Fluently Add Using Mental Math and Partial Sums

Introduction:  

Addition of a 2-Digit Number: 

We can add two 2-digit numbers in different ways as given below:

• One way: Add mentally by partial sums using blocks.
• Another way is to add partial sums using ‘mentally break apart as tens and ones.’

Add Mentally by Partial Sums Using Blocks: 

Let’s consider an example to understand the sum of 2-digit numbers by partial sum using place-value blocks.

Example 1:

Find 35 + 37.

Solution:

Step 1:

Represent 35 and 37 as place value blocks

Step 2:

Find the partial sum by adding tens and ones.

3 tens + 3 tens = 6 tens

5 ones + 7 ones = 12 ones

60 and 12 are partial sums.

Step 3:

Find the sum.

So, 35 + 37 = 72. 

Example 2:

Find 46 + 15.

Solution:

Step 1:

Represent 46 and 15 as place value blocks

Step 2:

Find the partial sum by adding tens and ones.

4 tens + 1 ten = 5 tens

6 ones + 5 ones = 11 ones

50 and 11 are partial sums.

Step 3:

Find the sum.

So, 46 + 15 = 61.

Add by Partial Sums Using Mentally Break Apart as Tens and Ones: 

Let’s consider another example to understand the sum of 2-digit numbers by mental math.

Example 3:

Find 53 + 18.

Solution:

Step 1:

Mentally break apart the numbers using tens and ones.

Step 2:

Find the partial sum by adding tens and ones.

50 + 10 = 60

3 + 8 = 11

60 and 11 are partial sums.

Step 3:

Find the sum.

So, 53 + 18 = 71. 

Example 4:

Find the sum of 23 and 71.

Solution:

Step 1:

Mentally break apart the numbers using tens and ones.

Step 2:

Find the partial sum by adding tens and ones.

20 + 70 = 90

3 + 1 = 4

90 and 4 are the partial sums.

Step 3:

Find the sum.

So, 23 + 71 = 94.

Model Question:

Question:

Henry has a collection of 18 stamps. Bruce has a collection of 26 stamps. How many stamps do they have in all? Write an addition problem by using partial sums.

Answer:

Number of stamps with Henry = 18

Number of stamps with Bruce = 26  

The total stamps they have in all = 18 + 26

Find the sum of 18 + 26.

Step 1:

Mentally break apart the numbers using tens and ones.

Step 2:

Find the partial sum by adding tens and ones.

10 + 20 = 30

8 + 6 = 14

30 and 14 are partial sums.

Step 3:

Find the sum.

18 + 26 = 44.

So, Henry and Bruce have a collection of 44 stamps in all. 

Activity:

Monica has 28 candies with her, and Simon has 16 candies with him. Help them to find how many candies do have in all. (Use partial sum. Add any way you choose)

Exercise:

Question 1:

Find the sum of 29 and 28 by partial sums using place value blocks.

Question 2:

Write the addition problem of 34 and 63. Use partial sum by using mental math.

Concept Summary

What We Have Learned:

• Add numbers by partial sums using mental math.
• Add numbers by partial sums using place value.
• Solve model questions related to addition.