuitive understanding of the

place value that underlies our system.

● Bag and label sets of 10 so that you can practise

counting together 10 and 1, 10 and 2, and so on.

● Provide Unifix cubes for building 5s in one

colour. Use these to build 10-sticks in two

colours. Use the 10-sticks with 1s to build

teen numbers.

● Introduce the dime as 10 cents, and use

dimes and pennies to practise teens. (This is

useful even for children who don’t count on.

Familiarity will help connect the conceptual

and procedural when it makes sense.)

❍ ● ● ❍ ❍


Teen Numbers continued

● Use place value blocks to practise building

teen numbers without counting from 1

(counting on from a given 10). Again, this

ability (verbal counting on) can be

developed ahead of the conceptual

understanding and can help children to

make the important shift to cardinal

counting on.

Teen Numbers continued


Counting by 10sCounting by 10s

Math Focus: Counting by 10s


● Unifix cubes

● 10-frames

● baggies or bundles holding sets of 10

● laminated dime shapes (enlarge Master 15)

● dimes


Can the children:

● count by 10s to 100?

● find sets that have been grouped in 10s?

● count up the value of given sets of 10, such

as five linking 10s trains?

● find that multiple of 10 on the 100 chart?

● given a multiple of 10 such as 40, use

materials to show 40?


● Practise the 10s chain like a song so it comes

easily. Gradually connect it to

representations for 10s.

● Use fingers and toes—the more real

connections the better.

● Have the children build 10s models (e.g.,

linking 10s trains with two groups of 5,

coloured 10-frames, bundles or baggies of

materials).

● Introduce dimes using large, laminated dime

shapes. Use real dimes, dropping them into

a dish as children count by 10s when they

hear the sound.

❍ ● ● ❍ ❍

● Practise counting by 10s on the 100 chart and

number line. Highlight multiples of 10 with a

colour and/or by size so the pattern jumps

out.

● Use 10-frames for students to build 10s and

add 10s. Read the values with them. (You can

use 10-frame mats or 10-holder egg cartons.)



Math Focus: Counting by 5s


● nickels and pennies

● number line

● 100 Chart (Master 9)


Can the children:

● count by 5s to 50?

● find sets that have been grouped in 5s?

● count up the value of given sets of 5, such as

7 hands?

● find multiples of 5 on the 100 chart?

● given a multiple of 5 such as 25, use

materials to model the number?


● Trace hands and cut out for practice with 5s.

Make a wall chart of hands (glue them in a

line left to right, with thumbs on the right).

With the children, count and label the chart,

using a different colour and size for the

multiples of 5 (the thumb numbers). Use the

whisper/count process to begin. Integrate

practice at counting by 5s into the routine.

● Highlight the 5s chain on the number line

and the 100 chart.

● Practise counting by 5s on both the hand

chart and the 100 chart.

● Introduce a motor pattern for the 5s

sequence (e.g., moving elbows back and

forth or some other active cue to connect

only with 5s).

❍ ● ● ❍ ❍

● Introduce nickels for counting by 5s. Use

soft-loud counting (1, 2, 3, 4, 5) to count out

the nickels. The children will gradually

internalize the count.

● Once counting by 5s is established, add

pennies so the students have practice

counting on to 5.

● Introduce the motor pattern for stars,

counting to 5 as each star is drawn. Up (1)

then down (2) to make a point (like an A),

across and up to the left (3), straight across to

the right (4), down to meet the starting point

(5). Count points together, labeling each star

in the count with 5, 10, 15. Use the set of stars

for counting and ordering practice.

1 ➠

2 ➠

4 ➠

3

➠

5➠

Start

6 ➠

7 ➠

9 ➠

8

➠

10➠

Start

11 ➠

12 ➠

14 ➠

13

➠

15➠

Start

16 ➠

17 ➠

19 ➠

18

➠

20➠

Start

21 ➠

22 ➠

24 ➠

23

➠

25➠

Start



Math Focus: Counting by 2s❍ ● ● ❍ ❍


● number line


● construction paper, clear MacTac and

duct tape


Can the children:

● count by 2s to 10? 20? Beyond?

● find sets that have been grouped by 2s?

● count up the value of given sets of 2, such as

5 pairs of shoes?

● find multiples of 2 on the 100 chart? Can

they see the pattern?

● use materials to show a multiple of 10?


● Count ears, eyes, feet or fingers for practice.

Think of all the real-life examples for 2s, and

use these for counting practice.

● Introduce soft-loud counting if needed. For

the 2s pattern, whisper the odd numbers,

and say the even numbers aloud. (This

allows children to build on their 1s counting

and see the connection.) Start to establish

the “song,” visually connecting to jumps on

the number line.

● Have the children trace footprints or draw

bikes on paper to make a 2s counting chart

for the wall. With the children, label the

count of feet or wheels with small odd

numbers and large even numbers (the visual

match to soft-loud counting). Integrate the

count-by-2s chain into the practice routine.

● Highlight the 2s chain on your number line

(e.g., with coloured circles, jumps of 2).

● Look for patterns on the 100 chart involving

2s and multiples of 2.

● Draw two footprints, and photocopy them

onto construction paper in two colours (e.g.,

15 pairs of blue, 15 pairs of green). Have the

children cut these out. Use these to make a

footprint model at the door at which the

children usually line up. Space the footprints

to model where they would stand in line.

Cover the line-up with clear MacTac, and

tape down the edges with duct tape. This will

make a durable counting model for a host of

mathematical ideas, including counting by

2s, dividing by 2s, doubling, problem solving,

odd and even numbers—and may even

simplify lining up single file!


Visual-Spatial Pattern Recognition

A B O U T T H E V I S UA L - S PAT I A L P AT T E R NR E C O G N I T I O N A C T I V I T I E S

This section is designed to provide sequenced development of

specific visual-spatial patterns that support early numeracy. Visual-

spatial patterns are quantities arranged in a way that helps the

brain recognize how many there are in the collection. Dice patterns

are examples of spatial arrangements that the brain can learn to

recognize without counting by 1s.

W h y a re v i s u a l - s p a t i a l s k i l l s i m p o r t a n t ?

Using systematic visual-spatial arrangements of quantity can

establish mental imagery of number that supports number sense.

In terms of mathematical power, recognizing quantities without

counting by 1s is the basis of grouping concepts. This skill is a

natural bridge between one-to-one and many-to-one

correspondence.

