1. Adding and
Subtracting to Solve
Problems
3.3 AB

2. Learning Goal
• You will be able to model addition and
subtraction using pictures, words, and numbers.
• You will be able to select addition or subtraction
and then solve problems involving whole
numbers.
Addition Subtraction
Pictures Words
Numbers Problems
Whole Numbers
Model
Using
Select
Solve

3. How Can You Model Addition?
• You can show addition in many ways. Some
ways are:
– pictures
– words
– number lines
– number sentences

4. Modeling Addition
• Let’s look at an addition problem and all the
ways you can model it.
• Kamal and his brother collect old keys. Kamal
has 8 keys. His brother has 5 keys. How many
keys do the boys have altogether?

5. Pictures
• Kamal and his brother collect old keys. Kamal
has 8 keys. His brother has 5 keys. How many
keys do the boys have altogether?

6. Words
• Kamal and his brother collect old keys. Kamal
has 8 keys. His brother has 5 keys. How many
keys do the boys have altogether?
• Here are a few way to record the addition in
this problem using words.
• _____ keys plus ____ keys equals _______
keys altogether.
• _____ plus _____ equals ______.
• The ____ of eight and nine is ______.

7. 8 9 10 11 12 13 15 16 17 18
Number Lines
• Kamal and his brother collect old keys. Kamal
has 8 keys. His brother has 5 keys. How many
keys do the boys have altogether?
• How would this look on a number line?
14

8. Number Sentences
• Kamal and his brother collect old keys. Kamal has 8
keys. His brother has 5 keys. How many keys do the
boys have altogether?
• How would you write this problem using a number
sentence?
• A number sentence, or equation, is formed with
numbers and mathematical symbols. It tells what
happens to the numbers and what the results are.
__ + __ = ___

9. Let’s do another one!
• Jenny walked 10 blocks to school. After
school she walked 12 blocks to her
grandmother’s house. Later she walked
9 blocks home. How many blocks did she walk in all?
• You can model this problem with pictures, words,
number lines, or a number sentence.
• What did you get? That’s right…she walked
____ blocks in all. ___ + ___ + ___ = ___

10. When Do You Use Addition?
• Use addition when you want to find the sum
of a group of numbers.
• The sum is the answer to an addition problem.
• Example: What is the sum of 12, 8, and 2?
• Answer: 12 + 8 + 2 = 22 The ____ is 22.

11. More About Addition
• Addition can also be used to find the total
number of objects in a group.
• You can two numbers if they have the same
labels, and you want a larger number.
• For example: Ted has 14 toy cars, and Anna
has 15 toy cars.
• How many toy cars do they have in all?
• Answer: ___ + ___ = ___
• They have 29 _________ in all.

12. Renaming or Regrouping
• In some addition problems you need to rename or
regroup numbers.
• When you add numbers and the sum is greater than
9, you need to rename.
• For example, 12 ones can be renamed as 1 ten and
2 ones.

13. Let’s practice adding some numbers!
• What is the sum of 476, 203, and 59?
• First, write the numbers in a column,
lining up the ones place.
• Lining up the numbers by their place
value is very important!

14. • Next, add the digits in
the ones place.
• 6 + 3 + 9 = 18
• Rename 18 ones as 1 ten
and 8 ones, and write
down the 8 in the ones
place and place one ten
above the tens place.

15. • Add the 1 to the other
digits in the tens place.
• 1 + 7 + 0 + 5 = 13
• Rename 13 tens as 1
hundred and 3 tens.
• Write down the 3 in the
tens place and place the 1
hundred in the hundreds
place.

16. • Add the 1 to the other
digits in the hundreds
place.
• 1 + 4 + 2 = 7
• Write down the 7 in the
hundreds place.
• The sum is 738.

17. You
Try
It!

18. How can you model subtraction?
• You can show subtraction in many ways. Some
ways include:
– pictures
– words
– number lines
– number sentences

19. Modeling with a Picture

20. What about on a number line?

21. You Try It!

22. When do you use subtraction?
• Use subtraction when you want to find the
difference between two values. The difference is
the answer to a subtraction problem.
• You subtract when your numbers have the same
label and you need a smaller number as your
answer.
• For example: Thomas has 18 markers. Claire has
21 markers. How many more markers does Claire
have than Thomas has?
• Answer: __ - __ = __ Claire has 3 more ______.

23. When else do you use subtraction?
• You also use subtraction when you want to
take away a part from a group.
• Example: There were 8 loaves of bread. At
lunch Paul used 3 loaves to make sandwiches.
How many loaves of bread were left?
• Answer: __ - __ = ___
• There were 5 ____________left.

24. Let’s Practice Subtracting!
• What is the
difference
between 81 and
57?
• First, line up the
numbers using the
ones place and
place the larger
number on top.
81
- 57

25. • Since, 7 is greater than 1 you can’t
just subtract.
• First you need to regroup
8 tens and 1 one to
7 tens and 11 ones.
• Subtract the numbers in the ones
place.
• 11 - 7 = 4
• Write down the 4 in the ones place.
81
- 57
7
4

26. • Now you can subtract the
numbers in the tens place.
• 7 - 5 = 2
• Write down the 2 in the tens
place.
• The difference is 24.
81
- 57
7
42

27. On Your Own!

28. On Your Own

29. On Your Own!

30. On Your Own!