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Strategies for Solving
Word Problems
MCS Math Cadre
12/09 - M. Bray
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In Your Table Group
Discuss
What are some problems your
students have with word problems? What are some ways you help your
students with solving word problems?
Record on the poster paper. Hang theposter on the wall.
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Gallery Walk
Have your group start at your poster.
When you hear the chime, walk to the nextposter (clockwise).
Discuss what is on the poster.
Listen for the chime. Then switch to thenext poster and discuss. Repeat for all
posters.Discuss any ah-has/similarities/new ideas
that you saw.
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STUDENTS MISGUIDE TO
PROBLEM SOLVING
RULE #1
If at all possible, avoid readingthe problem. Reading the
problem only consumes timeand causes confusion.
MCS Math Cadre12/09 - M. Bray By Lynn Nordstrom
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STUDENTS MISGUIDE TO
PROBLEM SOLVING
RULE #2
Extract the numbers from theproblem in the order they
appear. Be on the watch fornumbers written in words.
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STUDENTS MISGUIDE TO
PROBLEM SOLVING
RULE #3
If rule 2 yields three or morenumbers, the best bet is
adding them together.
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STUDENTS MISGUIDE TO
PROBLEM SOLVING
RULE #4
If there are only 2 numberswhich are approximately the
same size, then subtractionshould give the best results.
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STUDENTS MISGUIDE TO
PROBLEM SOLVINGRULE #5
If there are only two numbersand one is much smaller thanthe other, then divide if it goes
evenly.
.otherwise multiplyMCS Math Cadre12/09 - M. Bray By Lynn Nordstrom
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STUDENTS MISGUIDE TO
PROBLEM SOLVINGRULE #6
If the problem seems like it callsfor a formula, pick a formula
that has enough letters to useall the numbers given in theproblem.
MCS Math Cadre12/09 - M. Bray By Lynn Nordstrom
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RULE #7
If the rules 1-6 dont seem towork, make one last desperate
attempt.Take the set of numbers found byrule 2 and perform about twopages of random operationsusing these numbers.
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STUDENTS MISGUIDE TO
PROBLEM SOLVING
RULE #7You should circle about five or six
answers on each page just incase one of them happens to bethe answer.
You might get some partial creditfor trying hard.
By Lynn NordstromMCS Math Cadre12/09 - M. Bray
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MCS Math Cadre12/09 - M. Bray
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Operation Words
These words can be helpful for students todetermine what operation will be used in aproblem.
However, students still need to understandwhat the word problem means.
The operation words sometimes can bemistaken for the wrong operation.
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Long Beach Unified School District www.lbusd.k12.ca.usMCS Math Cadre12/09 - M. Bray
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Example
Toby buys two books at Tops
Bookstore. They cost $12.85
together. He pays with a $20 bill.How much change does Tobyreceive?
$12.85 + $20 = $32.85
$20 - $12.85 = $ 7.15
wrong operation
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Example
Robert wants to buy 3 notebooksthat cost $1.25 each. How much
do the notebooks cost all together,without tax?
3 + $1.25 = $4.25
3 x $1.25 = $3.75
wrong operation
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There are 3 fish tanks
labeled A, B, and C.B weighs 6 times as much
as A and twice as much asC. If C is 36 lbs. heavier
than A, find the totalweight of A, B, and C.
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Different Math StrategiesMake a List
Use Object/Act It Out
Make a Drawing/Use a Model
Make a Table
Make a Graph
Guess and Check/Experiment
Work BackwardUse a Pattern
Use LogicMCS Math Cadre12/09 - M. Bray
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Model Drawing
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8 Step Model Drawing
Based on the model drawing used by Singapore
Not the only method to solve word problems,but it can be used to solve most word problems
(about 80% of problems in math texts)
Model drawing helps generate other questionsthat can generate further learning based on the
same problem
Uses the concrete to pictorial to abstract stage.
MCS Math Cadre12/09 - M. Bray
Hogan, Bob and Char Forsten, 8-Step Model Drawing, Crystal Springs Books: 2007.
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MCS Math Cadre12/09 - M. Bray
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A picture (or a diagram)
is worth a
thousand words.
