Tape Diagrams
What is a tape diagram?
A tape diagram is a visual model (drawing) that can be used to represent
quantities and their relationship.
Why would I use a tape diagram?
Students are often taught to look for key words when solving a word problem in
math. However, the “key word” does not always tell you which operation to
use to solve the problem and results in an incorrect mathematical process. (see
example 1) Instead, students should think about how the numbers in the
problem relate to each other. By drawing a diagram, students can focus on the
relationship between the numbers in the problem and transform the words into
a correct numerical operation.
Example 1
John has 12 fewer pencils than Elizabeth. If John has 13 pencils, how many does
Elizabeth have?
Using the key word approach, a student would identify the word fewer. Fewer
often means to subtract. However, this problem calls for addition. A tape
diagram would help a student see that this is indeed an addition problem.
John
Elizabeth
13
12
?
Is it necessary to use tape diagrams for “easy” problems?
Yes, on simpler, one-step problems, students can build their confidence on
drawing and labeling tape diagrams to clarify the operation for the problem.
When they come to more complicated, multi-step problems, students will be
able to use a tape diagram to make sense of the problem. (see example 2)
Example 2
Mrs. Jones made 48 cupcakes. She sold
1
1
of them and gave 4 of the remainder to
4
her children. How many cupcakes did she have left?
A common mistake with this problem is to think that Mrs. Jones has
cupcakes remaining.
1
4
were sold and
1
4
1
2
of her
were given away. However, a tape
diagram can help to clarify the situation.
Step 1
Mrs. Jones’s cupcakes
12
12
12
12
2
2
2
2
1
4
of 48 = 12
Sold
Step 2
36 remaining cupcakes
1
9
children
9
9
9
4
of 36 =9
left
On what types of problems can I use a tape diagram?
Students can draw a diagram for every word problem that they need to solve.
Addition, subtraction, multiplication, division, comparisons, and ratios problems
can all be represented by a tape diagram. Also one-step and multi-step
problems can be represented with a tape diagram.
Where can I find more information about tape diagrams?
www.tinkingblocks.com good interactive site to practice using tape diagrams
https://www.engageny.org/sites/default/files/resource/attachments/04-introduction_to_tape_diagrams.pdf
sample problems focusing on ratios
http://commoncore.org/maps/math/video-gallery/solving-word-problems-with-tape-diagramsvideos
demonstrating tape diagrams