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Singapore Mathematics: Problem Solving by OJXgOy

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									        Singapore Mathematics:
             Problem Solving
       Linda King
 Singapore Math Coach
lking@windsor.k12.mo.us




                    By Linda King, Windsor C-1
    Singapore Math &
  Solving Word Problems

Singapore Math moves students through 3
  stages of learning:
   – Concrete
   – Pictorial
   – Abstract




                 By Linda King, Windsor C-1
     Singapore Math &
   Solving Word Problems

8-Step Model Drawing is a pictorial way to
  represent word problems. This method helps
  students to SEE the problem and can
  dramatically increase student understanding.
8-Step Model Drawing provides students with a
  framework that can be used to attack MOST
  word problems.




                    By Linda King, Windsor C-1
8 Steps for Model-Drawing

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 computation to the side or underneath.
8. Answer the question in a complete sentence.


                    By Linda King, Windsor C-1
Problem 1:


1. Adam read 8 books.
Haley read 6 books.
How many books did they read altogether?
(1st grade problem)




                      By Linda King, Windsor C-1
Step 1:
    Read the entire problem.


1. Adam read 8 books.
Haley read 6 books.
How many books did they read altogether?




                By Linda King, Windsor C-1
Step 2:
    Who is the problem about?


1. Adam read 8 books.
Haley read 6 books.
How many books did they read altogether?




                By Linda King, Windsor C-1
Step 2:
    Who is the problem about?

    1. Adam read 8 books.
    Haley read 6 books.
    How many books did they read
    altogether?

  Adam




                  By Linda King, Windsor C-1
Step 2:
    Who else is the problem about?



1. Adam read 8 books.
Haley read 6 books.
How many books did they read altogether?




                   By Linda King, Windsor C-1
Step 2:
    Who else is the problem about?

    1. Adam read 8 books.
    Haley read 6 books.
    How many books did they read altogether?

Adam



Haley




                  By Linda King, Windsor C-1
Step 3:
    What is the problem about?

    1. Adam read 8 books.
    Haley read 6 books.
    How many books did they read altogether?


Adam



Haley




                  By Linda King, Windsor C-1
Step 3: What is the problem about?

    1. Adam read 8 books.
    Haley read 6 books.
    How many books did they read altogether?

Adam’s
books

Haley’s
books




                  By Linda King, Windsor C-1
Step 4:
    Draw unit bars of equal length.

    Adam’s
    books

     Haley’s
     books




                 By Linda King, Windsor C-1
Step 4:
    Draw unit bars of equal length.

  Adam’s
  books

   Haley’s
   books




                 By Linda King, Windsor C-1
Step 5: Read each sentence, one at a time.

    Adam read 8 books.
   Adam’s
   books

   Haley’s
   books




                  By Linda King, Windsor C-1
Add the information to your drawing.

Adam read 8 books.


Adam’s
books

Haley’s
books




              By Linda King, Windsor C-1
Add the information to your drawing.

              Adam read 8 books.
Adam’s         1
          1         1       1       1       1   1   1
books

Haley’s                      At the beginning of
books                       1st grade, one unit bar
                               represents 1 unit.



                   By Linda King, Windsor C-1
Step 5:
    Read each sentence, one at a time.

    Haley read 6 books.
  Adam’s         1
             1        1       1       1       1   1   1
  books

   Haley’s
             1
   books




                     By Linda King, Windsor C-1
Add the information to your drawing.

              Haley read 6 books.
Adam’s         1
          1         1       1       1       1   1   1
books

Haley’s
          1
books




                   By Linda King, Windsor C-1
Add the information to your drawing.

              Haley read 6 books.
Adam’s         1
          1         1       1       1       1   1   1
books

Haley’s
          1    1    1       1       1       1
books




                   By Linda King, Windsor C-1
Step 5:
    Read each sentence, one at a time.

    How many books did they read
    altogether?
   Adam’s        1
             1        1       1       1       1   1   1
   books

   Haley’s
             1   1    1       1       1       1
   books




                     By Linda King, Windsor C-1
No new information. Move to step 6.



Adam’s        1
          1        1       1       1       1   1   1
books

Haley’s
          1   1    1       1       1       1
books




                  By Linda King, Windsor C-1
 Step 6:
 Put the question mark in place.

  How many books did they read
 altogether?
Adam’s        1
          1        1       1       1       1   1   1
books

Haley’s
          1   1    1       1       1       1
books




                  By Linda King, Windsor C-1
 Step 6:
 Put the question mark in your drawing.


