TABLE SETS - Texas Gateway · PDF filenumber of objects in the set regardless of their ... up to at least 100 by ones and tens beginning with any given number. ... Counts by tens with

TABLE SETS

©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1

Mathematics Achievement Academy Kindergarten – Grade 1: Day 1

Academic Vocabulary

Anchor Chart

Learning Progression

Magnitude

Numerical Fluency • Counting• Inclusion of Set: Cardinality and

Conservation• One-to-One Correspondence• Part-Whole Relationship

(Composing/Decomposing)• Relative Magnitude• Representations of Number• Subitizing (Perceptual and Conceptual)• Unitizing

Pre-Assessment

Quick Images

Rekenrek

Sample Learning Progression: Whole Number Concepts Kindergarten - Grade 1


Sample Learning Progression of Whole Number Concept Cards

Cut along the dotted lines. Relative Magnitude Magnitude of a number describes its distance from zero. Relative magnitude is the comparative distance or size of two or more numbers. Understanding the relative magnitude of numbers allows students to reason about the relationships between numbers. Children may express the relationships using comparative language or symbols.

One-to-One Correspondence It is matching two groups so each member of one group is matched up with an object from the second group and vice versa. It is also the ability to count objects so that each object counted is matched with one number word. It is imperative not to have the objects always in the same arrangements.

Part-Whole Relationships Seeing part-whole relationships reflects the ability to compose and decompose numbers by looking at the whole and the parts that make up that whole. This is one of the most important concepts in number sense.

Subitizing (Perceptual) It is the ability to name the number of objects in a set without counting the objects based on the arrangement of objects. It is perceptual understanding of magnitude rather than counting to determine the magnitude or value on a number line.

Cardinality The last number stated is the number of objects in the set. It is the ability to count a set of objects. When asked how many objects are in the set, a child can say the number of objects without recounting the objects.

Conservation It consists of having the child count the objects, tell how many objects there are, and tell how many objects are present without having to recount the objects when the objects are rearranged.



Subitizing (Conceptual) It is the ability to subitize the subgroups of a set and combine them to compose a whole.

Unitizing It is the ability to understand that items can be grouped to make a larger unit. For example, 10 ones can be grouped to make 1 ten. This also includes the understanding that the number 4 has a different value based on its place value location, such as 4 and 40.

4 tens 16 ones

40 + 10 + 6

30, 40, 50, 60, . . . 57, 56, 55, 54, . . . 45, 46, 47, 48, . . .

89 < 92

5

5 10 15 20 2 5

7



18 One Less One More

17 19

546 Less Than Greater Than

521 643

12 Less Than Equal To More Than

102 Less Than Greater Than

72 108

13 19 13 is less than 19.

19 is more than 13.35

30 + 5

2 hundreds 14 tens 16 ones 200 + 100 + 40 + 10 + 6

45 54 45 is less than 54.

I know because the digits in the tens places have values of 40 and 50. I know 40 is less than 50, so 45 is less than 54.

8 is more than 6.

6 is less than 8.



1,113

One thousand one hundred thirteen

1,000 + 100 + 10 + 3

676 632 676 > 632

The value of the digits in the hundreds place is the same. The value of the digit in the tens place in 676 is 70. The value of the digit in the tens place in 632 is 30. I know that 676 is greater than 632.

Hierarchical Inclusion

1 1 2 1 2 3 Hierarchical inclusion means when we construct a set of two, the value of one is included. When we construct a set of three, the value of two is included which also includes the value of one.

5 and 2 is 7. 3 and 3 is 6.



TEKS: Kindergarten Student Expectations Cards Copy on pink paper. Cut along the bold dotted lines. One set of cards is provided.

K(2)(A) Number and operations. The student is expected to count forward and backward to at least 20 with and without objects.

K(2)(B) Number and operations. The student is expected to read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures.

K(2)(C) Number and operations. The student is expected to count a set of objects up to at least 20 and demonstrate that the last number said tells the number of objects in the set regardless of their arrangement or order.

K(2)(D) Number and operations. The student is expected to recognize instantly the quantity of a small group of objects in organized and random arrangements.

K(2)(E) Number and operations. The student is expected to generate a set using concrete and pictorial models that represents a number that is more than, less than, and equal to a given number up to 20.

K(2)(F) Number and operations. The student is expected to generate a number that is one more than or one less than another number up to at least 20.

K(2)(G) Number and operations. The student is expected to compare sets of objects up to at least 20 in each set using comparative language.

K(2)(H) Number and operations. The student is expected to use comparative language to describe two numbers up to 20 presented as written numerals.

K(2)(I) Number and operations. The student is expected to compose and decompose numbers up to 10 with objects and pictures.

K(5) Algebraic reasoning. The student is expected to recite numbers up to at least 100 by ones and tens beginning with any given number.



TEKS: Grade 1 Student Expectations Cards Copy on green paper. Cut along the dotted lines. One set of cards is provided.

1(2)(A) Number and operations. The student is expected to recognize instantly the quantity of structured arrangements.

1(2)(B) Number and operations. The student is expected to use concrete and pictorial models to compose and decompose numbers up to 120 in more than one way as so many hundreds, so many tens, and so many ones.

1(2)(C) Number and operations. The student is expected to use objects, pictures, and expanded and standard forms to represent numbers up to 120.

1(2)(D) Number and operations. The student is expected to generate a number that is greater than or less than a given whole number up to 120.

1(2)(E) Number and operations. The student is expected to use place value to compare whole numbers up to 120 using comparative language.

1(2)(F) Number and operations. The student is expected to order whole numbers up to 120 using place value and open number lines.

1(2)(G) Number and operations. The student is expected to represent the comparison of two numbers to 100 using the symbols >, <, or =.

1(5)(A) Algebraic reasoning. The student is expected to recite numbers forward and backward from any given number between 1 and 120.

1(5)(B) Algebraic reasoning. The student is expected to skip count by twos, fives, and tens to determine the total number of objects up to 120 in a set.



TEKS: Grade 2 Student Expectations Cards Copy on yellow paper.

