Filling in Knowledge Gaps:

Critical lessons across grade levels

1-3 for students in grade 4-6

NCTM - 2015 Annual Meeting & Exposition - Boston

Cassy Turner

Cassy@SingaporeMathSource.com

SingaporeMathSource.com SingaporeMath.com

Cassy Turner

Cassy@singaporemathsource.com

Twitter Bio: Passionate about Singapore Math,

Teacher/Trainer/Coach/Treasure Hunter/ Learner

Answer to the ultimate question? 42.

Handout and slides at:

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resources/handouts

Development of Addition and Subtraction

Grade 1

Number Bonds

With strategies to 40 and 100

Grade 2

Vertical algorithm within 1000 (Main lessons)

Grade 3

Vertical algorithm within 10,000

Grades 4 - 6

Review and apply algorithm to larger numbers

2

?

10

2278

?

3B Mental

Math

4A Four Operations of Whole Numbers

4B Decimals

Development of Addition and Subtraction

Grade 1

Number Bonds

With strategies to 40 and 100

Grade 2

Vertical algorithm within 1000 (Main lessons)

Grade 3

Vertical algorithm within 10,000

Grades 4 - 6

Review and apply algorithm to larger numbers

7 + 6 = ?

Making Ten

3 3

7 + 6 = ?

Making Ten

3 4

22 - 3 = ?

Grade 1 - Addition and Subtraction: Numbers to 40

onestens

onestens

3-22

12

10 22

- 3

9

1

1

12

onestens

Grade 2

Development of Addition and Subtraction

Grade 1

Number Bonds

With strategies to 40 and 100

Grade 2

Vertical algorithm within 1000 (Main lessons)

Grade 3

Vertical algorithm within 10,000

Grades 4 - 6

Review and apply algorithm to larger numbers

Regrouping/Renaming

onestens24 + 37

110 10

1

11

1 1 1

1 1 1

1

101010

Regrouping/Renaming

onestens24 + 37

110 10

101010

10

24

+ 371

1

6

Addition and Subtraction – What’s Next?

Grades 3 - 6

Review and apply algorithm to larger

numbers

Development of Multiplication/Division

Grade 2

Understand multiplication and division as

related operations

Learn multiplication and division facts for 2,

3, 4, 5 and 10

2A

Multiplication

2A Division

Grade 3

Multiply a 2- or 3-digit number by a 1-digit

number

Division algorithm, including remainders

Learn multiplication and division facts for 6, 7, 8,

and 9.

Area & Perimeter

Development of Multiplication/Division

3A Multiplying Tens and Ones

36 x 3

30 610 10 10

1

11

11

1

onestenshundreds

10 10

10

10

10 10

10

10

10

1

11

11

1

1

11

11

1

1

11

11

1

onestenshundreds

10 10

10

10

10 10

10

10

10

1

11

11

1

1

11

11

1

1

11

11

1

10

onestenshundreds

10 10

10

10

10 10

10

10

10

1

1

1

11

11

1

10

100

3A Quotient and Remainder

53 ÷ 2= ?

tens

2

2 53

-4

1

10 10 101010

111

onestens111

111

11

11

53 ÷ 2= ?

tens ones

2

2 53

-4

1 3

10

10

10

10

1

onestens

11

11

11

1

1

11

11

6

-1 21

R 1

Grade 3

Multiply a 2- or 3-digit number by a 1-digit

number

Division algorithm, including remainders

Learn multiplication and division facts for 6,

7, 8, and 9.

Area & Perimeter

Development of Multiplication/Division

3A

Multiplication by 7

3A

Multiplication by 7

3B Area

Grade 4 Multiply with 10,000 by a 2-digit number

Find factors and multiples with 100

Use divisibility rules for 2, 3, 5, 6, 9 and 10

Use Order of Operations to solve expressions

Area, Perimeter & Volume

Grade 5 Divide numbers to 10,000 by a 2-digit divisor

Multiplication/Division – What’s Next?

Development of Fractions

Grade 1

Halves and fourths

Grade 2

Name and illustrate fractions as parts of a

whole to twelfths.

Order unit fractions

2B Fractions

Development of Fractions

Grade 3

Compare fractions by numerators and

denominators

Find equivalent fractions and simplest form of

a fraction

Fractions and Measurement

Fraction of a Set

3B Comparing

Fractions

3B

Equivalent

Fractions

3B Fractions and Measurement

Fractions – What’s Next?

Grade 4

Add and subtract like and related fractions

Convert between mixed numbers and

improper fractions

Multiply a fraction by a whole number

Grade 5

Multiply a fraction by a fraction

Divide a fraction by a whole number

Divide a whole number by a fraction

Decimal Development

Grade 3

Add and subtract money

Multiply & divide money

Grade 4

Understand, locate on a number line and

compare tenths, hundredths, thousandths

Apply four operations up to 2 decimal places

Convert fractions to decimals

Grade 5

Apply four operations up to 3 decimal places

Development of Bar Modeling

Grade 2

Examples in materials to explain fractions

Grade 3

Introduces part-whole and comparison models

for four operations

Explain equivalent fractions

Jamie has 6 apples.

Kara has 8 apples.

How many apples do they have altogether?

Jamie has 6 apples.

Kara has 8 apples.

How many apples do they have altogether?

6 8

?

They have 14 apples altogether.

?

86

Sam scored 9 points in the basketball game.

Keisha scored 6 points. How many more

points did Sam score than Keisha?

Sam

Keisha

Sam scored 9 points in the basketball game.

Keisha scored 6 points. How many more points

did Sam score than Keisha?

Sam

Keisha

?6

99

?6

A refrigerator costs $1739. An oven is $850 cheaper

than the refrigerator. Mrs. Coles buys both the

refrigerator and the oven. How much does she pay?

Step 1:

How much for the oven?

Step 2:

How much altogether?

fridge

oven?

$1739

$850?

$1739 – $850 = $889

The oven cost $889

$1739 + $889 = $2628

Mrs. Coles paid $2628 for the

oven and refrigerator.

3A Two-Step

Word Problems

Multiplication and

Division

Bar Modeling – What’s Next?

Grade 4

Two step word problems for four operations

Two step word problems involving fractions

and decimals

Grade 5

Multi-step word problems for four operations

Multi-step word problems with average rate,

ratio and percentage

Questions?

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