Model Drawing for PDF

7/15/2019 Model Drawing for PDF

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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.

MCS Math Cadre12/09 - M. Bray


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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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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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PROBLEM SOLVING

RULE #3

If rule 2 yields three or morenumbers, the best bet is

adding them together.



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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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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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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.



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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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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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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.


Hogan, Bob and Char Forsten, 8-Step Model Drawing, Crystal Springs Books: 2007.


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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.




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Alicia had $6 more than Bobby. IfBobby had $10, how much did they

have altogether?




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The 8 Step Process


2. Decide who is involved in the problem.




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have altogether?

Alicia

Bobby




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The 8 Step Process



3. Decide what is involved in the problem.




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have altogether?

Alicia

Bobby

s money

s money




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The 8 Step Process



3. Decide what is involved in the problem.4. Draw unit bars of equal length.




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have altogether?

Alicia

Bobby

s money

s money




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The 8 Step Process




5. Read each sentence, one at a time.




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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





6. Put the question mark in place.

MCS Math Cadre



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have altogether?

Alicia

Bobby

s money

s money

$ 10

$ 10

$ 6

?

MCS Math Cadre



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The 8 Step Process





6. Put the question mark in place.7. Work the computation to the side or

underneath.MCS Math Cadre



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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



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The 8 Step Process1. Read the entire problem.


3. Decide what is involved in the problem.

4. Draw unit bars of equal length.


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



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have altogether?

Alicia and Bobby had $26 altogether.

MCS Math Cadre



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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



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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

MCS Math Cadre

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

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

18

18 18 18 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

18

18 18 18 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

18

18 18 18 18 18

= 18 lbs.

= 54 lbs.

= 108 lbs.?

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

18

18 18 18 18 18

= 18 lbs.

= 54 lbs.

= 108 lbs.

18 + 108 + 54 = 180

?

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

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

12/09 - M. Bray


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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

MCS Math Cadre

12/09 - M. Bray


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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.

MCS Math Cadre

12/09 - M. Bray


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18 + 108 + 54 = 180

A + B + C = ?

The total weight of tanks A, B, and Cis 180 lbs.

MCS Math Cadre

12/09 - M. Bray


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MCS Math Cadre

Model Drawing for PDF

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