Cut along the bold dotted lines. One set of cards is provided.

2(2)(A) Number and operations. The student is expected to use

concrete and pictorial models to compose and decompose numbers up

to 1,200 in more than one way as a sum of so many thousands,

hundreds, tens, and ones.

2(2)(B) Number and operations. The student is expected to use

standard, word, and expanded forms to represent numbers up to 1,200.

2(2)(C) Number and operations. The student is expected to generate

a number that is greater than or less than a given whole number up to

1,200.

2(2)(E) Number and operations.

The student is expected to locate the position of a given whole number on

an open number line.

2(2)(F) Number and operations.

The student is expected to name the whole number that corresponds to a

specific point on a number line.

2(2)(D) Number and operations.

The student is expected to use place value to compare and order whole

numbers up to 1,200 using comparative language, numbers, and

symbols (>, <, or =).








Rapid Assessments: Teacher

Rapid Assessment 1 Provide students with counters. 1. Prompt students to create a set of 5.2. Prompt students to create a set of 14.

Rapid Assessment 2 1. Create a set of 8 counters in a random arrangement. Ask students, “How

many counters are in this set?”2. Create a set of 12 counters in a random arrangement. Ask students,

“How many counters are in this set?”

Rapid Assessment 3 1. Ask students to count orally by tens to 100.2. Ask students to count orally by ones from 25 to 50.

Rapid Assessment 1: Student Responses Student A created a set with: □ 5 counters□ _____ counters

Student B created a set with: □ 5 counters□ _____ counters

Student C created a set with: □ 5 counters□ _____ counters

Student A created a set with: □ 14 counters□ _____ counters

Student B created a set with: □ 14 counters□ _____ counters

Student C created a set with: □ 14 counters□ _____ counters

Rapid Assessment 2: Student Responses Student A □ Correct□ Another Number: ___□ No response

Student B □ Correct□ Another Number: ___□ No response

Student C □ Correct□ Another Number: ___□ No response

Student A □ Correct□ Another Number: ___□ No response

Student B □ Correct□ Another Number: ___□ No response

Student C □ Correct□ Another Number: ___□ No response

Rapid Assessment 3: Student Responses Student A □ Counts by tens without

errors□ Counts by tens with

errors

Student B □ Counts by tens without


errors

Student C □ Counts by tens without


errorsStudent A □ Counts by ones without

errors□ Counts by ones with

errors

Student B □ Counts by ones without


errors

Student C □ Counts by ones without


errors


Rapid Assessments: Observer

Rapid Assessment 1: Student Strategies Student A: □ Counted counters one at

a time.□ Pushed aside counters or

pointed to counters.□ Other:

Student B: □ Counted counters one at



Student C: □ Counted counters one at



Rapid Assessment 2: Student Strategies Student A: □ Counted objects by

touching each one onceand only once – but didnot say numbers outloud.

□ Touched objects and saidcounting numbers outloud for each one.

□ Said number wordsaloud but did not useone-to-onecorrespondence toaccurately count theobjects in the set.

□ Counted one or moreobjects more than once.

□ Rearranged objects intoa different formation andthen counted each objectonly once.

□ Said counting numbersaloud without touchingobjects.

□ None observed.

Student B: □ Counted objects by







□ None observed.

Student C: □ Counted objects by







□ None observed.

Rapid Assessment 3: Student Observation Student A: □ Skipped numbers.□ Paused at each multiple

of 10.

Student B: □ Skipped numbers.□ Paused at each multiple

of 10.

Student C: □ Skipped numbers.□ Paused at each multiple

of 10.


Rapid Assessment: Student A

Rapid Assessment 1 Count one object at a time and count aloud to create the sets.

Rapid Assessment 2 Touch each counter in the arrangement and say the counting number aloud as you touch each one.

Rapid Assessment 3 Count by tens correctly but pause between each multiple of ten. Count by ones correctly but pause at each multiple of 10 (i.e., 25, 26, 27, 28, 29, [pause] 30).


Rapid Assessment: Student B

Rapid Assessment 1 Push aside counters or point to counters to create the sets.

Rapid Assessment 2 Move the counters into a line then and correctly count the set of counters aloud.

Rapid Assessment 3 Count by tens correctly. Count by ones correctly.


Rapid Assessment: Student C

Rapid Assessment 1 Create the set incorrectly in an arbitrary way.

Rapid Assessment 2 Point to the counters as you count out loud. Count incorrectly by repeating a number in the sequence (i.e., 6, 7, 7, 8, 9, 10, 11, 12).

Rapid Assessment 3 Count by tens incorrectly by skipping numbers. Count by ones but start with 1, not 25. When you get to the teen numbers, forget the order of some of the numbers.


Progress Monitoring Card: Developing Whole Number Concepts

Student Name:

Counting

Count

and r

epre

sent

arr

angem

ents

of

obje

cts

up t

o 1

0.

Count

and r

epre

sent

arr

angem

ents

of

obje

cts

beyond 1

0.

Count

forw

ard

and b

ackw

ard

with o

r w

ithout

obje

cts

.

Recite n

um

bers

up t

o 1

00 u

sin

g m

ultip

les o

f 10.

Recite n

um

bers

up t

o 1

00 b

y o

nes.

Recite n

um

bers

forw

ard

and b

ackw

ard

up t

o 1

20.

Skip

-count

by t

ens t

o d

ete

rmin

e t

he t

ota

l num

ber

of

obje

cts

.

Skip

-count

by fiv

es t

o d

ete

rmin

e t

he t

ota

l num

ber

of

obje

cts

.

Skip

-count

by t

wos t

o d

ete

rmin

e t

he t

ota

l num

ber

of

obje

cts

.

Conserv

e n

um

bers

.

Instructional Sequence: Use Counting to Compare Numbers


Five Frame Cards Two sets of cards are provided.



Ten Frame and Double Ten Frame Cards





Comparing Numbers Cards

Cut along dotted lines.

