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

## McGraw-Hill My Math Grade 3 Answer Key Chapter 2 Lesson 2 Patterns in the Addition Table

Study the addition table for number patterns. Look for sets of numbers that follow a certain order.

**Math in My World**

Example 1

Danny colored a pattern of squares from left to right on the downward diagonal in yellow. Describe the pattern.

Even Numbers

Finish Danny’s pattern of even numbers. Color the squares.

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 There is a pattern of add 2.

When you add 2 to an even number, the sum is an even number.

Answer:

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 There is a pattern of add 2.

When you add 2 to an even number, the sum is an even number.

Odd Numbers

Start with the green square. Color the pattern of odd numbers on the downward diagonal in green. Write the numbers.

1, ___, __, ____, ____, ____, ___, ___, ___, ____

There is a pattern of add ___. When you add ____ to an odd number, the sum is an ___ number.

Answer:

1,3,5,7,9,11,13,15,17,19.

There is a pattern of add 2. When you add 2 to an odd number, the sum is an odd number.

Example 2

1. What pattern of numbers do you see in the diagonal of yellow boxes?

2. Look at the circled sum. Follow left and above to the circled addends.

3. Draw a triangle around the sum in the addition table that has the same addends. Follow left and above to its addends. Complete the number sentences.

Answer:

3 + 4 = 7

4 + 3 = 7

The two number sentences are an example of the Commutative property.

**Guided Practice**

**Describe Danny’s new pattern in the addition table below.**

Question 1.

When ____ is added to a number, the sum is that number.

Answer:

0

Explanation:

When 0 is added to a number, the sum is that number.

Question 2.

This is an example of the ____ Property of Addition.

Answer:

Identity

Explanation:

Identity property of addition states that if you add zero to a number, the sum is the same as the given number.

**Talk Math**

How do you find patterns in numbers?

**Independent Practice**

**Use the addition table.**

Question 3.

Shade a diagonal of numbers blue that show the sums equal to 8.

Answer:

Explanation:

diagonal of numbers blue that show the sums equal to 8 are

0 + 8 = 8, 1 + 7 = 8, 2 +6 = 8, 3 + 5 = 8, 4 + 4 = 8, 5 + 3 = 8, 6 + 2 = 8, 7 + 1 = 8, 8 + 0 = 8

Question 4.

Shade a diagonal of numbers green that show the sums equal to 5.

Answer:

Explanation:

The diagonal of numbers green that show the sums equal to 5 are

0 + 5 = 5, 1 + 4 = 5, 2 + 3 = 5, 3 + 2 =5, 4 + 1 = 5, 5 +0 = 5

Question 5.

Shade a row of numbers yellow that represent sums with one addend of 4.

Answer:

Explanation:

row of numbers yellow that represent sums with one addend of 4 are

4 +0 = 4, 4 + 1= 5, 4 + 2 = 6, 4 + 3 = 7 , 4 + 4 = 8, 4 + 5 = 9, 4 +6 = 10

Question 6.

Shade a column of numbers pink that represent sums with one addend of 6.

Answer:

Explanation:

a column of numbers pink that represent sums with one addend of 6 are

6 + 0= 6, 6 + 1 =7, 6 + 2= 8 , 6+ 3 = 9 ,6 + 4 = 10

Question 7.

Shade two squares purple that each represent the sum of 3 and 9. What property does this show?

Answer:

Explanation:

The sum of 3 and 9 is 12

3 + 9 = 12 , 9 + 3 = 12

This is commutative property of addition

Question 8.

Circle two squares that each represent a sum of 0 and 10. What two properties does this show?

Answer:

Explanation:

The sum of 10 and 0 = 10

10 + 0= 10 this is identity property

10 + 0 = 10 , 0 + 10 = 10 this is commutative property

Question 9.

Shade two addends red that have a sum of 8. Complete the number sentence. Write the greater addend first.

____ + ___ = 8

Answer:

Explanation:

two addends red that have a sum of 8 is 7 and 1

greater addend is 7

Use the Commutative Property of Addition and shade the other two addends red. Complete the other addition sentence.

____ + ____ = 8

Explanation:

The other two addends are 1 and 7.

1 + 7 = 8, 7 + 1 = 8 this shows commutative property of addition.