The suggestions in this section will help with:

● visual imagery and visual memory

● instant recognition of quantities without counting

● analyzing visual information

● combining, comparing and ordering visual information

● modeling using visual patterns

● spatial sense-making

C O N N E C T I O N TO T H E K - 1 E A R LYN U M E R A C Y A S S E S S M E N T

This section provides a scaffold for some and a learning

opportunity for others. As children work through the K-1

assessment, you will have an opportunity to see which children rely

heavily on spatial information. Often these children arrange

materials into patterns, and many perform strongly on the visual-

spatial tasks. These children can benefit from using their visual-

spatial strength as a scaffold for learning about number and will


benefit from the activities in this section. This section is also

valuable for children who struggled with the following tasks on the

Early Numeracy Assessment:


Item 10—Pattern Tasks

Item 12—Squares Puzzle

Item 16 (optional)—Cube Building

U S I N G T H E V I S UA L - S PAT I A L P AT T E R NR E C O G N I T I O N A C T I V I T I E S

The Visual-Spatial section of this resource includes 10 parts that are

cumulative, in that each part builds on the previous one. Within

each part is a set of brief activities from which you can choose one

or two each day. Depending on your group, with 5 minutes a day

devoted to these activities, a section may take between one and two

weeks to complete. The activities are meant to be quick and snappy,

with lots of celebration when students learn to recognize quantities

in different arrangements. Use the children’s responses to the

activities to gauge an appropriate pace.

Each of the activities in this section includes the following

headings:



● What might you try?


Visual-Spatial Pattern Recognition Activities


Building Visual Memory Building Visual Memory 81

Matching and Comparing Matching and Comparing Patterns 82

Patterns

More/Less and Ordering More/Less and Ordering 83

10-Frames Recognizing 0 to 5 in Relation to 10 84

Analyzing Number Patterns Analyzing Number Patterns 85

Doubles Symmetrical Number Patterns 86

Parts and Wholes Parts and Wholes 87

Patterns for 6 to 10 Patterns for 6 to 10 88

Seeing Groupings Seeing Groupings 89

Larger Quantities Larger Quantities 90

● ● ❍ ❍ ❍

● ● ❍ ❍ ❍

● ● ❍ ❍ ❍

● ● ❍ ❍ ❍

● ● ❍ ❍ ❍

❍ ● ● ❍ ❍

❍ ● ● ❍ ❍

❍ ● ● ❍ ❍

❍ ● ● ❍ ❍

❍ ● ● ❍ ❍


Building Visual MemoryBuilding Visual Memory

Math Focus: Building Visual Memory


● a tray with objects

● Dot Pattern Cards (enlarge Master 18)

● round counters

● Dice Mats, one per student (Master 16)

● dominoes

● Domino Mats, one per student (Master 17)


Before moving on to the next section, ensure

that the children can:

● recognize dot patterns 1 to 5 without counting

● display one-hand finger patterns for 1 to 5

without counting

● connect dot, domino and finger patterns for

1 to 5 without counting (i.e., given a domino,

the child shows fingers; given a dot pattern,

the child finds the appropriate domino)


V i s u a l Me m o r y G a m e s

● Place objects on a tray, starting with 3 or 4

items. Cover and remove one. Can the

children recall what is missing? Where it

was? Adapt this game with size, number and

type of items. Use an organized arrangement

for the items.

● Use matching games with pairs of matching

cards, starting with 5 or 6 pairs laid out in a

pattern. Have the children turn over two

cards; if they match, they keep them. (There

are many ways to adapt this game.)

R e c o g n i z i n g D o t Pa t t e r n s

● Introduce dot patterns using cards. Show 1

and 2, have the children practise saying the

number as fast as possible, and gradually add

3. Once the children can immediately

recognize and name 1, 2 and 3, add 4 and 5 to

the mix over the next few days.

● Show the children dot pattern cards, and

have them model the arrangement using

chips and dice mats. Develop a snappy

routine for this activity.

R e c o g n i z i n g D o m i n o Pa t t e r n s

● Introduce real dominoes. Look for patterns

for 1, 2, 3, 4, 5. Use activities as above,

including domino mats.

C re a t i n g F i n g e r Pa t t e r n s

● Using cards for 1-to-5 dot patterns, work

toward automatic finger pattern responses

on one hand. Use the hand pattern of 5 as a

reference point. Point out that 4 is easy (no

thumb). Work with these until the patterns

are automatic, not counted out one by one.

(e.g., When you show the 5-dice card, the

child shows 5 fingers without counting

them out.)

● ● ❍ ❍ ❍


Matching and Comparing PatternsMatching and Comparing Patterns

Math Focus: Matching and Comparing Patterns


● large Dot Pattern Cards and Domino Cards

(enlarge Masters 18 and 19)

● individual Dice and Domino Mats (Masters

16 and 17)

● round counters




● create dice patterns for 1 to 5 from memory

by choosing the correct number of counters

and arranging them on their dice mat

● show finger patterns with eyes closed and

without counting for numbers 1 to 5


R e c o g n i z i n g S i m i l a r i t i e s a n d D i f f e r e n c e s

● Use the cards, counters and mats to build

recognition of what is different and what

changes in each dot pattern from 1 to 5.

● Show 1 and have the children model it, then

show 2 and ask how they would change their

cards to make the 2 pattern.

● Encourage spatial language and detail. (e.g.,

“I need to move this dot down a bit and put

another dot above it.”)

B u i l d i n g V i s u a l Me m o r y f o r Pa t t e r n s

● Show a dot pattern card for three seconds,

then hide it and see if the students can

model the number. Then show the card and

● ● ❍ ❍ ❍

discuss what is the same and different about

their models and the card.

● Build matching patterns as above, using

domino cards and mats.

H i d d e n F i n g e r Pa t t e r n s

● Show a dot pattern card for 1 to 5. Have the

children look, create the finger pattern

behind their backs, then show it above their

heads without looking. Have them check

each other. Make this fast and fun. The idea is

to build mental imagery of what the finger

pattern looks like.

M a t c h i n g Pa t t e r n s O n e t o O n e

● Say a number from 1 to 5. Have the children

pick up that many counters and set them out

on their domino or dice mat in the pattern

for the number.


