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Sep 24, 2022

### Key Concepts:

• Associative property
• Commutative property

## 8.2.1 Introduction to addition table:

The addition table chart for the numbers 1 to 10 can be represented as shown in the figure below.

### Pattern:

Number pattern is a pattern or sequence in a series of numbers. This pattern generally establishes a common relationship between all numbers. For example: 0, 5, 10, 15, 20, 25, …

Associative property:

20 + 24 = 20 + (2 +22)

= (20 + 2) + 22

20 + 24 = 22 + 22

Commutative property:

20 + 24 = (16 + 4) + (18 + 6)

22 + 22 = (18 + 4) + (16 + 6)

The alternating odd and even numbers in the rows and columns are captured in the following picture:

The reason for the alternating pattern is that each time we move  to the box on the right or one below, we are adding one more to our sum. For example,

(2 + 3) +1 = 2 + (3 + 1) = 2+4

### Commutative Property.

Add the diagonals to any box.

2 + 4 = 6

3 + 3 = 6

Are the sums of the diagonals always equal?
6 + 8 + 10 = 24
8 + 8 + 8 = 24
6 is 2 less than 8; 10 is 2 more than 8.

## Exercise:

1. Write addition table for 4.
2. Write addition table for 6.

4. Find the next numbers

5. What numbers are missing?
33, ____, 53, _____, 73, 83, 93, _____

6. Identify the numbers by which the following series of numbers are skipping the counting?
123, 125, 127, 129, 131, 133, 135, 137

7. Use a number line to evaluate each of the following

8. The following problem is an example of which property?
(3+1)+2=3+(1+2)

9. What number fills in the blank?

i) 5 + ____ = 8 + 5

ii) 8 + 4  = ______ + 8

i) 79 + 1 = ______

ii) 173 + ______ = 174

iii) ______ + 1 = 1460

### What we have learned:

• Associative property
• Commutative property

## Concept Map:

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