4

is more than

8 15

is more than

18 is the same number as is the same number as

is less than is less than

6

is more than

6 13

is more than



10

is more than

10 13

is more than



11

is more than

1 7

is more than



19

is more than

19 18

is more than



_____

is more than

_____ _____

is more than

_____ is the same number as is the same number as



Using Anchor Charts Concept Process Repertoire

A record of meaningful information and ideas about a concept or vocabulary of the mathematics being studied that may grow over multiple lessons

A record of complex mathematics skills broken down into a sequence of steps and may be extended to include additional solution strategies

A record of multiple options to develop and emphasize flexibility, persistence, and strategic thinking

Example

Example

Example


Using Anchor Charts Concept Process Repertoire

A record of meaningful information and ideas about a concept or vocabulary of the mathematics being studied that may grow over multiple lessons

A record of complex mathematics skills broken down into a sequence of steps and may be extended to include additional solution strategies

A record of multiple options to develop and emphasize flexibility, persistence, and strategic thinking

Example

Example

Example

Generate Numbers


Number Cards: Set A – Kindergarten Two sets of cards are provided. Cut along dotted lines.

3 5 6 8

9 10 12 14

15 16 17 18

3 5 6 8

9 10 12 14

15 16 17 18

Generate Numbers


Number Cards: Set A – Grade 1 Two sets of cards are provided. Cut along dotted lines.

17 27 34 49

51 60 72 86

93 100 108 112

17 27 34 49

51 60 72 86

93 100 108 112

Generate Numbers


Number Cards: Set B – Kindergarten Two sets of cards are provided. Cut along dotted lines.

2 4 6 7

8 10 11 12

13 15 17 19

2 4 6 7

8 10 11 12

13 15 17 19

Generate Numbers


Number Cards: Set B – Grade 1 Two sets of cards are provided. Cut along dotted lines.

18 25 34 42

50 66 79 81

93 99 103 110

18 25 34 42

50 66 79 81

93 99 103 110


Comparing Numbers Using a Beaded Number Line


38

is greater than >

45 61

is greater than >

68 is equal to =

is equal to =

is less than <

is less than <

25

is greater than >

52 75

is greater than >

75 is equal to =

is equal to =

is less than <

is less than <

87

is greater than >

84 24

is greater than >

20 is equal to =

is equal to =

is less than <

is less than <

85

is greater than >

35 15

is greater than >

15 is equal to =

is equal to =

is less than <

is less than <

_____

is greater than >

_____ _____

is greater than >

_____ is equal to =

is equal to =

is less than <

is less than <


Supporting the Needs of Diverse Learners: Elements of Instructional Design

ConceptsMental Strategies, Procedures, and

Algorithms Applications

Manipulatives

Gestures/movement

Anchor charts

Pictures/visuals

Concrete to abstract

Pre‐teach academicvocabulary

Visuals of strategies

Multiple strategiespresented

Chunk information intoshort steps

Connections acrossrepresentations madeexplicit in student activities

Gestures to connect tocontent

Model correct speech andmathematical language


Supporting the Needs of Diverse Learners: Elements of Instructional Design

ConceptsMental Strategies, Procedures, and

Algorithms Applications

Manipulatives

Gestures/movement

Anchor charts

Pictures/visuals

Concrete to abstract

Pre‐teach academicvocabulary

Visuals of strategies

Multiple strategiespresented

Chunk information intoshort steps

Connections acrossrepresentations madeexplicit in student activities

Gestures to connect tocontent

Model correct speech andmathematical language


Speech/Language Impairments Characteristics

Expressive Language Disorder

Difficulty using oral language ortalking

Lacks variation in intonation or volumeof speech

Difficulty with imaginative play Impaired social language Difficulty describing, defining,

explaining, and retelling events Limited vocabulary often prompting

non-specific words (i.e., stuff) Difficulty with writing, spelling,

composing sentences, and answeringall but the most straightforwardquestions

Function words such as “the” and “is”and grammatical markers may beomitted

Receptive Language Disorder

Difficulty understanding oral languageor listening

Difficulty processing and retainingauditory information

Difficulty following verbal instructionsand directions

Difficulty answering questions outsidebasic question forms

Difficulty with verbal reasoning Difficulty filtering out background

noise Difficulty taking turns when talking in

conversation Difficulty maintaining learning and

conversation topics due to languagelimitations


Speech/Language Impairments Characteristics

Expressive Language Disorder

Difficulty using oral language ortalking

Lacks variation in intonation or volumeof speech

Difficulty with imaginative play Impaired social language Difficulty describing, defining,

explaining, and retelling events Limited vocabulary often prompting

non-specific words (i.e. stuff) Difficulty with writing, spelling,

composing sentences, and answeringall but the most straightforwardquestions

Function words such as “the” and “is”and grammatical markers may beomitted

Receptive Language Disorder

Difficulty understanding oral languageor listening

Difficulty processing and retainingauditory information

Difficulty following verbal instructionsand directions

Difficulty answering questions outsidebasic question forms

Difficulty with verbal reasoning Difficulty filtering out background

noise Difficulty taking turns when talking in

conversation Difficulty maintaining learning and

conversation due to languagelimitation


Strategies for Learning and Teaching for Students with SLI

Teach words and concepts using objects.

Progress activities from concrete to abstract.

Use a slower speech rate, if necessary, as this facilitates the processing of information.

Repeat information, language, sentences, phrases, and words more frequently.

Use consistent gestures when helping a student understand the meaning of a word that symbolizes an object or an action.Build consistency with the gestures within the grade-level team and department.

Use pictures or photographs to reinforce and review vocabulary that has been taught.

Add pictures within the story context for position and action words or use objects to model the story problem.

Give simple directions in sentence form to provide experiences in understanding sentences. Give directions in chunks of oneor two steps at a time.

Support the development of a peer buddy to help provide modeling for the student.

Allow the student to work at his/her own pace.

Develop procedures for how the student asks for help.

Model speech, and avoid overcorrecting.

Be patient with the student’s speech; rushing the student could result in frustration.