Adam’s        1
          1        1       1       1       1   1   1
books


Haley’s   1   1    1       1       1       1           ?
books




                  By Linda King, Windsor C-1
 Before working computation, add
 information to the drawing as needed.


Adam’s        1
          1        1       1       1       1   1   1
books


Haley’s   1   1    1       1       1       1           ?
books




                  By Linda King, Windsor C-1
 Before working computation, add
 information to the drawing as needed.


Adam’s        1
          1        1       1       1       1   1   1   8
books

                                               6
Haley’s   1   1    1       1       1       1           ?
books




                  By Linda King, Windsor C-1
 Step 7:
 Work the computation.


Adam’s        1
          1        1       1       1       1   1   1   8
books

                                               6
Haley’s   1   1    1       1       1       1           ?
books




                  By Linda King, Windsor C-1
 Step 7:
 Work the computation.


Adam’s        1
                                                         8
          1          1       1       1       1   1   1
books


Haley’s   1   1      1       1       1       1   6           ?
books
                  8 + 6 = 14 or count the unit bars



                    By Linda King, Windsor C-1
 Place the answer next to the question
 mark in your drawing.


Adam’s        1
                                                         8
          1          1       1       1       1   1   1
books
                                                             14

Haley’s   1   1      1       1       1       1   6           ?
books
                  8 + 6 = 14



                    By Linda King, Windsor C-1
 Step 8:
 Answer in a complete sentence.


Adam’s          1
                                                              8
           1            1       1       1       1   1   1
books
                                                                  14

Haley’s    1    1       1       1       1       1   6             ?
books
          8 + 6 = 14                1st graders fill in the
                                     blank in a sentence.

                       By Linda King, Windsor C-1
      Step 8:
      Answer in a complete sentence.


    Adam’s        1
                                                           8
              1        1       1       1       1   1   1
    books
                                                               14

    Haley’s                                        6           ?
              1   1    1       1       1       1
    books
                  8 + 6 = 14
Adam and Haley read 14 books altogether.


                      By Linda King, Windsor C-1
Problem 2:

                                                   40¢ each
2. Sara bought 2 pears.
She paid _____¢ .
(1st grade problem)




                      By Linda King, Windsor C-1
Step 1:
    Read the entire problem.

                                               40¢ each
2. Sara bought 2 pears.
She paid _____¢ .




                  By Linda King, Windsor C-1
Step 2: Who is the problem about?

                                               40¢ each
2. Sara bought 2 pears.
She paid _____¢ .




                  By Linda King, Windsor C-1
Step 2: Who is the problem about?

                                               40¢ each
2. Sara bought 2 pears.
She paid _____¢ .

Sara




                  By Linda King, Windsor C-1
Step 3: What is the problem about?


                                               40¢ each
2. Sara bought 2 pears.
She paid _____¢ .




                  By Linda King, Windsor C-1
Step 3: What is the problem about?


2. Sara bought 2 pears.                        40¢ each
She paid _____¢ .

Sara’s
pears




                  By Linda King, Windsor C-1
Step 4: Draw unit bars of equal length.


2. Sara bought 2 pears.                        40¢ each
She paid _____¢ .


Sara’s
pears




                  By Linda King, Windsor C-1
Step 4: Draw unit bars of equal length.


2. Sara bought 2 pears.                        40¢ each
She paid _____¢ .


Sara’s
pears




                  By Linda King, Windsor C-1
Step 5:
    Read each sentence, one at a time.


2. Sara bought 2 pears.                        40¢ each
She paid _____¢ .


Sara’s
pears




                  By Linda King, Windsor C-1
Add the information to your drawing.


2. Sara bought 2 pears.
She paid _____¢ .                              40¢ each



Sara’s
pears




                  By Linda King, Windsor C-1
Add the information to your drawing.


2. Sara bought 2 pears.
She paid _____¢ .                              40¢ each



Sara’s
pears     1       1




                  By Linda King, Windsor C-1
Step 5:
    Read each sentence, one at a time.

2. Sara bought 2 pears.
She paid _____¢ .                              40¢ each


Sara’s
pears
          1      1




                  By Linda King, Windsor C-1
     Add new information to your
     drawing.

2. Sara bought 2 pears.
                                                 40¢ each
She paid _____¢ .


Sara’s
pears     1         1




                    By Linda King, Windsor C-1
No new information in this sentence.
2. Sara bought 2 pears.
                                                 40¢ each
She paid _____¢ .