More/Less and OrderingMore/Less and Ordering

Math Focus: More/Less and Ordering


● large Dot Pattern Cards 1 to 5 (enlarge

Master 18)

● individual Dot Pattern Cards 1 to 5 (Master 18)

● dominoes

● pegboards and pegs



that with number to 5, the children can:

● name the number that is one more

● find the dot pattern card for one more

● name the number that is one less

● find the dot pattern card for one less

● order dot pattern cards

● find the hidden dot pattern card in a 1 to 5

sequence


O n e - Mo r e Pa t t e r n s

● Provide the children with individual dice

pattern cards 1 to 5. Call out numbers, and

ask them to show the appropriate card.

● Ask them to find the card that is one more

than the number you call. Encourage the

children to do this without counting. Ask

them to note what is different between the

dot pattern card for the called number and

the dot pattern card that is one more, using

language of position and quantity.

● Use dominoes to find one more.

O n e - L e s s Pa t t e r n s

● Show the children a dot pattern card between

2 and 5, and ask them which card has one

less dot. Cover a dot to illustrate one less, or

take away one, or hide one.

● Once the children find the card, discuss the

difference between the two in terms of

spatial arrangement.

● Use pegboards to build one-more/one-less

patterns.

O rd e r i n g D o t C a r d s

● Have the children order their dot pattern

cards from 1 (left) to 5 (right) without

counting (based on visual one-more-than).

● Then ask them to turn the cards over to hide

the dots. Call 5, and see if they can find where

5 is and show it. Repeat with other numbers.

● If appropriate, add in the 6-dot card at this

point, and repeat some of the previous

activities with the 1-to-6 set.

“What is special about 6?”

“What do you see in the dot pattern

arrangement?”

● ● ❍ ❍ ❍


10-Frames10-Frames

Math Focus: Recognizing 0 to 5 in Relation to 10● ● ❍ ❍ ❍


● 10-holder egg cartons, one per child (cut off

the last pair of holders in an egg carton)

● Dot Pattern Cards (Master 18)

● cubes


● 10-Frame Cards (Master 20)

● cards, 10cm x 10cm minimum

● dots and glue or stickers for making dot

pattern cards



that with number to 5, the children can:

● automatically recognize random and dice

patterns for 1 to 5

● model 1 to 5 using a 10-frame

● match dot patterns and 10-frame patterns

● name 10-frame patterns


3 - D 1 0 - Ho l d e r s

● Introduce 10-frames using egg cartons

with the last two holders cut off to make a

10-holder.

● Ask the children to make sets of 1 to 5, to

match a given dot pattern card.

● Introduce the idea of adding counters one at

a time to the top row, left to right.

● Whisper a different number from 1 to 5 for

each child to build with their 10-holder.

● Then ask the students which holds the least

and which the most. Ask them to order the

10-holders from least to greatest or most.

1 0 - Fr a m e s

● Introduce 10-frame mats and practise

building sets to match numbers 1 to 5.

Emphasize the left to right development

across the top row.

● Provide 10-frame cards for students to colour

to represent patterns for 1 to 5. Use the

created set to flash, and work toward

immediate recognition of the quantity.

● Add 6 into the mix.

R a n d o m Pa t t e r n s f o r 1 t o 5

● Have the students make sticker dot pattern

cards for 1 to 5, one set in the standard dice

patterns and one set in any arrangement

they like.

● Practise flashing and naming the patterns.

Once the cards are automatic, have the

children take them home to practise and

show their skill.


Analyzing Number PatternsAnalyzing Number Patterns

Math Focus: Analyzing Number Patterns


● 10-holders

● counters

● playing cards

● instruments (e.g., drum, bell, triangle)

● individual Dot Pattern Cards (Master 18)




● model and describe different arrangements

for 5

● recognize and describe likenesses and

differences in patterns to 5

● mentally count and tally up to 5 sounds


D e c o m p o s e / R e c o m p o s e Na m e s f o r Nu m b e r s

● Introduce the idea of many ways to make,

for example, 5.

● Have the children put 5 counters in their 10-

holder or on a 10-frame mat, then together

analyze patterns to find smaller groupings.

“Look at our ways to show 5. Lily has 4 and 1,

Tom has 2 and 2 and 1, and Sam has 2 and 3.”

● Further develop the decomposition idea

using two-handed finger patterns for

numbers 1 to 5.

“Show me 5. Now show me 5 using two

hands. Read your pattern for me.”

● ● ❍ ❍ ❍

● “Analyze” patterns for 1 to 5 on playing cards.

Ask the children how they are the same as or

different from dot pattern cards.

He a r i n g Nu m b e r Pa t t e r n s

● Count sound sequences (e.g., clapping,

drum, bell). Count and tally first with fingers,

then count mentally—this builds mental

imagery and one-to-one correspondence.

● Use rhythm, or groupings of 2, 3 or 4 beats as

the sequences grow.

● Using dot pattern cards, repeat the sound

patterns, but have the children show how

many using dot pattern cards.

● Clap patterns for the children to join in.

Continue and analyze (e.g., xxx xxx xxx).


DoublesDoubles

Math Focus: Symmetrical Number Patterns❍ ● ● ❍ ❍


● hole punches

● blank newsprint or thin paper

● construction paper or card in colours

● cards, approximately 10cm x 20cm for

making doubles pattern cards

● Ladybug Mats (Master 4)

● Ladybug Cards (Master 21)

● dominoes

● MIRAs or a mirror

● individual Domino Cards (Master 19)




● recognize symmetry doubles patterns for 2,

4, 6, 8.

● recognize domino doubles patterns for 2, 4,

6, 8.


Sy m m e t r y D o u b l e s

● Use hole punches with newsprint to make

and analyze symmetry dot patterns. Fold

and punch, open and describe.

● Work toward predicting where the matching

dots will be, using a chalk board example.

● Create 2, 4, 6, 8 and 10.

● Make some large, sturdy cards for group

practice. Glue onto contrasting paper so the

holes show.

● Using the ladybug mats, have the students

build a set to 5 on one side and then predict

where the matching set would go.

● Check some by folding and comparing, or

use a MIRA to check the symmetry.

● Children can make their own ladybug models

using Master 21. This can be done by

colouring or with hole punches (fold and

punch to get a symmetrical pattern).

D o m i n o D o u b l e s

● Using a set of dominoes, find doubles

dominoes and analyze them (not

symmetrical, but side by side).

