2. Why Bar Models?
- Makes an abstract word problem or equation pictorial. (Concrete → Pictorial → Abstract)
- Allows for deeper analysis and understanding of the problem by teaching students to:
Identify all information given and its relationship to other pieces of information
Identify missing information that needs to be found
Understand what mathematical operation needs to take place
- Bar modeling is a very versatile strategy!  It can be used for problems involving:
Addition, subtraction, multiplication, division, fractions, decimals, percentages, ratios
- Bar modeling trains students to think algebraically.
“develops students’ visual thinking capabilities and algebraic thinking and reinforces higher level thinking.”

3. 9 Steps to Model Drawing
1.  READ the entire problem.
2.  REPHRASE the question into a statement.
3.  WHO is involved in the problem?
4.  WHAT is involved in the problem?
5.  Draw BAR(s).
6.  Read each sentence ONE at a time.
7.  LABEL bar(s) and write a question mark for the unknown.
8.  Write an EQUATION and a NUMBER BOND.
9.  Write the answer in the blank to complete the statement.

4. Try a problem!
One number is 1/3 of another number. If the difference between the numbers is 26, find the two numbers.

5. ? 14 8 6 9 Steps to Model Drawing 1st Grade
Mike had 8 big blocks and 6 small blocks in a basket.  How many blocks are there in the basket? 14
There are ________ blocks in the basket.
8+6=14
9 Steps to Model Drawing
1.  READ the entire problem.
2.  REPHRASE the question into a statement.
3.  WHO is involved in the problem?
4.  WHAT is involved in the problem?
5.  Draw BAR(s).
6.  Read each sentence ONE at a time.
7.  LABEL bar(s) and write a question mark for the unknown.
8.  Write an EQUATION and a NUMBER BOND.
9.  Write the answer in the blank to complete the statement.
Mike’s
Blocks ? 8 6
Big
Small

6. 1st Grade
John has 15 marbles.  4 of them are outside the bag.  How many marbles are there in the bag? 11
There are ________ marbles in the bag.
15-4=11
9 Steps to Model Drawing
1.  READ the entire problem.
2.  REPHRASE the question into a statement.
3.  WHO is involved in the problem?
4.  WHAT is involved in the problem?
5.  Draw BAR(s).
6.  Read each sentence ONE at a time.
7.  LABEL bar(s) and write a question mark for the unknown.
8.  Write an EQUATION and a NUMBER BOND.
9.  Write the answer in the blank to complete the statement.
John’s
marbles 4 ? 15 in
out

7. 1st Grade
Mary has 11 storybooks.  She has 2 more storybooks than Sally.  How many storybooks does Sally have? 9
Sally has ________ storybooks. 11
11-2=9
9 Steps to Model Drawing
1.  READ the entire problem.
2.  REPHRASE the question into a statement.
3.  WHO is involved in the problem?
4.  WHAT is involved in the problem?
5.  Draw BAR(s).
6.  Read each sentence ONE at a time.
7.  LABEL bar(s) and write a question mark for the unknown.
8.  Write an EQUATION and a NUMBER BOND.
9.  Write the answer in the blank to complete the statement.
Mary’s storybooks ? 2
Sally’s storybooks ?

8. 3rd Grade
Pam has 4 times as much money as Kurt.  If Pam has $30 more than Kurt, how much money do they have in all?
They have ________ money in all.
$50
a) 1 unit, 30 ÷ 3=10
b) Pam+ Kurt,
= 50
9 Steps to Model Drawing
1.  READ the entire problem.
2.  REPHRASE the question into a statement.
3.  WHO is involved in the problem?
4.  WHAT is involved in the problem?
5.  Draw BAR(s).
6.  Read each sentence ONE at a time.
7.  LABEL bar(s) and write a question mark for the unknown.
8.  Write an EQUATION and a NUMBER BOND.
9.  Write the answer in the blank to complete the statement.
Pam’s
money 10 10 10 10 ?
$30
Kurt’s
money 10