Strategies for Learning and Teaching for Students with SLI

Teach words and concepts using objects.

Progress activities from concrete to abstract.

Use a slower speech rate, if necessary, as this facilitates the processing of information.

Repeat information, language, sentences, phrases, and words more frequently.

Use consistent gestures when helping a student understand the meaning of a word that symbolizes an object or an action.Build consistency with the gestures within the grade-level team and department.

Use pictures or photographs to reinforce and review vocabulary that has been taught.

Add pictures within the story context for position and action words or use objects to model the story problem.

Give simple directions in sentence form to provide experiences in understanding sentences. Give directions in chunks of oneor two steps at a time.

Support the development of a peer buddy to help provide modeling for the student.

Allow the student to work at his/her own pace.

Develop procedures for how the student asks for help.

Model speech, and avoid overcorrecting.

Be patient with the student’s speech; rushing the student could result in frustration.


Exit Slip: Day 1

Rate your level of proficiency and comfort for the content addressed.

Developing

Proficiency

Approaching

Proficiency

Meeting

Proficiency

Mastering

with

Proficiency

Whole Number Learning Progression ⃝ ⃝ ⃝ ⃝

Whole Number Concepts:

Counting ⃝ ⃝ ⃝ ⃝


Comparing Numbers ⃝ ⃝ ⃝ ⃝


Student Tools ⃝ ⃝ ⃝ ⃝

Support for Students with Speech and

Language Impairments ⃝ ⃝ ⃝ ⃝

Anchor Charts ⃝ ⃝ ⃝ ⃝

Rapid Assessments ⃝ ⃝ ⃝ ⃝

Additional Comments:

Exit Slip: Day 1


Developing

Proficiency

Approaching

Proficiency

Meeting

Proficiency

Mastering

with

Proficiency

Whole Number Learning Progression ⃝ ⃝ ⃝ ⃝


Counting ⃝ ⃝ ⃝ ⃝


Comparing Numbers ⃝ ⃝ ⃝ ⃝


Student Tools ⃝ ⃝ ⃝ ⃝

Support for Students with Speech and

Language Impairments ⃝ ⃝ ⃝ ⃝

Anchor Charts ⃝ ⃝ ⃝ ⃝

Rapid Assessments ⃝ ⃝ ⃝ ⃝





Academic Vocabulary Addition and Subtraction Problem Types

• Comparison• Joining• Part-Part-Whole• Separating

Anchor Chart Repertoire Chart

Balanced Pre-Assessment

Foundational-Bridging-Target Knowledge and Skills

Learning Progression

Numerical Fluency • Part-Whole Relationship (Composing/Decomposing)• Relative Magnitude• Subitizing (Perceptual and Conceptual)• Unitizing

Open Number Line

Quick Images

Representations of Number • Expanded Form• Standard Form

Running Record

Unknown


Guiding Questions for Balanced Pre-Assessment Toolkit Card What are the broad and deep ideas that students must master to be successful in

mathematics this year?

What are the concepts and procedures from the previous grade level that students shouldhave mastered?

What are the foundational knowledge and skillsthat students may use to build toward mastery?

What are the bridging knowledge and skills thatstudents may use to connect foundationalunderstandings to target understandings?

What are the target knowledge and skills inmathematics that students must master?


Guiding Questions for Balanced Pre-Assessment Toolkit Card What are the broad and deep ideas that students must master to be successful in

mathematics this year?

What are the concepts and procedures from the previous grade level that students shouldhave mastered?

What are the foundational knowledge and skillsthat students may use to build toward mastery?

What are the bridging knowledge and skills thatstudents may use to connect foundationalunderstandings to target understandings?

What are the target knowledge and skills inmathematics that students must master?


Activity Role Cards Copy on colored paper. Cut along dotted lines.

Teacher: • Follow the steps found on the teacher page in the

participant journal.• When prompted, video record students as they

work to solve word problems and as they explainhow they solved the problem.

Facilitator: Distribute materials and assist the teacher as needed.

Time keeper: Keep track of the allotted time and participate as a student in the activity.

Student: Participate in the activity as a kindergarten or grade 1 student by using the lesson materials as guided by the teacher.




Representing Numbers


Tens Cards Copy on green paper. Cut along dotted lines.

0 tens 0 tens 0 tens 1 ten 1 ten 1 ten 2 tens 2 tens 2 tens 3 tens 3 tens 3 tens 4 tens 4 tens 4 tens 5 tens 5 tens 5 tens 6 tens 6 tens 6 tens 7 tens 7 tens 7 tens 8 tens 8 tens 8 tens 9 tens 9 tens 9 tens



Ones Cards Copy on yellow paper. Cut along dotted lines.

0 ones 0 ones 0 ones 1 one 1 one 1 one 2 ones 2 ones 2 ones 3 ones 3 ones 3 ones 4 ones 4 ones 4 ones 5 ones 5 ones 5 ones 6 ones 6 ones 6 ones 7 ones 7 ones 7 ones 8 ones 8 ones 8 ones 9 ones 9 ones 9 ones


Standard Form Cards Cut along dotted lines.

79 25 48 54 61 33 86 52 17 99 108 120 116 110 101 112



Expanded Form: Hundreds Cards Copy on blue paper. Cut along dotted lines.

1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0



Expanded Form: Tens Cards Copy on yellow paper. Cut along dotted lines.

1 0 1 0 2 0 2 0 3 0 3 0 4 0 4 0 5 0 5 0 6 0 6 0 7 0 7 0 8 0 8 0 9 0 9 0 0 0 0 0

Expanded Form: Ones Cards

Copy on green paper.


1 2 1 2

3 4 3 4

5 6 5 6

7 8 7 8

9 0 9 0


More or Less Cards Cut along dotted lines.

More Less

More Less

More Less

More Less

More Less


Comparison Language Cards


is more than is less than is the same number as

is greater than is less than is equal to






Comparing Numbers Cards Cut along dotted lines.

0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9


Comparison Symbol and Word Cards Cut along dotted lines.

