All the solutions provided in McGraw Hill Math Grade 3 Answer Key PDF Chapter 2 Lesson 1 Addition Properties will give you a clear idea of the concepts.

In math, properties are rules you can use with numbers.

Math in My World

Example 1
Sid has 4 blue pens and 5 red pens. Mario has 5 blue pens and 4 red pens. How many pens does each boy have? Find 4 + 5. Then find 5 + 4.
4 + 5 = ____. Sid has ___ pens
5 + 4 = ____. Mario has ___ pens
This shows the Commutative Property of Addition. The order in which the numbers were added did not change the sum.
4 + 5 = 9. Sid has 9 pens
5 + 4 = 9. Mario has 9 pens
This shows the Commutative Property of Addition. The order in which the numbers were added did not change the sum.

Example 2
Anna practiced the piano for 3 hours on Friday. She did not practice at a!l on Saturday. How many hours did she practice altogether?
Find 3 + 0. Then find 0 + 3. This shows the Identity Property of Addition. The sum of any number and zero is the number.

Sometimes you may want to group numbers in a way that makes them easier to add in your head. This is mental math. 9 + 4 + 6 19 is a number sentence because it contains numbers, operations, and an equals sign.

Example 3
Matthew saw 9 sailboats, 4 rowboats, and 6 canoes on the lake. How many boats did he see altogether? Since 4 + 6 = 10, finding 4 + 6 is easier than finding 9 + 4.
The way in which the addends are grouped does not change the sum. This is the Associative Property of Addition.
(9 + 4) + 6 = 9 + (4 + 6) = 9 + 10 Associative Property of Addition
= 9 + 10 Add 4 + 6.
= 19 Add 9 and 10.
So, (9 + 4) + 6 = ____. There are ____ boats on the lake.
So, (9 + 4) + 6 = 19. There are 19 boats on the lake.

Talk Math
How can you use the Associative Property to add 7, 8, and 3? =7+8+3
Since 7+3 = 10, finding 7+3 is easier than finding 8+3
The way in which the addends are grouped does not change the sum. This is the Associative Property of Addition.
(7+3) + 8 =  10+ 8 Associative Property of Addition
= 18

Guided Practice

Find each sum. Draw a line to the correct addition property.  Explanation:
6+5=11
5+6=11
This shows the Commutative Property of Addition. The order in which the numbers were added did not change the sum.
(5+7)+3 = 5+(7+3) =5+10 =15
The way in which the addends are grouped does not change the sum. This is the Associative Property of Addition.
0+12=12
12+0=12
This shows the Identity Property of Addition. The sum of any number and zero is the number.

Independent Practice

Find each sum. Draw a line to the correct addition property.   Explanation:
8+2=10
2+8=10 and
9+2=11
2+9=11
This shows the Commutative Property of Addition. The order in which the numbers were added did not change the sum.
(2+5)+8 = 2+(5+8) =15 and
(4+6)+3 = 4+(6+3) =13
The way in which the addends are grouped does not change the sum. This is the Associative Property of Addition.
100+0=100
This shows the Identity Property of Addition. The sum of any number and zero is the number.

Algebra Use an addition property to complete.

Question 9.
6 + ___ = 6
Explanation:
6+0=6
This shows the Identity Property of Addition.
The sum of any number and zero is the number

Question 10.
(7 + 9) + ____ = (9 + 7) + 3
Explanation:
The way in which the addends are grouped does not change the sum. This is the Associative Property of Addition.
(7 + 9) + 3= (9 + 7) + 3 =19

Question 11.
9 + 2 = 2 + ____
Explanation:
9 + 2 = 2 + 9=11
This shows the Commutative Property of Addition. The order in which the numbers were added did not change the sum.

Question 12.
(8 + 3) + ___ = 8 + (3 + 2)
Explanation:
The way in which the addends are grouped does not change the sum. This is the Associative Property of Addition.
(8 + 3) + 2= 8 + (3 + 2) =13

Find each sum mentally.