9. 5th Grade
Peter has twice as many stickers as Joe. Joe has 20 less stickers than Emily. They have 300 stickers altogether. How many stickers does Peter have?
Peter has ________ stickers.
a) 300 – 20 = 280
b) 280 ÷ 4 = 70 (1 unit)
Peter’s
stickers ? 70 70
9 Steps to Model Drawing
1.  READ the entire problem.
2.  REPHRASE the question into a statement.
3.  WHO is involved in the problem?
4.  WHAT is involved in the problem?
5.  Draw BAR(s).
6.  Read each sentence ONE at a time.
7.  LABEL bar(s) and write a question mark for the unknown.
8.  Write an EQUATION and a NUMBER BOND.
9.  Write the answer in the blank to complete the statement.
C) Peter 70 x 2 = 140
Joe’s stickers
300 70
Emily’s
stickers 70 20

10. 5th Grade
There are 3 pieces of rope.  Rope A is 3 times as long as Rope B.  Rope C is 10.4 cm longer than Rope A.  The total length of all 3 ropes is cm.  How long is Rope C?
55.7
Rope C is ________cm long.
a) = 105.7
b) ÷ 7 = 15.1 (1 unit)
Rope A
15.1
15.1
15.1
c) Rope c =
(15.1x3) = 55.7
9 Steps to Model Drawing
1.  READ the entire problem.
2.  REPHRASE the question into a statement.
3.  WHO is involved in the problem?
4.  WHAT is involved in the problem?
5.  Draw BAR(s).
6.  Read each sentence ONE at a time.
7.  LABEL bar(s) and write a question mark for the unknown.
8.  Write an EQUATION and a NUMBER BOND.
9.  Write the answer in the blank to complete the statement.
116.1
Rope B
15.1 ?
Rope C
15.1
15.1
15.1
10.4

11. 5th Grade
Betsy made cupcakes for the class party.  1/3 of the cupcakes were chocolate.  2/5 of the remaining were vanilla and the remaining 12 cupcakes were strawberry.  How many cupcakes did Betsy make in all? 30
Betsy made ________cupcakes in all. 20
a) 12 ÷ 3 = 4
b) 5 x 4 = 20
Betsy’s
cupcakes ? 10 10 10
9 Steps to Model Drawing
1.  READ the entire problem.
2.  REPHRASE the question into a statement.
3.  WHO is involved in the problem?
4.  WHAT is involved in the problem?
5.  Draw BAR(s).
6.  Read each sentence ONE at a time.
7.  LABEL bar(s) and write a question mark for the unknown.
8.  Write an EQUATION and a NUMBER BOND.
9.  Write the answer in the blank to complete the statement.
c) 10 x 3 = 30 4
chocolate 4 4 4 4 4
Vanilla
Strawberry

12. 5th Grade
The ratio of Carla’s postcards to Juan’s postcards was 2:5.  If together they had a total of 35 postcards, how many more postcards did Juan have than Carla? 15
Juan had ________ more postcards than Carla.
a) 35 ÷ 7 = 5 (1 unit)
b) 5 x 3 = 15 ?
Carla’s
postcards 5 5
9 Steps to Model Drawing
1.  READ the entire problem.
2.  REPHRASE the question into a statement.
3.  WHO is involved in the problem?
4.  WHAT is involved in the problem?
5.  Draw BAR(s).
6.  Read each sentence ONE at a time.
7.  LABEL bar(s) and write a question mark for the unknown.
8.  Write an EQUATION and a NUMBER BOND.
9.  Write the answer in the blank to complete the statement. 35
Juan’s
postcards 5 5 5 5 5

13. One number is 1/3 of another number
One number is 1/3 of another number. If the difference between the numbers is 26, find the two numbers. 13
The two numbers are ________ and _________. 39
a) 26 ÷ 2 = 13 (1 unit)
Num. 1 = 13
Num . 2 (13x3 =39)
Number 1 13
9 Steps to Model Drawing
1.  READ the entire problem.
2.  REPHRASE the question into a statement.
3.  WHO is involved in the problem?
4.  WHAT is involved in the problem?
5.  Draw BAR(s).
6.  Read each sentence ONE at a time.
7.  LABEL bar(s) and write a question mark for the unknown.
8.  Write an EQUATION and a NUMBER BOND.
9.  Write the answer in the blank to complete the statement. 26
Number 2 13 13 13