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The 8 Step Process
1. Read the entire problem.
MCS Math Cadre12/09 - M. Bray
Hogan, Bob and Char Forsten, 8-Step Model Drawing, Crystal Springs Books: 2007.
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Alicia had $6 more than Bobby. IfBobby had $10, how much did they
have altogether?
MCS Math Cadre12/09 - M. Bray
Hogan, Bob and Char Forsten, 8-Step Model Drawing, Crystal Springs Books: 2007.
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The 8 Step Process
1. Read the entire problem.
2. Decide who is involved in the problem.
MCS Math Cadre12/09 - M. Bray
Hogan, Bob and Char Forsten, 8-Step Model Drawing, Crystal Springs Books: 2007.
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Alicia had $6 more than Bobby. IfBobby had $10, how much did they
have altogether?
Alicia
Bobby
MCS Math Cadre12/09 - M. Bray
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The 8 Step Process
1. Read the entire problem.
2. Decide who is involved in the problem.
3. Decide what is involved in the problem.
MCS Math Cadre12/09 - M. Bray
Hogan, Bob and Char Forsten, 8-Step Model Drawing, Crystal Springs Books: 2007.
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Alicia had $6 more than Bobby. IfBobby had $10, how much did they
have altogether?
Alicia
Bobby
s money
s money
MCS Math Cadre12/09 - M. Bray
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The 8 Step Process
1. Read the entire problem.
2. Decide who is involved in the problem.
3. Decide what is involved in the problem.4. Draw unit bars of equal length.
MCS Math Cadre12/09 - M. Bray
Hogan, Bob and Char Forsten, 8-Step Model Drawing, Crystal Springs Books: 2007.
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Alicia had $6 more than Bobby. IfBobby had $10, how much did they
have altogether?
Alicia
Bobby
s money
s money
MCS Math Cadre12/09 - M. Bray
Hogan, Bob and Char Forsten, 8-Step Model Drawing, Crystal Springs Books: 2007.
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The 8 Step Process
1. Read the entire problem.
2. Decide who is involved in the problem.
3. Decide what is involved in the problem.4. Draw unit bars of equal length.
5. Read each sentence, one at a time.
MCS Math Cadre12/09 - M. Bray
Hogan, Bob and Char Forsten, 8-Step Model Drawing, Crystal Springs Books: 2007.
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Alicia had $6 more than Bobby. IfBobby had $10, how much did they
have altogether?
Alicia
Bobby
s money
s money
$ 10
$ 10
$ 6
MCS Math Cadre
12/09 - M. BrayHogan, Bob and Char Forsten, 8-Step Model Drawing, Crystal Springs Books: 2007.
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The 8 Step Process
1. Read the entire problem.
2. Decide who is involved in the problem.
3. Decide what is involved in the problem.4. Draw unit bars of equal length.
5. Read each sentence, one at a time.
6. Put the question mark in place.
MCS Math Cadre
12/09 - M. BrayHogan, Bob and Char Forsten, 8-Step Model Drawing, Crystal Springs Books: 2007.
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Alicia had $6 more than Bobby. IfBobby had $10, how much did they
have altogether?
Alicia
Bobby
s money
s money
$ 10
$ 10
$ 6
?
MCS Math Cadre
12/09 - M. BrayHogan, Bob and Char Forsten, 8-Step Model Drawing, Crystal Springs Books: 2007.
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The 8 Step Process
1. Read the entire problem.
2. Decide who is involved in the problem.
3. Decide what is involved in the problem.4. Draw unit bars of equal length.
5. Read each sentence, one at a time.
6. Put the question mark in place.7. Work the computation to the side or
underneath.MCS Math Cadre
12/09 - M. BrayHogan, Bob and Char Forsten, 8-Step Model Drawing, Crystal Springs Books: 2007.
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Alicia had $6 more than Bobby. IfBobby had $10, how much did they
have altogether?
Alicia
Bobby
s money
s money
$ 10
$ 10
$ 6
?$10 + $10 = $20
$20 + $6 = $26OR
$10 + $6 = $16
$16 + $10 = $26
MCS Math Cadre
12/09 - M. BrayHogan, Bob and Char Forsten, 8-Step Model Drawing, Crystal Springs Books: 2007.