> is greater

than

< is less than

= is equal

to

> is greater

than

< is less than

= is equal

to

> is greater

than

< is less than

= is equal

to

> is greater

than

< is less than

= is equal

to

> is greater

than

< is less than

= is equal

to

> is greater

than

< is less than

= is equal

to


Numbers to Compare Cards Cut along dotted lines.

120 111 103 100 118

92 70 81 42 25

18 67 56 70 92

24 52 65 76 29

120 111 103 100 118

92 70 81 42 25

18 67 56 70 92

24 52 65 76 29


Place Value Puzzle Cut along dotted lines.

114 > ___04 118 < 1___0 2___ = 27

72 > ___8 4 < ___ 84 = ___4

91 > 9___ 90 < 10___ 32 = 3___

120 > 1___2 6___ < 98 ___05 = 105

___0 > 87 ___5 < 60 ___7 > 13

100 > ___3 ___0 < 95 84 > ___9

___ > 7 52 < ___6 11___ < 118

70 > ___2 17 < ___1 4___ > 39

Sample Learning Progression: Addition and Subtraction Kindergarten - Grade 1


TEKS: Kindergarten Student Expectations Cards Copy on pink paper. Cut along the bold dotted lines. Three sets of cards are provided. K(3)(A) Number and operations. The student is expected to model the action of joining to represent addition and the action of separating to represent subtraction.

K(3)(B) Number and operations. The student is expected to solve word problems using objects and drawings to find sums up to 10 and differences within 10.

K(3)(C) Number and operations. The student is expected to explain the strategies used to solve problems involving adding and subtracting within 10 using spoken words, concrete and pictorial models, and number sentences.

K(3)(A) Number and operations. The student is expected to model the action of joining to represent addition and the action of separating to represent subtraction.



K(3)(A) Number and operations. The student is expected to model the action of joining to represent addition and the action of separating to represent subtraction.



Sample Learning Progression: Addition and Subtraction Kindergarten - Grade 1


TEKS: Grade 1 Student Expectations Cards Copy on green paper. Cut along the dotted lines. One set of cards is provided. 1(3)(B) Number and operations. The student is expected to use objects and pictorial models to solve word problems involving joining, separating, and comparing sets within 20 and unknowns as any one of the terms in the problem such as 2 + 4 = [ ]; 3 + [ ] = 7; and 5 = [ ] – 3.

1(3)(C) Number and operations. The student is expected to compose 10 with two or more addends with and without concrete objects.

1(3)(D) Number and operations. The student is expected to apply basic fact strategies to add and subtract within 20, including making 10 and decomposing a number leading to a 10.

1(3)(E) Number and operations. The student is expected to explain strategies used to solve addition and subtraction problems up to 20 using spoken words, objects, pictorial models, and number sentences.

1(3)(F) Number and operations. The student is expected to generate and solve problem situations when given a number sentence involving addition or subtraction of numbers within 20.

1(5)(D) Algebraic reasoning. The student is expected to represent word problems involving addition and subtraction of whole numbers up to 20 using concrete and pictorial models and number sentences.

1(5)(E) Algebraic reasoning. The student is expected to understand that the equal sign represents a relationship where expressions on each side of the equal sign represent the same value(s).

1(5)(F) Algebraic reasoning. The student is expected to determine the unknown whole number in an addition or subtraction equation when the unknown may be any one of the three or four terms in the equation.

1(5)(G) Algebraic reasoning. The student is expected to apply properties of operations to add and subtract two or three numbers.


Learning Progression Kindergarten: Addition and Subtraction of Whole Numbers


Learning Progression Grade 1: Addition and Subtraction of Whole Numbers


Question Mark Cards

Cut along dotted lines. Twelve cards are provided.

? ? ?

? ? ?

? ? ?

? ? ?


Comparison Mat Cut along the dotted lines and glue or tape the three pieces together where indicated.

Glue or tape Glue or tape Glue or tape


Types of Addition and Subtraction Word Problems Joining and Separating Problems

• An action or change that occurs over time is involved.• An initial quantity (start) is increased/decreased by a particular quantity

(change) to get a final quantity (result).• The start, change, or result may be unknown.

Part-Part-Whole Problems • An action is NOT involved.• A change over time is NOT involved.• A relationship between a whole quantity and two (or more) parts make up the whole quantity.• A part or the whole may be unknown.

whole

part part

Comparison Problems

• An action is NOT involved.• A change over time is NOT represented.• A comparison of two distinct sets is involved.• One set is labeled the referent, and the other is

labeled the compared set.• The difference, the larger quantity, or the smaller

quantity may be unknown. • The referent, the compared set, or the difference

may be unknown.

larger quantity

smaller quantity difference

Result

Change

Start


Types of Addition and Subtraction Word Problems Joining and Separating Problems

• An action or change that occurs over time is involved.• An initial quantity (start) is increased/decreased by a particular quantity

(change) to get a final quantity (result).• The start, change, or result may be unknown.

Part-Part-Whole Problems • An action is NOT involved.• A change over time is NOT involved.• A relationship between a whole quantity and two (or more) parts make up the whole quantity.• A part or the whole may be unknown.

whole

part part

Comparison Problems • An action is NOT involved.• A change over time is NOT represented.• A comparison of two distinct sets is involved.• One set is labeled the referent, and the other is

labeled the compared set.• The difference, the larger quantity, or the smaller

quantity may be unknown.• The referent, the compared set, or the difference

may be unknown.

larger quantity

smaller quantity difference

Result

Change

Start

Addition and Subtraction Problem Types


Joining Problems Start Unknown

David had some baseball cards. Kayla gave him 3 baseball cards. Now he has 12 baseball cards. How many baseball cards did David have at the start?

Change Unknown David had 5 baseball cards. Then Kayla gave him some baseball cards. Now he has 10 baseball cards. How many baseball cards did Kayla give David?

Result Unknown* David had 6 baseball cards. Kayla gave him 2 baseball cards. How many baseball cards does David have now?