● With the students’ help, create doubles

pattern cards in domino format for 1, 2, 3, 4

and 5. Use these for group practice in

recognizing sets of 2, 4, 6, 8 and 10.

● Make smaller practice cards to send home for

practice as the children begin to recognize

the groupings of 2, 4, 6, 8 and 10.


Parts and WholesParts and Wholes

Math Focus: Parts and Wholes❍ ● ● ❍ ❍



● counters, Unifix cubes

● interlocking construction blocks (such as

Lego or Duplo)

● paper and felts for making the wall display of

10s patterns



that the children can recognize different

patterns for 6, 8 and 10, using:

● domino formats

● interlocking construction blocks

● 10-frame formats

● finger formats


1 0 - Fr a m e Pa t t e r n s

● Review patterns for 1 to 5, then gradually

work up to 10, using 10-frame mats and

counters.

● Always emphasize adding on to the 5, to

establish 5 as a benchmark.

“Is it more than 5? Where is 5? How many

more?”

● Practise doubles finger patterns for 6, 8 and

10, using matching finger sets on each hand

(3+3, 4+4, 5+5). Work toward automatic

showing of fingers without counting one

by one.

2 s Pa t t e r n s

● Use interlocking construction blocks to build

recognition of dot patterns in rows of two

(blocks come in 2, 4, 6, 8 dot patterns).

“Find me a 6.”

● Practise counting by 2s in conjunction.

● Explore how doubles patterns can be created

on the 10-frame using top-and-bottom

matching. Compare these patterns to the

construction blocks.

Nu m b e r Pa t t e r n s

● Highlight seeing parts and patterns within

quantities. Use Unifix cubes to develop colour

patterns. (e.g., “Make a train of 6 with two

colours. Mary, use 3 red and 3 blue, 6 in all.

Glen, use 2 white, 2 red and 2 white, 6 in all.”)

● Break the colours apart, and stack them into

an array 3+3, 2+2+2.

● Repeat with eight blocks.

Pa t t e r n s f o r 1 0

● Make a wall display of many ways to show 10:

trace two hands, colour a full 10-frame, draw

construction block dots, make a 10 domino.

● Build a pyramid, counting out four round

chips for the base (1,2,3,4,). Count on 5,6,7

for the second layer, then 8, 9 then 10.


Patterns for 6 to 10Patterns for 6 to 10

Math Focus: Patterns for 6 to 10❍ ● ● ❍ ❍


● Dice Pattern Cars (enlarge Master 7)

● individual sets of Dice Pattern Cards (Master 7)


● counters

● poster paper for 10s arrangements

● blank cards to make 10s patterns for practice

(use stiff card, approximately 10cm x 10cm)




● match different patterns for numbers.

● recognize 6, 8, 9 and 10 in different

arrangements (7 may take longer).

● name a full 10-frame as 10.


Pa t t e r n s f o r 6 t o 1 0

● Develop finger patterns for 6 to 10 using 5+x,

count on to 5.

● Use 10-frames and counters to count on to 5,

making 6 (5+1), 7 (5+2), 8 (5+3), 9 (5+4) and

10. Encourage the children to practise

recognizing the numbers based on how

many less than 10.

● Analyze 6 to 10 cards to find component

parts (partitioning spatial patterns).

“I see 3+3+3…that makes 9.”

● Provide 1 to 5 cards for students to use to

combine and get 6 to 10 (e.g., two 3s for 6, 3

and 4 for 7). Check with pattern cards for 6 to

10 and dominoes patterns.

● Use counters on 10-frames to discover all the

arrangements for 6, then 8.

● Make a wall display.

● Practise describing each arrangement.

● Create nifty patterns for numbers to 10 (e.g.,

a stack of 3, 2, 1 as a model for 6).

● Make posters of nifty arrangements.

● Make cards of arrangements that the

children particularly like, and use them to

practise recognition.


Seeing GroupingsSeeing Groupings

Math Focus: Seeing Groupings


● Geoboards (Master 27) and elastics

● Double 10-Frame Mats (Master 22)

● counters

● large square grid paper

● crayons and scissors




● recognize parts within wholes with

quantities to 10 using visual patterns.

● recognize all 10-frame arrangements.

● recognize groupings for quantities to 10

using different arrangements.

● show finger groupings for numbers to 10.

(For numbers above 5, children should show

5 without counting plus x more fingers.)


S e e i n g Pa t t e r n s w i t h i n Nu m b e r s

● Develop conceptual subitizing (seeing

groups within groups) by combining small

groups. Work on a floor or table with

counters (6, 8, 9 and 10 work well for this).

“Make 3 rows of 3. What have you got?”

“Find a pattern for 8. Show me.”

● Ask the children to show 8 pegs on a geoboard

and analyze the different ways to do it. Look

for recognizable groupings within 8.

● Have the students colour large square grid

paper to show 6 (2x3), 8 (2x4), 9 (3x3) and 10

(2x5). Cut these out, and use them to practise

seeing the arrangements two different ways

(e.g., 6 is two 3s or three 2s).

● Emphasize counting on to a group you

recognize. (e.g., “I see 4, and 2 more is 5, 6.”)

Pay special attention to 7 (6 and 1 more, 5

and 2 more, 4+3).

● Practise finger patterns for numbers above 5

(“Show me 6”). Recognizing the hand as 5 or

two hands as 10 should be automatic. How

many more than 5 is 6, 7, 8, 9? Practise 9 as

one less than 10. Have the children show the

numbers above their heads.

A d d i n g o n t o 1 0

● Introduce counting on to a full 10-frame to

develop teen numbers. (Ensure that students

can say the number chain to at least 20 before

attempting this and that they have had lots of

exposure to numbers to at least 30.)

● Use the double 10-frame mat. Have the

children build 10 on one frame, then add 1, 2,

3 and so on to the other, naming 10 and ___

(e.g., 10 and 2, 12 in all).

❍ ● ● ❍ ❍


Larger QuantitiesLarger Quantities

Math Focus: Larger Quantities❍ ● ● ❍ ❍


● square tiles or blocks

● cards for making group practice patterns for

teen numbers

● Double 10-Frame Mats (Master 22)

● Double 10-Frame Cards (Master 23) for take-

homes



This section is the springboard for moving into

two-digit number patterns. 5s and 10s are the

building blocks of two-digit numbers.

● Can the children recognize 5s and 10s

without counting when presented in spatial

arrangements?