Sara’s
pears     1         1




                    By Linda King, Windsor C-1
Is there any other information that I
     could add to the drawing?
2. Sara bought 2 pears.
She paid _____¢ .                              40¢ each


Sara’s
pears
          1       1




                  By Linda King, Windsor C-1
Add this information to your drawing.

2. Sara bought 2 pears.
She paid _____¢ .                              40¢ each


Sara’s
pears
          1       1




                  By Linda King, Windsor C-1
Add this information to your drawing.

2. Sara bought 2 pears.
She paid _____¢ .                              40¢ each


Sara’s   40¢
pears
          1       1




                  By Linda King, Windsor C-1
Step 6: Put the question mark in place.

2. Sara bought 2 pears.
She paid _____¢ .                              40¢ each


Sara’s   40¢
pears
          1       1




                  By Linda King, Windsor C-1
Step 6: Put the question mark in place.

2. Sara bought 2 pears.
She paid _____¢ .                              40¢ each


Sara’s   40¢
pears
          1       1          ?¢



                  By Linda King, Windsor C-1
Is there any more information that we
     could add to the drawing?

2. Sara bought 2 pears.
She paid _____¢ .                              40¢ each



         40¢
Sara’s
pears
          1       1         ?¢



                  By Linda King, Windsor C-1
Is there any more information that we
     could add to the drawing?

2. Sara bought 2 pears.
She paid _____¢ .                              40¢ each


Sara’s   40¢    (40¢)
pears
          1       1          ?¢



                  By Linda King, Windsor C-1
Step 7: Work computation.
2. Sara bought 2 pears.
   She paid _____¢ .


Sara’s   40¢     (40¢)
pears                       ?¢
          1        1




                   By Linda King, Windsor C-1
Step 7: Work computation.
2. Sara bought 2 pears.
   She paid _____¢ .


Sara’s   40¢     (40¢)
pears                       ?¢
          1        1

40 + 40 = 80




                   By Linda King, Windsor C-1
Place the answer in the drawing next to
     the question mark.
2. Sara bought 2 pears.
   She paid _____¢ .


Sara’s   40¢     (40¢)
pears                       ?¢
          1        1

40 + 40 = 80




                   By Linda King, Windsor C-1
Place the answer in the drawing next to
     the question mark.
2. Sara bought 2 pears.
   She paid _____¢ .


Sara’s   40¢     (40¢)
pears                       ?¢         80
          1        1

40 + 40 = 80




                   By Linda King, Windsor C-1
Step 8: Answer in a complete sentence.
2. Sara bought 2 pears.
   She paid _____¢ .


Sara’s   40¢     (40¢)
pears                       ?¢         80
          1        1

40 + 40 = 80




                   By Linda King, Windsor C-1
Step 8: Answer in a complete sentence.
2. Sara bought 2 pears.
   She paid _____¢ .


Sara’s   40¢     (40¢)
pears                       ?¢         80
          1        1

40 + 40 = 80
 She paid 80¢.


                   By Linda King, Windsor C-1
Problem 3:

                                                   70¢
3. Devi has 55¢. She wants to buy the pen.

She needs ________¢ more.
(1st grade problem)




                      By Linda King, Windsor C-1
Step 1: Read the entire problem.

                                                 70¢
3. Devi has 55¢. She wants to buy the pen.

She needs ________¢ more.




                    By Linda King, Windsor C-1
Step 2: Who is the problem about?

                                                 70¢
3. Devi has 55¢. She wants to buy the pen.

She needs ________¢ more.




                    By Linda King, Windsor C-1
Step 2: Who is the problem about?

                                                 70¢
3. Devi has 55¢. She wants to buy the pen.
She needs ________¢ more.

 Devi




                    By Linda King, Windsor C-1
Step 3: What is the problem about?

                                                 70¢
3. Devi has 55¢. She wants to buy the pen.
She needs ________¢ more.

 Devi




                    By Linda King, Windsor C-1
Step 3: What is the problem about?

                                                 70¢
3. Devi has 55¢. She wants to buy the pen.
She needs ________¢ more.

 Devi’s
 money




                    By Linda King, Windsor C-1
Step 4: Draw unit bars of equal length.

                                                 70¢
3. Devi has 55¢. She wants to buy the pen.
She needs ________¢ more.

Devi’s
money




                    By Linda King, Windsor C-1
Step 4: Draw unit bars of equal length.

                                                 70¢
3. Devi has 55¢. She wants to buy the pen.
She needs ________¢ more.