Separating Problems Start Unknown

David had some baseball cards. He gave 4 baseball cards to Kayla. Now he has 8 baseball cards. How many baseball cards did David have at the start?

Change Unknown David had 14 baseball cards. He gave some baseball cards to Kayla. Now he has 9 baseball cards. How many baseball cards did David give to Kayla?

Result Unknown* David had 10 baseball cards. He gave 1 baseball card to Kayla. How many baseball cards does David have now?

Part-Part-Whole Problems Part Unknown

David has 13 baseball cards. He has 7 new baseball cards. The rest are old baseball cards. How many old baseball cards does David have?

Whole Unknown* David has 4 old baseball cards and 6 new baseball cards. How many baseball cards does David have altogether?

Comparison Problems Difference Unknown

David has 12 baseball cards. Kayla has 9 baseball cards. How many more baseball cards does David have than Kayla?

Larger Unknown Kayla has 5 baseball cards. David has 8 more than Kayla. How many baseball cards does David have?

Smaller Unknown David has 14 baseball cards. He has 7 more baseball cards than Kayla. How many baseball cards does Kayla have?

* Kindergarten

Addition and Subtraction Problem Types


Joining Problems Start Unknown

David had some baseball cards. Kayla gave him 3 baseball cards. Now he has 12 baseball cards. How many baseball cards did David have at the start?

Change Unknown David had 5 baseball cards. Then Kayla gave him some baseball cards. Now he has 10 baseball cards. How many baseball cards did Kayla give David?

Result Unknown* David had 6 baseball cards. Kayla gave him 2 baseball cards. How many baseball cards does David have now?

Separating Problems Start Unknown

David had some baseball cards. He gave 4 baseball cards to Kayla. Now he has 8 baseball cards. How many baseball cards did David have at the start?

Change Unknown David had 14 baseball cards. He gave some baseball cards to Kayla. Now he has 9 baseball cards. How many baseball cards did David give to Kayla?

Result Unknown* David had 10 baseball cards. He gave 1 baseball card to Kayla. How many baseball cards does David have now?

Part-Part-Whole Problems Part Unknown

David has 13 baseball cards. He has 7 new baseball cards. The rest are old baseball cards. How many old baseball cards does David have?

Whole Unknown* David has 4 old baseball cards and 6 new baseball cards. How many baseball cards does David have altogether?

Comparison Problems Difference Unknown

David has 12 baseball cards. Kayla has 9 baseball cards. How many more baseball cards does David have than Kayla?

Larger Unknown Kayla has 5 baseball cards. David has 8 more than Kayla. How many baseball cards does David have?

Smaller Unknown David has 14 baseball cards. He has 7 more baseball cards than Kayla. How many baseball cards does Kayla have?

* Kindergarten


Accommodations for English Language Learners

Visuals for vocabulary Peer interaction

Use of anchor charts Gestures for memorization of academicconcepts

Use of graphic organizers Use of sentence stems/frames

Use of manipulatives Pre-teach academic vocabulary


Accommodations for English Language Learners

Visuals for vocabulary Peer interaction

Use of anchor charts Gestures for memorization of academicconcepts

Use of graphic organizers Use of sentence stems/frames

Use of manipulatives Pre-teach academic vocabulary


Supporting Students with Diverse Needs

Text to Speech (TTS) www.naturalreaders.com

Super Tools for Teachers www.esc4.net/UDL

UDL Tech Toolkit http://udltechtoolkit.wikispaces.com

Institute of Education Sciences (IES) What Works In Math? http://ies.ed.gov/ncee/wwc/MathHome.aspx


Supporting Students with Diverse Needs

Text to Speech (TTS) www.naturalreaders.com

Super Tools for Teachers www.esc4.net/UDL

UDL Tech Toolkit http://udltechtoolkit.wikispaces.com/

Institute of Education Sciences (IES) What Works In Math? http://ies.ed.gov/ncee/wwc/MathHome.aspx


Exit Slip: Day 2


Developing

Proficiency

Approaching

Proficiency

Meeting

Proficiency

Mastering

with

Proficiency


Subitizing ⃝ ⃝ ⃝ ⃝


Representing, Comparing, and Ordering ⃝ ⃝ ⃝ ⃝


Composing and Decomposing Numbers ⃝ ⃝ ⃝ ⃝

Addition and Subtraction

Learning Progression ⃝ ⃝ ⃝ ⃝

Support for Students who are English

Language Learners ⃝ ⃝ ⃝ ⃝

Pre-Assessment ⃝ ⃝ ⃝ ⃝

Problem Types ⃝ ⃝ ⃝ ⃝


Exit Slip: Day 2


Developing

Proficiency

Approaching

Proficiency

Meeting

Proficiency

Mastering

with

Proficiency


Subitizing ⃝ ⃝ ⃝ ⃝


Representing, Comparing, and Ordering ⃝ ⃝ ⃝ ⃝


Composing and Decomposing Numbers ⃝ ⃝ ⃝ ⃝

Addition and Subtraction

Learning Progression ⃝ ⃝ ⃝ ⃝

Support for Students who are English

Language Learners ⃝ ⃝ ⃝ ⃝

Pre-Assessment ⃝ ⃝ ⃝ ⃝

Problem Types ⃝ ⃝ ⃝ ⃝





Academic Vocabulary Anchor Chart

• Concept

Feedback • Intervention• Process• Task

Fractions • Partition

Learning Progression • Addend• Associative Property• Commutative Property• Difference• Equation• Expression• Minuend• Subtrahend• Sum

Practice • Blocked• Interleaved• Skill

Fact Cards

Cut along the dotted lines. Two sets of cards provided.

+8 8 8 3+ 10 5+

10 3+ 3 3+ 8 5+

8 1+ 7 7+ 9 10+

2 10+ +2 2 8 4+

+8 8 8 3+ 10 5+

10 3+ 3 3+ 8 5+

8 1+ 7 7+ 9 10+

2 10+ +2 2 8 4+

Fact Building for Addition and Subtraction


+ 1 or –1 + 2 or –2

+ or – 0 Ten Facts Decompose, Then

Make 10 Doubles and Near

Doubles

Students build on their understanding of counting by exploring addition facts with an addend of 1 or 2 and subtraction facts with a

subtrahend of 1 or 2.