● Are the children established in their patterns

to 10?

● Can the children find 10s in a greater

pattern, such as a 100 chart?


S e e i n g Pa t t e r n s W i t h i n Q u a n t i t i e s

● Have the children draw grids of buildings

with floors and rooms (e.g., two floors, two

rooms on each floor). Next ask them to build

what they have drawn with tiles or blocks.

“Who has a different building?” (describe

rectangles in terms of number of rows)

● Analyze buildings (e.g., 3 floors tall, 2 rooms

wide, 2+2+2, 6 rooms in all).

● Practise verbal descriptions. Remember to

emphasize recognizing chunks (i.e., each

floor, not one-by-one counting).

● Emphasize the vocabulary of position (e.g.,

top floor, bottom floor, second from the top,

left, middle, right).

Te e n Nu m b e r s

● Create dot pattern cards for teen numbers

using a 10 grouping (choose the children’s

favourite arrangement) and dice patterns for

the 1s. Practise analyzing the patterns so that

children accept the 10, see the other part and

mentally combine the 10 and x to get the

teen number.

● Create a set of 10-frame cards for the teen

numbers, both a large set for group practice

and a small set for individual practice and to

take home.

S e e i n g 1 0 s i n 1 0 0

● Using the 100 charts, have the students look

for 10s within the 100—not rows of 10 this

time but 10-frames, 2x5 chunks. “Colour the

10-frames each a different colour. How many

10s did you find in the 100 chart?”

● Create a blank wall chart of the 100 chart and

record the numbers the children know: 1 to

10 and the counting pattern for 10s down the

right-hand side. Add only the patterns all the

children know, leaving the other numbers

blank.


Math Playground

A B O U T T H E M AT H P L AYG R O U N D A C T I V I T I E S

Math Playground provides fun, hands-on spatial explorations in a

context that allows success for all and lets the spatial thinkers shine.

The Math Playground activities are opportunities for children to

model, draw and use mental imagery. The activities in this section

are designed to be revisited often. Once the materials have been

gathered, most of the activities require very little preparation or

instruction. Once a few students learn how to use the activities,

they can teach others.

These activities are designed to be:

● highly engaging and cooperative in nature

● play-like and interactive

● flexible and responsive to the needs of the group

● easily adapted and modified by the teacher

W h y a re s p a t i a l e x p l o r a t i o n s i m p o r t a n t ?

Spatial thinking is a key aspect of numeracy. It involves the ability to

use spatial information to construct meaning. Spatial activities

involving hands-on experiences provide the sensory input that

helps children develop mental imagery—a building block to

making sense of mathematics. The spatial explorations in this

section provide positive boosts for children’s self-confidence and

self-esteem. These activities are opportunities to enhance children’s

critical thinking and problem-solving abilities while having fun.


Like the section on Visual-Spatial Pattern Recognition, this section

provides a scaffold for some and a learning opportunity for others.

Children who perform strongly on visual-spatial tasks can benefit

from using their visual-spatial strength as a scaffold for learning

about number. These children will benefit from the activities in this

section. This section is also valuable for children who struggled with

the following tasks on the Early Numeracy Assessment:


Item 10—Pattern Tasks


Item 12—Squares Puzzle

Item 16 (optional)—Cube Building

U S I N G T H E M AT H P L AYG R O U N D A C T I V I T I E S

These spatial explorations are divided into five areas of

concentration:

● Shapes

● Pattern Blocks

● Tangrams

● Puzzles

● Number Lines

You will notice that the format for these activities differs from that

of the previous sections. Math Playground activities are easy to use,

and the directions are given in simple point form.

G u i d e l i n e s f o r Us i n g t h e Ma t h P l a y g r o u n d

As you use these activities, ask plenty of questions to help you

understand the children’s thinking:

● How did you do that?

● How did you know that?

● Tell me how you did that.

● If you’re not sure, how can we find out?

● Yes, that’s right. But how did you know it was right?

● Can you think of another way we could do this?

● Where have you done that before to help you solve a problem?

Look for indications that the children:

● have a good eye for detail and colour;

● think in pictures and images and learn through visuals;

● see solutions to problems by visualization; and,

● use the spatial arrangement of materials to help them make sense.


List of Materials for Math Playground Activities

Shape Detective • no materials needed

Shape Tickle • no materials needed

Shape Bag • set of tangrams and a paper bag for each pair

Shape Construction • toothpicks and mini-marshmallows

Playdough Shapes • playdough

Rice Shapes • dyed rice and a large, shallow container

Building Constructions • interlocking construction blocks (e.g., Lego or Duplo)

Shape Hunt • assorted shapes and a box or hat

Rubber Shapes • Geoboard and elastics for each student (Master 27)

Shape Memory • pairs of cards with matching shapes

Shape Bingo • Bingo Cards (Master 28)

Exploration • pattern blocks (for every activity)

Cover the Blocks • Cover the Blocks (Masters 29, 30, 31)

Cover and Copy • Cover and Copy (Master 32)

Pattern Block Challenge • Pattern Block Challenge (Master 33)

Combinations • Combinations (Masters 34, 35, 36)

How Many? • How Many Triangles? (Masters 37 to 41)

Exploration Time • multiple sets of tangrams (for every activity)

Tangram Creations • tangrams

Tangram Matching • Tangram Matching (Master 42)

Tangram Cover-Up • Tangram Cover Up (Masters 43 to 49)

Tangram Tales • book Grandfather Tang’s Journey by Ann Tompert

Tangram Detective • tangrams

Jigsaw Names • two matching pieces of card per child (10cm x 20cm or so)

Number Puzzles • two cards, one with 1-10 Number Line as model (Master 10)

Colour Jumps • tape and felts to make unnumbered floor number line, beanbags

Number Jumps • floor number line marked 0 to 10

Race to the End • Number Lines (Master 10), dice, counters


ShapeShape

S H A P E D E T E C T I V E

● Have the children take turns being a “shape

detective.”

● The detective gives the group clues about

the shape he or she is thinking of. (e.g., “It

has four sides and has the word angle in it.”)

S H A P E T I C K L E

● The students take turns drawing a shape on

their partner’s back.

● The partner guesses what shape is drawn.

S H A P E B AG

● Have the children work with a partner.

● One student chooses a shape from a pile of

concealed tangrams.

● He or she secretly puts it into a paper bag.

