Break Apart Numbers and Add Using Partial Sums

Introduction:

Break apart the addends to find the sum.

Break Apart Numbers:

Addition of a 2-digit number: 

Break apart the addends in different ways to find the sum.

Example 1:

Find 25 + 18.

Solution:

One way:

Break apart the second addend to make a 10.

Another way: 

Break apart the second addend into tens and ones.

Add 25 + 10 = 35.

Next, 35 + 5 = 40.

Then, 40 + 3 = 43.

So, 25 + 18 = 43.

Example 2:

Find 37 + 14.

Solution:

One way:

Break apart the second addend to make a 10.

So, 37 + 14 = 51.

Another way: 

Break apart the second addend into tens and ones.

Add 37 + 10 = 47.

Next, 47 + 3 = 50.

Then, 50 + 1 = 51.

So, 37 + 14 = 51.

Example 3:

Find 64 + 16.

Solution:

One way:

Break apart the second addend to make a 10.

So, 64 + 16 = 80.

Another way: 

Break apart the second addend into tens and ones.

Add 64 + 10 = 74.

Then, 74 + 6 = 80.

So, 64 + 16 = 80.

Model Question:

Question:

Toby has 34 crayons. Paul has 58 crayons. How many crayons do they have in all? Solve the problem mentally. Show the steps of breaking apart numbers to add.

Answer:

Number of crayons with Toby = 34

Number of crayons with Paul = 58  

The total crayons they have in all = 34 + 58

Find 34 + 58.

One way:

Break apart the second addend to make a 10.

34 + 58 = 92.

So, they have 92 crayons in all.

Another way: 

Break apart the second addend into tens and ones.

Add 34 + 50 = 84.

Next, 84 + 6 = 90.

Then, 90 + 2 = 92.

34 + 58 = 92.

So, they have 92 crayons in all.

Activity: 

Break apart addends as tens and ones. Color the sheet as per the code.

Code:

80 + 9 = orange

60 + 7 = blue

40 + 8 = blue

70 + 5 = green

50 + 7 = green

30 + 6 = blue

Exercise

Question 1:

Find the sum of 24 and 48 using mental math.

Question 2:

Find the sum of 39 and 17 using mental math.

Question 3:

Find using mental math. Draw pictures of blocks if needed.

Question 4:

Kevin plants 27 trees. Ronald plants 44 trees. How many trees do they plant in all?

Question 5:

Oliver has 23 marbles. Jack has 28 marbles. How many marbles do they have in all?

Question 6:

19 students are playing football. 23 students are skating. How many students are there in all?

Question 7:

Add tens and ones to solve. One number makes both equations true. Find the missing number.

41 + ⎕ = 52

Question 8:

Add tens and ones to solve. One number makes both the equations true. Find the missing number.

31 + ⎕ = 44

⎕ + 44 = 57

Question 9:

Find 16 + 62.

Question 10: Find 33 + 29.

Concept Summary

What We Have Learned

• Understand how to break apart addends in different ways.
• Add numbers using mental math by breaking apart the addends.
• Solve model questions using place value strategies.