Question 13.
(7 + 1) + 9 = ____
Explanation:
The way in which the addends are grouped does not change the sum. This is the Associative Property of Addition.
(7 + 1) + 9 = 7 + (1 + 9)=7+10=17

Question 14.
(7 + 5) + 5 = _____
Explanation:
The way in which the addends are grouped does not change the sum. This is the Associative Property of Addition.
(7 + 5) + 5 = 7 + (5 + 5)=7+10=17

Question 15.
Complete the number sentence for the figures below which shows the Associative Property of Addition.  Explanation:
The way in which the addends are grouped does not change the sum. This is the Associative Property of Addition.
(3 + 5) + 4 = 3 + (5 + 4)=3+9=12

Problem Solving

Write a number sentence and identify the property.

Question 16.
In three baseball games, the Tigers scored 7, 4, and 6 runs. How many runs did the Tigers score in all 3 games?
(____ + 4) + 7 = _____ (6+ 4) + 7 = 10 + 7 = 17
Explanation:
The way in which the addends are grouped does not change the sum. This is the Associative Property of Addition.
(6+ 4) + 7 = 10 + 7 = 17

Question 17.
Mathematical PRACTICE 4 Model Math Kelly collected 16 vacation brochures last summer. This summer she did not collect any brochures. How many brochures did she collect altogether?
Explanation:
16+0=16
This shows the Identity Property of Addition. The sum of any number and zero is the number

Question 18.
Mrs. Jackson bought 3 blue notebooks and 9 red notebooks. Mr. Mendez bought 9 blue notebooks and 3 red notebooks. How many notebooks did they each buy? Explanation:
3 +9 =9 + 3 = 12
This shows the Commutative Property of Addition. The order in which the numbers were added did not change the sum.

HOT Problems

Question 19.
Mathematical PRACTICE 2 Reason Can the Commutative Property be used for subtraction? Explain.
Explanation:
The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer.

Question 20.
? Building on the Essential Question How can addition properties help me add whole numbers?
we can add any two whole numbers that will also result in a whole number.
It doesn’t depends on the order.

### McGraw Hill My Math Grade 3 Chapter 2 Lesson 1 My Homework Answer Key

Practice

Draw lines to match each property of addition with its correct example. Explanation: Explanation:
This shows the Identity Property of Addition.
The sum of any number and zero is the number
The way in which the addends are grouped does not change the sum.
This is the Associative Property of Addition.
This shows the Commutative Property of Addition.
The order in which the numbers were added did not change the sum.

Find each sum mentally.

Question 4.
46 + 0 = ____
____ property
46 + 0 = 46
Identity property
Explanation:
This shows the Identity Property of Addition.
The sum of any number and zero is the number

Question 5.
(7 + 9) + 3 = ____ 7 + (9 + 3) = ____
____ property
(7 + 9) + 3 = 19, 7 + (9 + 3) = 19
Associative property
Explanation:
The way in which the addends are grouped does not change the sum.
This is the Associative Property of Addition.

Find each sum. Identify the addition property.

Question 6.
(6 + 8) + 2 = ____
(6 + 8) + 2 = 16
Associative property
Explanation:
The way in which the addends are grouped does not change the sum.
This is the Associative Property of Addition.

Question 7.
3 + (2 + 4) = ____
3 + (2 + 4) = 9
Explanation:
The way in which the addends are grouped does not change the sum.
This is the Associative Property of Addition.

Problem Solving

Question 8.
Mathematical PRACTICE 1 Make Sense of Problems Pedro and Jamal collected yellow and red leaves. They each collected the same total number of leaves. How many red leaves did Jamal collect? 9 leaves
Explanation:
9 + 5 = 14
14 – 5 = 9
So, Jamal collected 9 red leaves

Vocabulary Check

Draw a line to match the vocabulary word(s) to its example. Explanation: Explanation:
This shows the Identity Property of Addition.
The sum of any number and zero is the number
The way in which the addends are grouped does not change the sum.
This is the Associative Property of Addition.
This shows the Commutative Property of Addition.
The order in which the numbers were added did not change the sum.

Test Practice

Question 13.
Which number sentence is an example of the Associative Property?
A. 5 + 1 = 3 + 3
B. 583 + 0 = 583
C. (8 + 2) + 5 = 8 + (2 + 5)
D. 3 + 5 = 5 + 3