● The other student reaches inside the bag

and uses his or her knowledge of shapes to

determine what shape is inside the bag.

S H A P E C O N S T RU C T I O N

● Have the children use toothpicks and

marshmallows to build a variety of shapes.

● You may want to provide cards as models for

children who need additional support.

P L AY D O U G H S H A PE S

● Introduce playdough to the group.

● Have the students make shapes with their

playdough.

● Other Ideas with Playdough

- Once the students are comfortable

creating playdough shapes, have them

work with a partner.

- Ask the students to take turns closing

their eyes and using their sense of touch

to determine what shape their partner

has made.

- Encourage the students to explain to their

partner how they guessed the shape. (e.g.,

“It is a closed shape. It is round. Is it a

circle?”)

R I C E S H A P E S

● Have the children dye white rice with food

colouring.

● Place the rice in a large bowl.

● Encourage the children to use their fingers to

practise tracing shapes in the rice.

B U I L D I N G C O N S T RU C T I O N S

● Give the students interlocking construction

blocks (e.g., Lego).

● Ask them to build a construction using as

many shapes as they can.

● Share the students’ constructions, and

discuss what shapes have been incorporated

into the construction.

S H A P E H U N T

● Have the students select a shape out of a hat

or box.

● With the group, name the shape and discuss

its properties.

● Invite the students to hunt for that shape in

the classroom environment.

● When they find an example of their shape,

have them draw or sketch their object on a

piece of paper and report back to the group.


● For example, if the student chose a rectangle,

they could sketch the window pane.

R U B B E R S H A PE S

● Have the students use a geoboard and

rubber bands to create different shapes.

● This could be a quick activity where the

teacher concentrates on creating one shape,

or the group could work for a longer time,

making a variety of shapes.

R U B B E R S H A PE S F O L L OW- U P

● Have the students re-create a shape on their

geoboard from the previous day.

● Give each student a geoboard (Master 27—

enlarge the grids as necessary).

● Ask the students to experiment with

different ways of drawing the same shape on

their page (e.g., three different squares).

S H A P E M E M O RY

● Have the students play in pairs, taking turns

flipping over cards with a variety of shapes

on them.

● If a pair matches, the student wins the cards

and takes another turn.

● The student who is able to remember and

locate the most matching shapes wins the

game.

S H A P E B I N G O

● Give each child a unique bingo card (can be

made from Master 28).

● Explain how the column and row identifiers

work.

● Show the children a card with a picture on it.

● Ask the students to see if their card fits.

● The first student to fill their bingo card wins!

O t h e r I d e a s f o r S h a p e B i n g o

● Use a 5cm x 5cm or 5cm x 8cm card.

● Use numerals rather than shapes.

● Have the students play with a partner rather

than the whole group.


Pattern BlocksPattern Blocks

E X P L O R AT I O N

● Have the students build a variety of pattern

block pictures.

● This activity can be open-ended, or you can

offer directing statements. (e.g., “Let’s try to

build a garden.” “Let’s make spaceships.”)

C OV E R T H E B L O C K S

● Give each child a Cover the Blocks sheet

(Masters 29, 30, 31).

● Have the children cover the patterns with

blocks that match.

● Once they have done this, they can colour

the pattern to match the blocks.

C OV E R A N D C O P Y

● Give each child a Cover and Copy sheet

(Master 32).

● Have the children cover each pattern with

blocks.

● Have them copy the pattern again beside the

covered picture.

● Ask the children to trace the blocks or draw

them using the model.

P AT T E R N B L O C K C H A L L E N G E

● Give each child a Pattern Block Challenge

sheet (Master 33).

● Ask: “Who can fill this shape up with blocks

without going over the edges?”

● Encourage the children to show the different

strategies they use.

● Discuss which strategies were more effective

and why.

● Extend this activity by asking: “What is the

fewest number of blocks that cover the

shape? The greatest number?” Encourage the

children to estimate and check. Make a chart

to show the various ways.

C O M B I N AT I O N S

● Give the students a Combinations sheet

(Masters 34, 35, 36).

● Ask them to see how many different ways

they can make the shape using a variety of

pattern blocks. Have the students colour

their ways and/or record them in the charts

at the bottom of the page.

H OW M A N Y T R I A N G L E S ?

● Give the students a copy of How Many

Triangles? (Masters 37, 38, 39, 40, 41) and ask:

“How many triangles fit in this shape?”

● Explore the children’s thinking processes by

asking them to explain how they arrived at

their answer.

● Extend this activity by asking: “Can any other

colour of block cover the patterns?” (Blue will

cover the most and leads to a discussion of

half units.) “How many of that colour will it

take? What do you notice about how many it

takes?” (It takes half as many as the green

triangles.) “Why?”


TangramsTangrams

E X P L O R AT I O N T I M E

● Some children will not be familiar with

tangram shapes. Provide one set per child if

possible, but for exploration, mix sets together.

● By beginning with a period of free

exploration time, the children are able to

experiment and gain confidence with this

new material.

● Later, show the children how many pieces

there are in one set, and store each set in a

zip-lock bag. The children can trace one full

set of 7 pieces onto a card to use for checking

a complete set. This can help them be

responsible for the sets.

T A N G R A M C R E AT I O N S

● Encourage the students to use a variety of

tangrams to make pictures and designs from

their imagination.

T A N G R A M M ATC H I N G

● Have the students match the tangram pieces

to a variety of shapes (e.g., Master 42).

● Use multiple sets of tangrams.

● Have the students create new matching

puzzles for others to try.

T A N G R A M C OV E R - U P

● A set of Tangram Cover-Up sheets (Masters

43 to 49) is provided to help the children

practise covering the shapes with an

increasing level of difficulty.

T A N G R A M T A L E S

● Read Grandfather Tang’s Journey by Ann

Tompert to the group.

● Ask the students to tell a story using their

tangrams.

● Encourage them to transform existing

creations into new ones to enhance and

develop their story.

T A N G R A M D E T E C T I V E

● Pose a question for the “detective” to solve.

(e.g., “How many triangles are in a

parallelogram?” “How many triangles are in

an octagon?”)

● Help the students use the tangrams to solve

these problems.


PuzzlesPuzzles

J I G S AW N A M E S

● Have the students print their names on two

pieces of card (roughly 10cm x 20cm). For

children who do not yet print, print on one

card, and have them copy on the other.