Devi’s
money




                    By Linda King, Windsor C-1
Step 5: Read each sentence, one at a time.

 3. Devi has 55¢. She wants to buy the pen.
 She needs ________¢ more.                        70¢




 Devi’s
 money




                     By Linda King, Windsor C-1
Add the information to the problem.

 3. Devi has 55¢. She wants to buy the pen.
 She needs ________¢ more.                        70¢




 Devi’s
 money




                     By Linda King, Windsor C-1
Add the information to the problem.

 3. Devi has 55¢. She wants to buy the pen.
 She needs ________¢ more.                        70¢




 Devi’s
               55¢
 money

              This unit bar represents Devi’s
              money. Transition at end of 1st
                   grade: one bar = 55¢.

                     By Linda King, Windsor C-1
Step 5: Read each sentence, one at a time.

 3. Devi has 55¢. She wants to buy the pen.
 She needs ________¢ more.                        70¢




 Devi’s
               55¢
 money




                     By Linda King, Windsor C-1
Add the information to the problem.

 3. Devi has 55¢. She wants to buy the pen.
 She needs ________¢ more.                        70¢




 Devi’s
               55¢
 money




                     By Linda King, Windsor C-1
There is no new information to add to the
    drawing in this sentence.

 3. Devi has 55¢. She wants to buy the pen.
 She needs ________¢ more.                        70¢




 Devi’s
               55¢
 money




                     By Linda King, Windsor C-1
Step 5: Read each sentence, one at a time.

 3. Devi has 55¢. She wants to buy the pen.
 She needs ________¢ more.                        70¢




 Devi’s
               55¢
 money




                     By Linda King, Windsor C-1
Add information to the problem.


 3. Devi has 55¢. She wants to buy the pen.
 She needs ________¢ more.                        70¢




 Devi’s
               55¢
 money




                     By Linda King, Windsor C-1
3. Devi has 55¢. She wants to buy the pen.
She needs ________¢ more.                        70¢




Devi’s
              55¢       more
money




                    By Linda King, Windsor C-1
    How much money does she need in all?
    Add the information to the problem.

3. Devi has 55¢. She wants to buy the pen.
She needs ________¢ more.                        70¢




Devi’s
              55¢       more
money




                    By Linda King, Windsor C-1
Add this information to your drawing.

 3. Devi has 55¢. She wants to buy the pen.
 She needs ________¢ more.                        70¢


                  70¢
 Devi’s
               55¢       more
 money




                     By Linda King, Windsor C-1
Step 6: Put the question mark in place.

 3. Devi has 55¢. She wants to buy the pen.
 She needs ________¢ more.                        70¢


                  70¢
 Devi’s
               55¢       more
 money




                     By Linda King, Windsor C-1
Step 6: Put the question mark in place.

 3. Devi has 55¢. She wants to buy the pen.
 She needs ________¢ more.                        70¢


                  70¢
 Devi’s
               55¢       more
 money

                             ?



                     By Linda King, Windsor C-1
Is there any other information that I could
     add to the drawing?

 3. Devi has 55¢. She wants to buy the pen.
 She needs ________¢ more.                        70¢


                  70¢
 Devi’s
               55¢       more
 money

                             ?



                     By Linda King, Windsor C-1
No other information.

 3. Devi has 55¢. She wants to buy the pen.
 She needs ________¢ more.                        70¢


                  70¢
 Devi’s
               55¢       more
 money

                             ?



                     By Linda King, Windsor C-1
Step 7: Computation.

 3. Devi has 55¢. She wants to buy the pen.
 She needs ________¢ more.                        70¢


                  70¢
 Devi’s
               55¢       more
 money

                             ?



                     By Linda King, Windsor C-1
Step 7: Computation.

 3. Devi has 55¢. She wants to buy the pen.
 She needs ________¢ more.

                  70¢
 Devi’s
               55¢       more                     70 – 55 = 15
 money

                             ?



                     By Linda King, Windsor C-1
Place the answer by the question mark.

 3. Devi has 55¢. She wants to buy the pen.
 She needs ________¢ more.

                  70¢
 Devi’s
               55¢       more                     70 – 55 = 15
 money

                             ?      15




                     By Linda King, Windsor C-1
Step 8: Answer in a complete sentence.

 3. Devi has 55¢. She wants to buy the pen.
 She needs ________¢ more.

                  70¢
 Devi’s
               55¢       more                     70 – 55 = 15
 money

                             ?        15




                     By Linda King, Windsor C-1
Step 8: Answer in a complete sentence.