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The 8 Step Process1. Read the entire problem.
2. Decide who is involved in the problem.
3. Decide what is involved in the problem.
4. Draw unit bars of equal length.
5. Read each sentence, one at a time.
6. Put the question mark in place.
7. Work the computation to the side or
underneath.8. Answer the question in a complete
sentence.MCS Math Cadre
12/09 - M. BrayHogan, Bob and Char Forsten, 8-Step Model Drawing, Crystal Springs Books: 2007.
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Alicia had $6 more than Bobby. IfBobby had $10, how much did they
have altogether?
Alicia and Bobby had $26 altogether.
MCS Math Cadre
12/09 - M. BrayHogan, Bob and Char Forsten, 8-Step Model Drawing, Crystal Springs Books: 2007.
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The 8 Step vs. 4 Step Process
Read the entire problem.
Decide who is involved in the problem. Decide what is involved in the problem.
Draw unit bars of equal length.
Read each sentence, one at a time.
Put the question mark in place.
Work the computation to the side orunderneath.
8. Answer the question in a complete sentence.
Read to
Understand
Plan
Solve
Check
MCS Math Cadre12/09 - M. Bray
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Nowits your turn
MCS Math Cadre
12/09 - M. Bray
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There are 3 fish tanks
labeled A, B, and C.B weighs 6 times as much
as A and twice as much asC. If C is 36 lbs. heavier
than A, find the totalweight of A, B, and C.
MCS Math Cadre
12/09 - M. Bray
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Fish Tank A
Fish Tank B
Fish Tank C
weight
weight
weight
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12/09 - M. Bray
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Fish Tank A
Fish Tank B
Fish Tank C
weight
weight
weight
B weighs 6 times as much as A
MCS Math Cadre
12/09 - M. Bray
B i h i h C
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Fish Tank A
Fish Tank B
Fish Tank C
weight
weight
weight
B weighstwice as much as C
MCS Math Cadre
12/09 - M. Bray
If C i 36 lb h i th A
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If C is 36 lbs. heavier than A
Fish Tank A
Fish Tank B
Fish Tank C
weight
weight
weight
36
18 18
MCS Math Cadre
12/09 - M. Bray
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Fish Tank A
Fish Tank B
Fish Tank C
weight
weight
weight
36
18 18
18
18
MCS Math Cadre
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Fish Tank A
Fish Tank B
Fish Tank C
weight
weight
weight
36
18 18
18
18
18
18 18 18 18 18
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Fish Tank A
Fish Tank B
Fish Tank C
weight
weight
weight
36
18 18
18
18
18
18 18 18 18 18 ?
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Fish Tank A
Fish Tank B
Fish Tank C
weight
weight
weight
36
18 18
18
18
18
18 18 18 18 18
= 18 lbs.
= 54 lbs.
= 108 lbs.?
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Fish Tank A
Fish Tank B
Fish Tank C
weight
weight
weight
36
18 18
18
18
18
18 18 18 18 18
= 18 lbs.
= 54 lbs.
= 108 lbs.
18 + 108 + 54 = 180
?
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Fish Tank A
Fish Tank B
Fish Tank C
weight
weight
weight
36
18 18
18
18
18
18 18 18 18 18
= 18 lbs.
= 54 lbs.
= 108 lbs.
18 + 108 + 54 = 180
The combined weight of fish tanks A, B, and C is 180 pounds.
?
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Solving Algebraically
B = 6A
B = 2C
6A = 2C
2 2
B weighs 6 times as much as A and twice as much as C
6A = 2C
3A = CMCS Math Cadre
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Solving Algebraically
3A = C
A + 36 = C
A + 36 = 3A
-A -A
36 = 2A
2 218 = A
If C is 36 lbs. heavier than A
(From previous slide)
A + 36 = 3A
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Solving Algebraically
C = A + 36
A = 18
B = 6 x 18B = 108
C = 18 + 36C = 54
B = 6A
Substitute the value of A into the original equations.
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Solving Algebraically
18 + 108 + 54 = 180
A + B + C = ?
The total weight of tanks A, B, and Cis 180 lbs.
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MCS Math Cadre