Are you smarter than a fifth grader?

1. The ratio of children to pet dogs in Brian’s neighborhood is 4:1. There are 11 dogs in the neighborhood; how many children live there?

2. Deana packages tiles in a factory. Tiles are packed 8 per package, and shipped in boxes containing 12 packages per box. There are 100 tiles at her station. Can she fill a shipping box?

Yes, with 4 left over.

44 children

Back to Basics

Presented by Mrs. Phyllis Prestamo

Supervisor of Applied Sciences

Roxbury Public Schools

New Jersey Core Curriculum Content

Standards - 2004

4.1 Number and Numerical Operations4.2 Geometry & Measurement4.3 Patterns & Algebra4.4 Data Analysis, Probability, & Discrete Math4.5 Mathematical Processes

New Standards due out January 2010

NJ is participating along with 48 other states/territories in drafting a

“Common Core of K-12 Math Standards”

February

Fundamental Premise

All students must have a solid grounding in mathematics to function effectively in today’s world.

from Memo dated 7/10/09 from Willa Spicer, Deputy Commissioner & Sandra M. Alberti, Director, Office of Math and Science Education

Areas of Agreement:

•Automatic recall of basic facts: Computational fluency in whole number arithmetic is vital. Computational fluency requires automatic recall of addition and multiplication facts from 0-12 and an understanding of the underlying mathematical ideas.

•Calculators: Calculators can have a useful role even in the lower grades, but must be used judiciously so as not to impede the acquisition of fluency with basic number facts and computational procedures.

•Learning Algorithms: Students should be able to fluently and accurately use basic algorithms to add, subtract, multiply and divide whole numbers.

•Fractions: Understanding the number meaning of fraction is critical.

•Teaching Mathematics in “real-world” contexts: Applied problems can motivate and introduce mathematical ideas.

from Memo dated 7/10/09 from Willa Spicer, Deputy Commissioner & Sandra M. Alberti, Director, Office of Math and Science Education

It’s a Fact• Permanent learning of basic facts is stored in long term memory and can be later retrieved quickly when needed without much thought.

• Students who automatically know their basic facts are better able to master more complex operations and are better equipped to tackle math applications in all subjects.

• Research has shown (D. Klein, 2005) that progress in Mathematics in students who do not know their basic number facts often grinds to a halt by the end of elementary school.

•Youngsters who have not mastered whole number arithmetic by the end of 4th grade are at risk of later becoming remedial students in mathematics. (T. Loveless 2003)

• All children are able to master the basic facts through drill once they have constructed a strategy for a particular set of facts.

• Mastering of the basic facts requires frequent rehearsal and practice and should occur on a daily basis.

The Goal

The goal for mastery of the basic facts is automaticity. A student is considered to have achieved automaticity when he or she can give an answer to a basic fact in less than 3 seconds without using finger counting.

Building Understanding

Practice activities developed around how the brain makes and

stores long-term memories should precede drill and should be designed to build students’ conceptual understanding.

Teaching Sequence

Mathematics is a discipline of connected ideas. Knowledge of a single concept or skill

is often the foundation for many aspects within the discipline. New concepts cannot be formed if the prerequisite concepts and skills

are not well established. Curriculum is organized into a careful sequence of

clustered strategies.

GRADE 1 Addition & Subtraction Facts to 181st quarter - Count on 1, 2, 3 addition2nd quarter - Count back 0, 1 subtraction3rd quarter - Doubles/doubles +1, +2, +3 addition3rd quarter - Count back 0, 1, 2 subtractionMake a “10”

GRADE 2 Addition & Subtraction Facts to 18Review – count on 1, 2, 3 additionReview – doubles/doubles +1, 2, 3 additionReview – count back 1, 2, 3 subtractionReview – make “10”Fact FamiliesSkip counting x2, x5, x10

GRADE 3 Addition & Subtraction Facts to 18Review – addition/subtraction to 18Multiplication 0-10 & Division 1-10Doubling = x21st quarter – x0, x1, x2, x52nd quarter – x0, x1, x2, x3, x4, x5 and ÷1, 2, 53rd quarter – x0-10 and ÷1, 2, 3, 4, 5, 10End of year – Multiplication 0-10 & division 1-10

GRADE 4 Multiplication 0-12 & Division 1-12Review – Multiplication 0-10 & division 1-102nd quarter x11 & ÷113rd quarter x12 & ÷12End of Year - Multiplication 0-12 & division 1-12

GRADE 5 & 6 Multiplication 0-12 & Division 0-12Review all facts 0-12

X 0 1 2 3 4 5 6 7 8 9

0 0 0 0 0 0 0 0 0 0 0

1 0 1 2 3 4 5 6 7 8 9

2 0 2 4 6 8 10 12 14 16 18

3 0 3 6 9 12 15 18 21 24 27

4 0 4 8 12 16 20 24 28 32 36

5 0 5 10 15 20 25 30 35 40 45

6 0 6 12 18 24 30 36 42 48 54

7 0 7 14 21 28 35 42 49 56 63

8 0 8 16 24 32 40 48 56 64 72

9 0 9 18 27 36 45 54 63 72 81

TEN FACTS TO MEMORIZE

4 Stages of

Teaching & Learning

Example:

“Use tens multiplication strategy for the fives facts”

Introduce the strategy Hands on activities - manipulatives are used to model a strategy

4 x 10 = 40

10 x 4 = 40

4 x 5 =

5 x 4 =

“I know ten fours are forty, so five fours must be half of that--–twenty.”

Reinforce the strategyThese activities are designed to make links between the concrete/pictorial

and symbolic representations.

8 x 10 = _____

____ x ____ = _____

80

8 5 40

Practice the factsAt this stage students should use mental computation only and fast recall is

stressed.

10 45 25 20

35 15 45 25

30 35 15 40

The player rolls a “four” and says “four tens are forty, so four fives are twenty” and covers the twenty.

Extend the strategyOnce mastered, the strategies and skills can be applied to new contexts and

new situations. Students are encouraged to go beyond.

10 x 18 = ______ so 5 x 18 = _______

10 x 26 = ______ so 5 x 26 = _______

10 x 22 = ______ so 5 x 22 = _______

10 x 15 = ______ so 5 x 15 = _______150

260

90

130

220 110

180

75

Later students will then vary this strategy by halving and doubling other factors: e.g. 14 x 35 has the same answer as 7 x 70 which is

much easier to calculate mentally.

So…

What can I do to help my child?

• Play Games• Use your computer• Use Art• Read about Math • Talk about Math

Play Games

WGB - 163

New Jersey

Use Your Computer

Use Art

Read About Math

Talk About Math

100’s Chart1 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

x 2

100’s Chart1 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

x 3

100’s Chart1 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

x 4

100’s Chart1 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

x 9

&

x 8

Let’s Explore

References•Adding It Up: Helping children learn mathematics, National Research Council, 2001 Book on the web: http://books.nap.edu/openbook.php?record_id=9822&page=R1

•Math Fluency: Scholastic Research Foundation Paper www2.scholastic.com/browse/article.jsp?id=324&print=1

•Trends in Math Achievement: The Importance of Basic Skills – Tom Loveless, Brown Center on Educational Policy, The Brookings Institute www.brookings.edu/speeches/2003/0206education_loveless.aspx

•Bloom, B. (1986, Feb.) Automaticity: the hands and feet of genius. Educational Leadership, 43 (5), 70-77.

•Burnett, James (2008) Developing the Essential Strategies for Computation. Origo Education. www.origomath.com

• Klein, D. (2005). The state of math standards. Thomas B. Fordham Foundation Washington, DC www.edexcellence.net