● One card becomes a model to which the

child refers to, while the other is cut between

the letters to create a puzzle. For young

children, gradually work up to cuts between

every letter.

● Ask the child to compare each letter to the

model and determine how each letter is the

same or different from the rest.

O T H E R I D E A S F O R J I G S AW N A M E S

● Have the students draw pictures and cut

them into puzzles.

● Ask the students to switch jigsaw names with

a partner.

N U M B E R P U Z Z L E S

● Have the students make a puzzle based on

the number line (1-10).

● Use one piece as a model to which the child

can refer. On it, write the numbers 1-10.

● On the other piece, have the students write

the numbers 1-10 and cut between them to

create a puzzle (or use Master 10).

● Challenge the children to put the numbers

in the correct order.

● Ask the children to compare each number to

the model and determine how each number

is the same or different from the rest.

O t h e r I d e a s f o r N u m b e r P u z z l e s

● Challenge the students by making number

puzzles to 20 or 50.

● Ask the students to assemble the puzzle in

descending order.


Number LinesNumber Lines

C O L O U R J U M P S

● Make an unnumbered floor line—a line with

a clear starting point (0) and equally spaced

marks for units of roughly one footstep in

length.

● Place different coloured beanbags or coloured

tiles at different points along the line.

● Ask the students to count how many jumps

to the green tile or how many jumps from

the green to the yellow tile. “How many jumps

back to the red tile, from the yellow tile?”

N U M B E R J U M P S

● Change the floor line to a numbered floor line.

● Using the number line (0-10), students line

up at 0 and take turns following the teacher’s

directions: “Jump to 5 on one leg and to 10

on the other.”

● The entire group counts with the student.

● Discuss the difference between the left and

right leg jumps.

● Pose a variety of problems. (e.g., Find a

different way to reach 10 by jumping with

your left and right legs.)

O t h e r I d e a s f o r N u m b e r J u m p s

● Ask the students to share their thinking with

a friend.

● Have the students record their thoughts

visually on paper and/or model them to the

small group.

R A C E TO T H E E N D

● Have the children place a counter at 0 on

their number line and then take turns rolling

a die (0-10, 0-20, 0-50, depending on ability).

● Have the students count out the number they

roll, using their marker to keep track.

● The first one to reach the end of the number

line wins.


Name: _____________________________________________________

Master 1: Sorting BoardsMaster 1: Sorting Boards


Name: _____________________________________________________

Master 2: Two-column Bar GraphMaster 2: Two-column Bar Graph


Name: _____________________________________________________

Master 3: Comparison StripsMaster 3: Comparison Strips


Name: _____________________________________________________

Master 4: Ladybug MatMaster 4: Ladybug Mat


Name: _____________________________________________________

Master 5: Ten-frame MatMaster 5: Ten-frame Mat


Name: _____________________________________________________

Master 6: Dice Game Record SheetMaster 6: Dice Game Record Sheet

11111 22222 33333 44444 55555 66666


Master 7: Dot Pattern CardsMaster 7: Dot Pattern Cards

Name: _____________________________________________________


Name: _____________________________________________________

Master 8: Numeral Cards 0–9Master 8: Numeral Cards 0–9

55 55566 666

77 77788 888

99 999

00 00011 111

22 22233 333

44 444


Name: _____________________________________________________

Master 9: 100 ChartMaster 9: 100 Chart

11111 22222 33333 44444 55555 66666 77777 88888 99999 1010101010

1111111111 1212121212 1313131313 1414141414 1515151515 1616161616 1717171717 1818181818 1919191919 2020202020

2121212121 2222222222 2323232323 2424242424 2525252525 2626262626 2727272727 2828282828 2929292929 3030303030

3131313131 3232323232 3333333333 3434343434 3535353535 3636363636 3737373737 3838383838 3939393939 4040404040

4141414141 4242424242 4343434343 4444444444 4545454545 4646464646 4747474747 4848484848 4949494949 5050505050

5151515151 5252525252 5353535353 5454545454 5555555555 5656565656 5757575757 5858585858 5959595959 6060606060

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9191919191 9292929292 9393939393 9494949494 9595959595 9696969696 9797979797 9898989898 9999999999 100100100100100


Name: _____________________________________________________

Master 10: Number LinesMaster 10: Number Lines

0000 01111 1

2222 23333 3

4444 45555 5

6666 67777 7

8888 89999 9

101010

10 10•

••

••

••

••

••

0000 01111 1

2222 23333 3

4444 45555 5

6666 67777 7

8888 89999 9

101010

10 10•

••

••

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0000 01111 1

2222 23333 3

4444 45555 5

6666 67777 7

8888 89999 9

101010

10 10•

••

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Name: _____________________________________________________

Master 11: Record Sheet 1Master 11: Record Sheet 1

Activity Estimate Actual


Name: _____________________________________________________

Master 12: Record Sheet 2Master 12: Record Sheet 2

Activity Estimate Actual


Name: _____________________________________________________

Master 13: 5-Way Sorting MatMaster 13: 5-Way Sorting Mat


Name: _____________________________________________________

Master 14: 100 Chart GridMaster 14: 100 Chart Grid

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100


Name: _____________________________________________________

Master 15: Coin Cut-outsMaster 15: Coin Cut-outs


Name: _____________________________________________________

Master 16: Dice MatMaster 16: Dice Mat


Name: _____________________________________________________

Master 17: Domino MatMaster 17: Domino Mat


Master 18: Dot Pattern CardsMaster 18: Dot Pattern Cards

Name: _____________________________________________________


Name: _____________________________________________________

Master 19a: Domino CardsMaster 19a: Domino Cards


Name: _____________________________________________________

Master 19b: Domino CardsMaster 19b: Domino Cards


Name: _____________________________________________________

Master 20: Ten-frame CardsMaster 20: Ten-frame Cards


Name: _____________________________________________________

Master 21: Ladybug CardsMaster 21: Ladybug Cards


Name: _____________________________________________________

Master 22: Ten-frame MatsMaster 22: Ten-frame Mats


Name: _____________________________________________________

Master 23: Double Ten-frame CardsMaster 23: Double Ten-frame Cards


Name: _____________________________________________________

Master 24: Pattern CardsMaster 24: Pattern Cards


Name: _____________________________________________________

Master 25: Pattern Game BoardMaster 25: Pattern Game Board


Name: _____________________________________________________

Master 26: Small 100 ChartsMaster 26: Small 100 Charts

11111 22222 33333 44444 55555 66666 77777 88888 99999 1010101010

1111111111 1212121212 1313131313 1414141414 1515151515 1616161616 1717171717 1818181818 1919191919 2020202020

