The document summarizes key properties of addition: 1) The commutative property states that the order of addends does not change the sum, so a + b = b + a. 2) The associative property states that the grouping of addends does not change the sum, so (a + b) + c = a + (b + c). 3) Examples and exercises are provided to illustrate how to apply the commutative and associative properties when rewriting addition problems by changing the order or grouping of addends.

1. Chapter 1 - Lesson 4:
Properties of Addition

2. I am me!
You cannot change
My identity!
property/ˈprɑːpərti/: tính chất

3. 7 + 2 = 9
sum /sʌm/: tổng
attend /əˈtend/: số hạng

4. 3 + 4 + 2 = 3 + (4 + 2)
regroup/ˌriːˈɡruːp/
nhóm lại

5. a + 2
placeholder/ˈpleɪshoʊldər/: ẩn số

6. Car a Car b
Car aCar b
commute/kəˈmjuːt/(v): giao hoán
commutative /kəˈmjuːtətɪv/(a)
tính giao hoán

7. (3 + 4) + 2
parentheses/pəˈrenθəsɪs/:
dấu ngoặc đơn
remain /rɪˈmeɪn/:
số còn lại, phần còn lại

8. 1. The Commutative Property
a + b = b + a

9. 1. The Commutative Property
a + b = b + a
Rule: The order in which numbers are
added does not change the sum
Ex: 5 + 4 = 4 + 5 = 9

10. (a + b) + c = a + (b + c)
a c
b
a c
b
THEN THEN
associate/əˈsəʊsieɪt/(v): kết hợp
associative/əˈsoʊʃiətɪv/(a): có tính kết
hợp

11. a c
b
Here are three associates.
b calls a first He calls c last
If he called C first, then
called A, would it have
made a difference?
NO!

12. (a + b) + c = a + (b + c)
THEN THEN
2. The Associative Property
Rule: The way numbers are
grouped for adding does not change
the sum
Ex: (4 + 3) + 2 = 4 + (3 + 2)

13. 2. The Associative Property
Note: You do the addition in the
parentheses first.
(3 + 4) + 2 = 3 + (4 + 2)
7 + 2 = 3 + 6
9 = 9

14. Exercise A:
Write each addition problem a
different way using the commutative
property. Think of letters as
placeholders for numbers.
1. 2 + 5
2. 3 + 7
6. a + 6
7. y + 7

15. Exercise B:
Using the associative property,
regroup each problem. Think of
letters as numbers
1. (1 + 2) + 3
2. (6 + 3) + 10
3. (a + 7) + 10
4. (6 + y) + x

16. Exercise C:
Show that the sums remain equal
1. (5 + 2) + 3 = 5 + (2 + 3)
2. (6 + 10) + 15 = 6 + (10 + 15)

17. Exercise E:
Which property of addition is shown,
commutative or associative?
1. 5 + x = x + 5
2. (x + y) + z = x + (z + y)