Students explore addition facts with an addend of zero and subtraction facts with a subtrahend of zero.

Students explore addition facts with two addends that result in a sum of 10.

Students explore addition facts with an addend of 7, 8, or 9 and a second addend that is decomposed to make

10 with 7, 8, or 9.

Students explore facts with the same addends, doubles, facts with addends of only a difference of one, and near

doubles.

7 + 1 = 8 5 – 1 = 4

2 + 0 = 2 5 – 0 = 5

1 + 9 = 10 3 + 7 = 10

9 + 6 9 + 1 + 5

10 + 5 = 15

8 + 8 = 16 8 + 9 = 17

Think Addition Down Through 10 Take From 10

Students explore subtraction facts

by thinking about the relationship between the quantity in the subtrahend and a quantity that

composes to make the quantity of the minuend.

Students explore subtraction facts by decomposing the subtrahend in order to find a difference of 10. They then subtract the remaining

quantity from 10.

Students explore subtraction facts by decomposing the minuend into a 10 and the remaining quantity. The subtrahend is subtracted from

10, and the remaining quantities are composed to determine the difference.

12 5

5 12

15 8

15 5 3

10 3 7

15 8

10 5 8

10 8 5

2 5 7

Fact Building for Addition and Subtraction

+ 1 or –1

+ 2 or –2 + or – 0 Ten Facts

Decompose, Then

Make 10

Doubles and Near

Doubles

Students build on their understanding of

counting by exploring addition facts with an addend of 1 or 2 and subtraction facts with a subtrahend of 1 or 2.

Students explore addition facts with

an addend of zero and subtraction facts with a subtrahend of zero.


two addends that result in a sum of 10.


an addend of 7, 8, or 9 and a second addend that is decomposed to make 10 with 7, 8, or 9.

Students explore facts with the same

addends, doubles, facts with addends of only a difference of one, and near doubles.

7 + 1 = 8 5 – 1 = 4

2 + 0 = 2 5 – 0 = 5

1 + 9 = 10 3 + 7 = 10

9 + 6 9 + 1 + 5

10 + 5 = 15

8 + 8 = 16 8 + 9 = 17

Think Addition Down Through 10 Take From 10

Students explore subtraction facts

by thinking about the relationship between the quantity in the subtrahend and a quantity that composes to make the quantity of the minuend.

Students explore subtraction facts by decomposing the subtrahend in order to find a difference of 10. They then subtract the remaining quantity from 10.

Students explore subtraction facts by decomposing the minuend into a 10 and the remaining quantity. The subtrahend is subtracted from 10, and the remaining quantities are

composed to determine the difference.

12 5

5 12

15 8

15 5 3

10 3 7

15 8

10 5 8

10 8 5

2 5 7



Fact Cards

8 1 6 4 3 0

7 4 18 9 2 0

6 7 5 2 7 5

16 9 4 5 5 3

8 3 4 4 8 2

3 2 3 7 6 1

9 4 8 7 7 7

19 10 13 6 5 5


Expression Cards 1-10

Cut along the dotted lines.

3 6+2 4+

2 1+

1 2+ 5 5+5 3+ 2 6+1 1+

0 2+

6 1+ 3 4+

4+10+12+2

6 4+ 0 5+

+1 01+3

+4 5+3 3

Expression Cards 10-20

Cut along the dotted lines.

7 3+ 2 8+ 2 9+

8 3+ 6 6+ 9 3+

12 3+ 10 5+ 9 9+

10 8+ 9 7+ 8 8+

7 7+ 9 5+ 4 4 4+ +

4 3 3+ + 7 7 4+ + 5 5 6+ +

2 6 3+ + 10 2 2+ + 7 3 5+ +


Meaningful Practice

Skill Practice

Primary focus on buildingprocedural fluency

Repetitive practice for aspecific skill

Promotes automaticity Increases ability to perform

math tasks quickly Allows brain to focus on

more challenging problem-solving steps

Blocked Practice

Narrow focus on specificcontent Skills and processes are the

same/similar for everyproblem

One given process ispracticed

Promotes learning of new skillor process Knowledge of content and

strategies are introducedjust prior to practice

The rigor of practice isreduced because choice ofstrategy or process is notrequired between problems

Interleaved Practice

Wide focus on broad content Skills and processes are

different across theproblems

Focuses on interpretingsituations and determiningthe process

Promotes decision making andproblem solving Knowledge of content and

strategies are from newlyintroduced as well asprevious learning

The rigor of practice isincreased because studentsmust choose the strategy orprocess


Meaningful Practice

Skill Practice

Primary focus on buildingprocedural fluency

Repetitive practice for aspecific skill

Promotes automaticity Increases ability to perform

math tasks quickly Allows brain to focus on

more challenging problem-solving steps

Blocked Practice

Narrow focus on specificcontent Skills and processes are the

same/similar for everyproblem

One given process ispracticed

Promotes learning of new skillor process Knowledge of content and

strategies are introducedjust prior to practice

The rigor of practice isreduced because choice ofstrategy or process isreduced between problems

Interleaved Practice

Wide focus on broad content Skills and processes are

different across theproblems

Focuses on interpretingsituations and determiningthe process

Promotes decision making andproblem solving Knowledge of content and

strategies are from newlyintroduced as well asprevious learning

The rigor of practice isincreased because studentsmust choose the strategy orprocess


Sample Learning Progression Grade 1: Fraction Concepts

Developing Fraction Concepts

Grade 1: Fraction Concepts

Data Collection

Identify examples and non-examples of halves and fourths

Readiness For

Grade 2

Pre-Assessment

Partition two-dimensional figures into two and four fair shares or equal parts and describe the

parts using words


Sample Learning Progression Grade 1: Fraction Concepts

Developing Fraction Concepts

Grade 1: Fraction Concepts

Data Collection

Identify examples and non-examples of halves and fourths

Readiness For

Grade 2

Pre-Assessment

Partition two-dimensional figures into two and four fair shares or equal parts and describe the

parts using words


Example and Non-Example Cards Cut along the dotted lines.

