Modeling Addition and Subtraction Problems

1. Using the Tape Diagram
Modeling in Mathematics
?

2. It is a visual representation of details and
actions in a problem.
It is a tool to help us think logically when
making computations.
7 3
x

3. • A tape diagram fosters number sense because bars are
proportional and have meaning
10
4 6
10
8 2

4. Let’s consider the this problem using the tape diagram.
Fred has 6 toys. Mary has 2 toys. How many toys do they have
altogether?
T
6 2
The tape diagram allows us to put parts together to
get the total number of toys and reinforces the
notion that Ted has more than Mary. It makes us
more thoughtful about where to put the numbers.

5. T
6 2
T is the same as 6+2
T=6+2
T=8
There are 8 toys altogether.
*Since the parts are the same size as the whole, it
reinforces that equal means ‘same as’.

6. Number Model:
_____________+_____________=_____________
_____________=_____________+_____________

8. Beginning Change End
Addition Part Add (join) a Part Total
Subtraction Total Subtract (separate) a
Part
Part

9. Number Model:
_____________+_____________=_____________

10. Start Change End
+ =

11. Total Amount Unknown Picture
The team had 8 runs. They scored 2 more. How many do they
have in all?
8+2=R
Amount Joined Unknown Picture
John has $2 in his piggy bank. He needs $10 to buy the new toy
he wants. How much more does he need to save to have enough
money?
2+D=10
Initial Amount Unknown Picture
Mary added 5 books to her library. Now she has 10 books in her
library. How many books did she start with?
B+5=10
R
8 2
10
2 D
10
B 5

12. Using the tape diagram to model
Subtraction
Number Model:
_____________-_____________=_____________

13. Start Change End
- =
There were 4 butterflies sitting on a branch. 2 flew away. How many were left?

14. Amount Remaining Unknown # Story
•Suzie had $10. She spent $8 on lunch. How much money does
she have left over?
•10-8=x
Amount Separated Unknown •John had to read 10 books over the summer. He only has 2 left
to read. How many books did he read?
•10-x=8
Initial Amount Unknown •Jim ate 5 cookies out of the box. He only has 5 left. How many
were in the box?
•X-5=5
10
8 x
10
x 8
x
5 5

15. Larger Smaller
Amount Amount
- =
Jim has 5 butterflies. Mary has 2. How many more butterflies
does Jim have than Mary?

16. Number Model:
5-2=3

17. Amount More (or Less) Unknown
c
Difference
# Story
•Ted has 10 crayons. Neil has 4 crayons.
•How many more crayons does Ted have than Neil?
•How many fewer crayons does Neil have than Ted?
•10-4=c
Smaller Amount Unknown
6
Difference
•Ted had 10 crayons. Neil has 6 less than Ted. How many
crayons does Neil have?
•10-6=c
Larger Part Unknown
5
Difference
•Ted Has 5 crayons. Neil has 5 more than Ted. How many
crayons does Neil have?
•5+5=c
10
4
10
c
c
5