Strip Diagrams
TEKS:
4.5A The student is expected to represent multi-step problems involving all
four operations with whole numbers using strip diagrams and equations with
a letter standing for the unknown quantity.
Note:
Strip Diagrams are a tool designed to help students solve math word
problems accurately and efficiently. Students model mathematical
relationships and identify known and unknown quantities. The model
provides students with an image that organizes information and simplifies
the problem solving process. By modeling the word problems, students
develop strong reasoning skills which will help them as they transition to
algebra. Students are familiar with solving multi-step word problems, now
they will use strip diagrams as a tool to solve these problems.
Example:
Alicia has $6 more than Bobby. If Bobby has $10, how much did they have
altogether?
The example below might be how one student solved the problem.
Student’s work Example:
Using strip diagrams to solve the
problem:
(filled in during discussion)
Step 1: 10 +6=16
Step 2: 10+16= 26
$6
Alicia
money:
Alicia and Bobby had $26 altogether
$10
?
Bobby’s
money:
$10
Solution: Alicia has $10+ $6=$16
And Bobby has $10 So altogether,
they have $26. Because
10+10+6=26
Modeling the problem helps the
student visualize the relationships
among the different quantities.
Strip Diagrams Broken Down Into Steps:
Step 1: Read the entire problem.
Alicia has $6 more than Bobby. If Bobby has $10, how much did they have
altogether?
Step 2: Decided who is in the problem. Alicia and Bobby
Step 3: Decide what is involved in the problem. Money
Step 4: Draw unit bars: here we are drawing unit bars of equal length for
each person to represent that they have the same amount of money.
Step 5: Read each sentence, 1 at a time to fill in the information.
Step 6: Put a ? in the place to show the information we need to find out.
(When students are comfortable with the question mark switch to use a
letter to represent the unknown)
Step 7: write an equation and work computation to the side.
Step 8: Answer in a complete sentence to check for
reasonableness.
Example
Carlie sold 32 raffle tickets for the school fundraiser. That’s 4 times as many
as many as Caroline sold. How many more raffle tickets did Carlie sell than
Caroline?
The example below might be how one student solved the problem.
Student’s work Example
Using strip diagrams
(filled in after discussion)
Step 1: Divide 32 by 4
32÷4=8
Step 2: Subtract 8 from 32.
32-8= 24
Carlie sold 24 more raffle tickets
than Caroline.
32 tickets
Carlie
Tickets:
Caroline
Tickets:
?
Solution:
4 blocks = 32 tickets
1 block =8 tickets
3 blocks = 8x3=? So the answer is
24. Carlie sold 24 more tickets than
Caroline.
Modeling the problem helps the
student visualize the relationships
among the different quantities.
Step by Step:
Step 1: Read the entire problem.
Carlie sold 32 raffle tickets for the school fundraiser. That’s 4 times as many
as many as Caroline sold. How many more raffle tickets did Carlie sell than
Caroline?
Step 2: Decided who is in the problem. Carlie and Caroline
Step 3: Decide what is involved in the problem. Raffle tickets
Step 4: Draw unit bars: here we are drawing unit bars of equal length for
each girl to remind us that are equal.
Step 5: Read each sentence 1 at a time to fill in the information.
Step 6: Put a ? in the place to show the information we need to find out.
(When students are comfortable with the question mark switch to use a
letter to represent the unknown)
Step 7: write an equation and work computation to the side.
Step 8: Answer in a complete sentence to check for reasonableness.
32 tickets
Each person started with 1 block.
Carlie has 4 blocks to show that she
Carlie tickets:
sold 4 times as much as Caroline.
Then draw a line over Carlie tickets
to show she sold 32 as stated in the
Caroline tickets:
word problem.
?
Solution:
4 blocks = 32 tickets
1 block =8 tickets
3 blocks = “?” (what we are trying
to figure out)
Since 1 block is = to 8 tickets
8 x 3 =? So ?=24
If students are ready use letter “t”
for tickets instead of “?”