**Problem Solving**

**Use the addition table.**

Question 10.

**Mathematical PRACTICE 5 Use Math Tools** Mario stacked 8 boxes. She had no more boxes to stack. Find the total number of boxes stacked. Shade two squares that each represent the sum. Write two number sentences.

____________________

What two properties does this show?

____________________

____________________

Answer: 8

Two properties are Commutative and identity property of addition.

Explanation:

Mario stacked 8 boxes.

She had no more boxes to stack.

total number of boxes stacked are 8

8 +0 = 8 , Identity

8 + 0 = 8 , 0 + 8 = 8 , Commutative property

Question 11.

Pedro ran 3 miles on Sunday and 2 miles on Monday. Find the total number of miles he ran. Shade two squares that each represent the sum. Write two number sentences.

____________________

What property does this show?

____________________

Answer: 5

Commutative property

Explanation:

Pedro ran 3 miles on Sunday and 2 miles on Monday

the total number of miles he ran is 3 + 2 = 5 miles

3 + 2 = 5, 2 +3 = 5, Commutative

**HOT Problems**

Question 12.

**Mathematical PRACTICE 4 Model Math** Write a real-world problem for which you can use the addition table and the Commutative Property of Addition to solve. Then solve.

Answer:

In real-world it is important to solve faster. Commutative property and addition table can help us solve an operation faster.

Explanation:

The commutative property tells us that the result of an addition or multiplication is always the same, regardless of the order of the elements with which it operates.

The order of the addends does not change the result, no matter the order in which you put the addends, you will always get the same result.

Question 13.

**? Building on the Essential Question** How can addition patterns help me add mentally?

Answer:

Addition pattern help me to know what kind of number should result when finding the sum of two addends.

Explanation:

You can use place value to help add by increasing the digit in one place at a time.

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

**Practice**

**Use the addition table above.**

Question 1.

Shade a diagonal of odd numbers red.

Answer:

Explanation:

Odd numbers are 1,3,5,7,9,11,13,15,17,19

Question 2.

Shade a diagonal of even numbers yellow.

Answer:

Explanation:

Even numbers are 0,2,4,6,8,10,12,14,16,18,20

**Use the addition table**

Question 3.

Circle two squares that each represent a sum of 3 and 4. This shows the Commutative Property of Addition.

3 + 4 = ___ and 4 + 3 = ____

Answer: 7

Explanation:

3 + 4 = 7 and 4 + 3 = 7

Question 4.

Circle the two addends which make a sum of the shaded 12. Write the number sentence.

Answer:

Explanation:

The sum of 8 + 4 = 12

The two addends are 8 and 4

Question 5.

Shade a diagonal of numbers green that show the sums equal to 9.

Answer:

Explanation:

The sum of 1 + 3 + 5 = 9

Question 6.

Shade a row of numbers yellow that represents sums with one addend of 10.

Answer:

Explanation:

10 + 0 = 10 as 0 is the one which shows the sum = 10 with one addend of 10

It shows identity property

**Problem Solving**

Question 7.

**Mathematical PRACTICE 3 Justify Conclusions** Jasmine had 11 friends over at her house. Every time the doorbell rang, 2 more friends arrived. The doorbell rang 3 times. How many friends did Jasmine have over altogether?

Answer:

17

Explanation:

Jasmine had 11 friends over at her house

Every time the doorbell rang, 2 more friends arrived.

The doorbell rang 3 times.

so 2 + 2+ 2 = 6

sum of 11 and 6 = 17

Total number of friends did Jasmine have over altogether is 17

Question 8.

Steve colors the following sums on an addition table. If he continues the pattern, will the numbers continue to be even? Explain.

12, 14, 16, 18

Answer:

Yes

Explanation:

When you add 2 to an even number, the sum is an even number.

As the above pattern is an even number pattern it continues to be even.

**Test Practice**

Question 9.

Danielle is saving for a bicycle. Her last 4 bank deposits are shown in the table. If the pattern continues, how much will her next bank deposit be?

A. $2

B. $16

C. $17

D. $19

Answer:

C

Explanation:

If the pattern continues, her next bank deposit be $17

As the pattern follows addition of 2,

9+2 = 11 and 15 +2 = 17