Card A Card B

Card C Card D

Card E Card F

Card G Card H


Workstation 1: Example and Non-Example Sorting Cards Cut along the dotted lines.


Effective Feedback: Task Feedback

• You have all the questions about _____ correct.

• Question _____ is incorrect. You forgot to _____.

• Your solution to question _____ is correct.

• When you _____, the _____ was done incorrectly.

• Although you got the answer correct, you _____ incorrectly.

• The answer to question _____ is incorrect because it looks like you are confusing

_____ with _____.


Effective Feedback: Task Feedback

• You have all the questions about _____ correct.

• Question _____ is incorrect. You forgot to _____.

• Your solution to question _____ is correct.

• When you _____, the _____ was done incorrectly.

• Although you got the answer correct, you _____ incorrectly.

• The answer to question _____ is incorrect because it looks like you are confusing

_____ with _____.


Effective Feedback: Process Feedback

• I see that you are _____, and that is working for you.

• How would the thinking you used for question _____ help you understand question

_____?

• Have you thought of using _____ to solve the problem?

• I see that you used _____ to _____. Have you thought about using _____?

• How would the process we learned when we _____ help you _____?

• You chose to use a _____ to answer the question. How could _____ have helped you?

• Think back to when you used _____ to solve the problem. How can that help

you solve _____?

• How would the process you used for question _____ help you find your mistake

in question _____?


Effective Feedback: Process Feedback

• I see that you are _____, and that is working for you.

• How would the thinking you used for question _____ help you understand question

_____?

• Have you thought of using _____ to solve the problem?

• I see that you used _____ to _____. Have you thought about using _____?

• How would the process we learned when we _____ help you _____?

• You chose to use a _____ to answer the question. How could _____ have helped you?

• Think back to when you used _____ to solve the problem. How can that help

you solve _____?

• How would the process you used for question _____ help you find your mistake

in question _____?


Effective Feedback: Intervention Feedback

• Remember when we learned about ____? This can help you solve the problem because

_____.

• Using _____ did not always _____. How could you use _____ to solve the problem?

• Doing all of the thinking in your head did not help you solve the problem. Try showing your

thinking by _____.

• Remember when we learned about _____? Try using that process first.

• Your method required you to _____. How could you use _____ to solve the problem?

• Remember to _____ before choosing _____.

• How could you _____ when you _____?

• The _____ appeared useful in solving the problem. How could you use this idea to _____?


Effective Feedback: Intervention Feedback

• Remember when we learned about ____? This can help you solve the problem because

_____.

• Using _____ did not always _____. How could you use _____ to solve the problem?

• Doing all of the thinking in your head did not help you solve the problem. Try showing your

thinking by _____.

• Remember when we learned about _____? Try using that process first.

• Your method required you to _____. How could you use _____ to solve the problem?

• Remember to _____ before choosing _____.

• How could you _____ when you _____?

• The _____ appeared useful in solving the problem. How could you use this idea to _____?


Curriculum and Instruction for Gifted/Talented Students

Districts meet the needs of gifted/talented students by modifying the __________, __________, and

_________ of the curriculum and instruction ordinarily provided by the school.

• WHAT• TEKS• Instructional Materials

• HOW• Instructional Activities• Instructional Grouping

• EVIDENCE• Student Demonstration

of Mastery

Content Process Product Examples:

Next grade-level TEKS Higher magnitude of

numbers

Examples: G/T small groups Separate G/T stations

Examples: Video Written report Performance task


Curriculum and Instruction for Gifted/Talented Students Districts meet the needs of gifted/talented students by modifying the __________, __________, and

_________ of the curriculum and instruction ordinarily provided by the school.

• WHAT• TEKS• Instructional Materials

• HOW• Instructional Activities• Instructional Grouping

• EVIDENCE• Student Demonstration

of Mastery

Content Process Product Examples:

Next grade-level TEKS Higher magnitude of

numbers

Examples: G/T small groups Separate G/T stations

Examples: Video Written report Performance task


Exit Slip: Day 3


Developing

Proficiency

Approaching

Proficiency

Meeting

Proficiency

Mastering

with

Proficiency

Addition and Subtraction:

Representing Problem Situations ⃝ ⃝ ⃝ ⃝


Generating and Solving Problem Situations ⃝ ⃝ ⃝ ⃝

Addition and Subtraction Facts ⃝ ⃝ ⃝ ⃝

Properties of Operations, The Equal Sign,

Determining the Unknown ⃝ ⃝ ⃝ ⃝

Learning Progression: Fractions

and Fraction Concepts ⃝ ⃝ ⃝ ⃝

Support for Students who are

Gifted/Talented ⃝ ⃝ ⃝ ⃝

Meaningful Practice ⃝ ⃝ ⃝ ⃝

Types of Feedback ⃝ ⃝ ⃝ ⃝


Exit Slip: Day 3


Developing

Proficiency

Approaching

Proficiency

Meeting

Proficiency

Mastering

with

Proficiency


Representing Problem Situations ⃝ ⃝ ⃝ ⃝


Generating and Solving Problem Situations ⃝ ⃝ ⃝ ⃝

Addition and Subtraction Facts ⃝ ⃝ ⃝ ⃝

Properties of Operations, The Equal Sign,

Determining the Unknown ⃝ ⃝ ⃝ ⃝

Learning Progression: Fractions

and Fraction Concepts ⃝ ⃝ ⃝ ⃝

Support for Students who are

Gifted/Talented ⃝ ⃝ ⃝ ⃝

Meaningful Practice ⃝ ⃝ ⃝ ⃝

Types of Feedback ⃝ ⃝ ⃝ ⃝



Documents

TABLE SETS - Texas Gateway · PDF filenumber of objects in the set regardless of their ... up to at least 100 by ones and tens beginning with any given number. ... Counts by tens with