whole numbers addition & subtraction

Whole Numbers Addition & Subtraction

Marshall Cavendish Institute

Peggy Foo

Learning Outcomes

State the purpose of number bonds Use addition and subtraction strategies

Number Bonds

Number bonds are different combinations of numbers that make up a given number.

Different Types of Bonds

2 + 3 = 5

67 - 56 = 11

7 X 8 = 5680 ÷ 10 = 8

7 – 1 + 5 x 2 = 16

Purposes

Number bonds lay a strong foundation for learning addition and subtraction efficiently.

Number bonds also enhance mental computations

Activities for Lower Grades

Using the magnets and 10-frame How many bonds are there to make 10?

Use concrete manipulative Generate different possible ways/ bonds Move to pictorial stage

Extension

What are the different sums that you can get with different sets of whole numbers?

What can you observe? What can you observe about the number in the middle? What can you observe about the sums?

Open-ended task (with more than 1 sum) Generate different possible ways/ bonds Problem-solving task

Addition Strategies using Number Bonds Near-10 Strategy

1

2

3

1

23

The Doubles Strategy

1

2

3

1

23

Addition Strategies using Number Bonds

Near-100 Strategy

245 + 98

Addition Strategies using Number Bonds

Near-100 Strategy

245 + 98

Rewrite 98 as (100-2)

Add 245 + 100 = 345

We add more than we should

345 – 2 = 343

Debriefing

The ability to see numbers in different combinations is developing number sense/ number concept.

How many ways to find the value of

43 + 29

Additional Strategies using Number Bonds

Using Hundred Chart

43 + 29 = 43 + 30-1 (near-ten strategy)= 73-1= 72

43 + 29 = 60 + 12 (place value concept)= 72

Subtraction Strategies using Number Bonds Addition bonds for Subtraction

16 – 9

Subtraction Strategies using Number Bonds Addition bonds for Subtraction

16 – 9

16 is made up of (10 + 6)

Use 10 – 9 = 1

Add 1 to 6 (remaining number in the bond)

1 + 6 = 7

Subtraction Strategies using Number Bonds Near-100 Subtraction Strategy

256 - 97

Subtraction Strategies using Number Bonds Near-100 Subtraction Strategy

256 - 97

Rewrite 97 as (100 – 3)

256 – 100 = 156

Subtract more than we should

156 + 3 = 159

How many ways to find the value of 67- 49

Subtraction (renaming once)

67-49 = 67-50 +1 (near 10 strategy)

= 17+1

= 18

67-49 = 18 (place value concept)

Place Value Concept

To add and subtract using formal algorithms

Use place value concept to develop conceptual understanding

Use base ten

Summary

Concrete-Pictorial-Abstract Approach Aim to develop conceptual understanding

before procedural understanding (Richard Skemp)

Summary Mental Strategies

involving number bondsFormal Algorithm

Addition Strategies:

1) Near-10 Strategy

2) The doubles Strategy

3) Near-100 Strategy

Place value concept

Subtraction Strategies:

1) Addition Bonds for subtraction

2) Near-100 Subtraction Strategy