Solving Word
Problems using
TAPE DIAGRAMS
CMC South
October 25TH, 2014
Presented by
Tracey Dunn
traceyd@ers.tcoe.org
GOALS

Explore the visual representation of tape
diagrams as a tool to solve word
problems and support student learning.
Rate yourself from 1 to 5 on
how familiar you are with tape
diagrams and using them with
students?
WHAT IS A TAPE DIAGRAM?
CCSS Glossary:
•
Tape Diagram: A drawing that looks like a
segment of tape, used to illustrate number
relationships. Also known as a strip diagram, bar
model, fraction strip, or length model.
25
15
WORD PROBLEMS
•
Read the problem.
•
Write an answer sentence.
•
What are we trying to find? A total? A
part? Are we comparing?
•
Draw a sketch representing the problem.
•
Use your diagram to solve the problem.
•
Check the answer.
Commoncoretools.me
6
2.OA.1
Represent and solve problems involving addition
and subtraction
Use addition and subtraction within 100 to
solve one- and two- step word problems
involving situations of adding to, taking from,
putting together, taking apart, and comparing
with unknowns in all positions, e.g., by using
drawings and equations with a symbol for the
unknown number to represent the problem.
Addition and
Subtraction
Problem
Types
K-5 Progression
on
Counting and
Cardinality
and
Operations and
Algebraic Thinking
http://commoncoretools.files.wordpress.com/2011/05/ccss_progression_cc_oa_k5_2011_05_302
ADDITION AND SUBTRACTION PROBLEM TYPES
•
9 boys and 8 girls were in the class. How many
total children were in the class?
•
17 children were in the class. 9 were boys and
the rest were girls. How many girls were in the
class ?
•
17 children were in the class. There were some
boys and 8 girls. How many boys were in the
17
class?
9
Boys
8
Girls
COMPARISON:
ADDITION/SUBTRACTION
•Ali
had $9. Maria had $5. How many more
dollars did Ali have than Maria?
Ali
had $9. Maria had $5. How many fewer
dollars did Maria have than Ali?
Al
i
Maria
9
5
4
10
A Pencil and a Sticker
2.OA.1
A
pencil costs 59 cents,
and a sticker costs 20
cents less. How much do
a pencil and a sticker
cost together?
www.illustrativemathematics.org
Multiplication and Division
Problem Types
http://www.cde.ca.gov/be/st/ss/documents/ccssmathstandardaug2013.pdf
13
3.OA.3
Represent and solve problems involving
multiplication and division
 Use multiplication and division within 100 to
solve word problems in situations involving
equal groups, arrays, and measurement
quantities, e.g., by using drawings and
equations with a symbol for the unknown
number to represent the problem.
14
Gifts from Grandma
3.OA.3
 Juanita
spent $9 on each of her 6
grandchildren at the fair. How much
money did she spend?
 Nita bought some games for her
grandchildren for $8 each. If she spent a
total of $48, how many games did Nita
buy?
 Helen spent an equal amount of money
on each of her 7 grandchildren at the fair.
If she spent a total of $42, how much did
each grandchild get?
www.illustrativemathematics.org
15
Two Interpretations of
Division
 Maria
cuts 12 feet of ribbon into 3 equal
pieces so she can share it with her two sisters.
How long is each piece?
 Maria
has 12 feet of ribbon and wants to wrap
some gifts. Each gift needs 3 feet of ribbon.
How many gifts can she wrap using the
ribbon?
www.illustrativemathematics.org
16
4.OA.2
Use the four operations with whole numbers to
solve problems.
 Multiply or divide to solve word problems
involving multiplicative comparison, e.g., by
using drawings and equations with a symbol
for the unknown number to represent the
problem, distinguishing multiplicative
comparison from additive comparison.
17
Multiplication
Carla
has 4 packages of silly
bands. Each package has 8 silly
bands in it. Agustin is supposed
to get 15 fewer silly bands than
Carla. How many silly bands
should Agustin get?
http://commoncoretools.files.wordpress.com/2011/05/ccss_progression_cc_oa_k5_2011_05_302.p
df
18
Comparing Money Raised– 4.OA.2
a.
Helen raised $12 for the food bank last year and she raised
6 times as much money this year. How much money did
she raise this year?
www.illustrativemathematics.org
19
Comparing Money Raised– 4.OA.2
Sandra raised $15 for the PTA and Nita
raised $45. How many times as much
money did Nita raise as compared to
Sandra?
www.illustrativemathematics.org
20
Comparing Money Raised– 4.OA.2
a.
Sandra raised $15 for the PTA and Nita raised $45. How
many times as much money did Nita raise as compared to
Sandra?
www.illustrativemathematics.org
21
Comparing Money Raised– 4.OA.2
Luis raised $45 for the animal shelter,
which was 3 times as much money as
Anthony raised. How much money did
Anthony raised?
www.illustrativemathematics.org
22
Comparing Money Raised– 4.OA.2
Luis raised $45 for the animal shelter, which was 3 times as
much money as Anthony raised. How much money did
Anthony raised?
www.illustrativemathematics.org
23
Two-Step Problems
CC & OA
Progression
Page 28
http://commoncoretools.files.wordpress.com/2011/05/ccss_progression_cc_oa_k5_2011_05_302.p
df
24
Multiplicative Comparison
A
big penguin will eat 3 times as
much fish as a small penguin. The
big penguin will eat 420 grams of
fish. All together, how much will
the two penguins eat?
http://commoncoretools.files.wordpress.com/2011/05/ccss_progression_cc_oa_k5_2011_05_302.pdf
25
Multiplicative Comparison
CC & OA
Progression
Page 29
http://commoncoretools.files.wordpress.com/2011/05/ccss_progression_cc_oa_k5_2011_05_302.pdf
http://www.mathplayground.com/t
hinkingblocks.html
28
Multiplicative Comparison
Model

a.
b.
c.
d.
There are four groups of students in a hall. There
are twice as many boys as girls in each group.
In Group A, there are 12 girls. How many boys
are there in Group A?
In Group B, there are 12 boys. How many
students are there in Group B?
In Group C, there are 12 students. How many
girls are there in Group C?
In Group D, there are 12 more boys than girls.
How many students are there in group D?
PLANS
How
do you plan to use tape
diagrams with your students?
What
are your next steps with tape
diagrams?
Progressions
http://ime.math.arizona.edu/progressions/
www.illustrativemathematics.org
33
Resources
Common

Core Connect
http://commoncore.tcoe.org
Tracey
Dunn
traceyd@ers.tcoe.org
Strongly))
Disagree)
Questions
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Example
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