2121212121 2222222222 2323232323 2424242424 2525252525 2626262626 2727272727 2828282828 2929292929 3030303030

3131313131 3232323232 3333333333 3434343434 3535353535 3636363636 3737373737 3838383838 3939393939 4040404040

4141414141 4242424242 4343434343 4444444444 4545454545 4646464646 4747474747 4848484848 4949494949 5050505050

5151515151 5252525252 5353535353 5454545454 5555555555 5656565656 5757575757 5858585858 5959595959 6060606060

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9191919191 9292929292 9393939393 9494949494 9595959595 9696969696 9797979797 9898989898 9999999999 100100100100100

11111 22222 33333 44444 55555 66666 77777 88888 99999 1010101010

1111111111 1212121212 1313131313 1414141414 1515151515 1616161616 1717171717 1818181818 1919191919 2020202020

2121212121 2222222222 2323232323 2424242424 2525252525 2626262626 2727272727 2828282828 2929292929 3030303030

3131313131 3232323232 3333333333 3434343434 3535353535 3636363636 3737373737 3838383838 3939393939 4040404040

4141414141 4242424242 4343434343 4444444444 4545454545 4646464646 4747474747 4848484848 4949494949 5050505050

5151515151 5252525252 5353535353 5454545454 5555555555 5656565656 5757575757 5858585858 5959595959 6060606060

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9191919191 9292929292 9393939393 9494949494 9595959595 9696969696 9797979797 9898989898 9999999999 100100100100100

11111 22222 33333 44444 55555 66666 77777 88888 99999 1010101010

1111111111 1212121212 1313131313 1414141414 1515151515 1616161616 1717171717 1818181818 1919191919 2020202020

2121212121 2222222222 2323232323 2424242424 2525252525 2626262626 2727272727 2828282828 2929292929 3030303030

3131313131 3232323232 3333333333 3434343434 3535353535 3636363636 3737373737 3838383838 3939393939 4040404040

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9191919191 9292929292 9393939393 9494949494 9595959595 9696969696 9797979797 9898989898 9999999999 100100100100100

11111 22222 33333 44444 55555 66666 77777 88888 99999 1010101010

1111111111 1212121212 1313131313 1414141414 1515151515 1616161616 1717171717 1818181818 1919191919 2020202020

2121212121 2222222222 2323232323 2424242424 2525252525 2626262626 2727272727 2828282828 2929292929 3030303030

3131313131 3232323232 3333333333 3434343434 3535353535 3636363636 3737373737 3838383838 3939393939 4040404040

4141414141 4242424242 4343434343 4444444444 4545454545 4646464646 4747474747 4848484848 4949494949 5050505050

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7171717171 7272727272 7373737373 7474747474 7575757575 7676767676 7777777777 7878787878 7979797979 8080808080

8181818181 8282828282 8383838383 8484848484 8585858585 8686868686 8787878787 8888888888 8989898989 9090909090

9191919191 9292929292 9393939393 9494949494 9595959595 9696969696 9797979797 9898989898 9999999999 100100100100100


Name: _____________________________________________________

Master 27: GeoboardsMaster 27: Geoboards


Name: _____________________________________________________

Master 28: Bingo CardsMaster 28: Bingo Cards

B I N G O


Name: _____________________________________________________

Master 29: Cover the Blocks 1Master 29: Cover the Blocks 1

1.

3.

5.

4.

2.

6.

7.

8.

Cover the patterns with blocks.

Colour the patterns to match the blocks.


Name: _____________________________________________________


1. 2.

3.

4.5.

Cover the patterns that match.



Name: _____________________________________________________


1. 2.

3.

4.

Cover the patterns that match.



Name: _____________________________________________________

Master 32: Cover and CopyMaster 32: Cover and Copy

1.

2.

3.

4.

Cover the patterns with blocks.Copy with the blocks. Trace andrecord.


Name: _____________________________________________________

Master 33: Pattern Block ChallengeMaster 33: Pattern Block Challenge


Name: _____________________________________________________

Master 34: Combinations 1Master 34: Combinations 1

How can you fill this shape in 2 or 3 different ways?


Name: _____________________________________________________




Name: _____________________________________________________




Name: _____________________________________________________

Master 37: How Many Triangles? 1Master 37: How Many Triangles? 1

How many triangles does it take to build this design?

S

How did you know?


Name: _____________________________________________________



How did you know?

S


Name: _____________________________________________________



How did you know?

S


Name: _____________________________________________________



How did you know?

S


Name: _____________________________________________________



How did you know?

S


Name: _____________________________________________________

Master 42: Tangram MatchingMaster 42: Tangram Matching

Match the piece to these shapes.


Name: _____________________________________________________

Master 43: Tangram Cover-up 1Master 43: Tangram Cover-up 1

Cover each shape.


Name: _____________________________________________________


Cover each shape.

2.

1.


Name: _____________________________________________________


Cover each shape.

2.

1.


Name: _____________________________________________________


Cover each shape.

2.

1.


Name: _____________________________________________________


Cover each shape.


Name: _____________________________________________________


Cover each shape.


Name: _____________________________________________________


Cover each shape.


Master 50: Surprise Box Record SheetMaster 50: Surprise Box Record Sheet

Name: _______________________________ Date: _______________

Date: _______________

Teacher/Class: ________________________ Date: _______________

Skill: To 5 To 10 Beyond Comments

Count sets accurately

Count back from

Recognize numerals

Compare and order sets

Match numerals and sets

Compare sets

Compare numerals

Order sets and numerals

Increase/decrease

Invariance for sets

Verbal counting on

Counting on with materials

Describe parts and wholes

Decompose/recompose/rename

Find a missing part (5+?=8)

Date Completed Comments

Part One

Part Two

Part Three

Part Four

Part Five

Part Six

Part Seven


Master 51: Large Traingles for TriangleChallenge

Master 51: Large Traingles for TriangleChallenge

Name: _____________________________________________________


Master 52: Squared PaperMaster 52: Squared Paper

Name: _____________________________________________________


Master 53: Triangle PaperMaster 53: Triangle Paper

Name: _____________________________________________________


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