 3. Devi has 55¢. She wants to buy the pen.
 She needs 15¢ more.

                  70¢
 Devi’s        55¢       more                     70 – 55 = 15
 money
                             ?        15




                     By Linda King, Windsor C-1
Problem 4:

4. There were 287 people in a hall.
52 of them were children.
How many adults were there?
(2nd grade problem)


      Begin with      Steps 1 through 4
       of the 8-Steps for Model-Drawing.


                       By Linda King, Windsor C-1
Problem 4:                       After Step 4.


4. There were 287 people in a hall.
52 of them were children.
How many adults were there?




people


          Now do Step 5, adding information,
               one sentence at a time.

                    By Linda King, Windsor C-1
Problem 4:          Step 5: After 1st sentence.


4. There were 287 people in a hall.
52 of them were children.
How many adults were there?

                   287

people




                    By Linda King, Windsor C-1
Problem 4:          Step 5: After 2nd sentence.


4. There were 287 people in a hall.
52 of them were children.
How many adults were there?

                    287
         children
people
            52


                     By Linda King, Windsor C-1
Problem 4:          Steps 5 & 6: Place the question
                    mark, using the information in
                         the third sentence.

4. There were 287 people in a hall.
52 of them were children.
How many adults were there?

                       287

people   children        (adults)?
           52

                        By Linda King, Windsor C-1
Problem 4:           Step 7: Computation.



4. There were 287 people in a hall.
52 of them were children.
How many adults were there?

                    287

people   children    (adults)?
           52

                    By Linda King, Windsor C-1
Problem 4:              Step 7: Completed.

4. There were 287 people in a hall.
52 of them were children.
How many adults were there?


                     287
people   children    (adults)?
           52                     235
                                                 287 – 52 = 235



                    By Linda King, Windsor C-1
Problem 4 completed:
4. There were 287 people in a hall.
52 of them were children.
How many adults were there?


                     287
people   children    (adults)?
           52                     235
                                                 287 – 52 = 235

         There were 235 adults.

                    By Linda King, Windsor C-1
Problem 5:

5. Tracy bought 6 bags of oranges.
There were 10 oranges in each bag.
How many oranges did she buy altogether?
(2nd grade problem)


       Try this one on your own using the
         8 Steps for Model Drawing.


                      By Linda King, Windsor C-1
   Problem 5 Drawing:
   5. Tracy bought 6 bags of oranges.
   There were 10 oranges in each bag.
   How many oranges did she buy altogether?

           1    2          3          4          5    6

Tracy’s   10   10        10         10           10   10
oranges
                                ?




                    By Linda King, Windsor C-1
      Problem 5 Solution:
      5. Tracy bought 6 bags of oranges.
      There were 10 oranges in each bag.
      How many oranges did she buy altogether?

               1      2          3          4          5    6

  Tracy’s     10    10         10         10           10   10
  oranges
                                      ?         60
6 x 10 = 60 or
10 + 10 + 10 + 10 + 10 + 10 = 60


                   Tracy bought 60 oranges.


                          By Linda King, Windsor C-1
Problem 6:

6. There are 304 girls in a school.
There are 46 fewer boys than girls.
a. How many boys are there in the school?
b. How many children are there in the school?
(2nd grade problem)


       Try this one on your own using the
          8 Steps for Model Drawing.
                      By Linda King, Windsor C-1
Problem 6 Drawing:
 6. There are 304 girls in a school.
 There are 46 fewer boys than girls.
 a.   How many boys are there in the school?
 b.   How many children are there in the school?

                     304
 girls

                                                      b)?
 boys          a)?                 fewer
                                    - 46




                         By Linda King, Windsor C-1
   Problem 6 Solution:
     6. There are 304 girls in a school.
     There are 46 fewer boys than girls.
     a.   How many boys are there in the school?
     b.   How many children are there in the school?

                          304
     girls

                                                          b)?   562
     boys          a)?    258          fewer
                                        - 46
 304 – 46 = 258
258 + 304 = 562          There are 258 boys in the school.
                         There are 562 children in the school.

                             By Linda King, Windsor C-1
Problem 7:

7. Melissa has 6 postcards.
Sally has 3 times as many postcards as Melissa.
How many more postcards does Sally have than
     Melissa?
(3rd grade problem)


Try this one on your own using the 8 Steps
   for Model Drawing.


                      By Linda King, Windsor C-1
 Problem 7 Drawing:
7. Melissa has 6 postcards.
Sally has 3 times as many postcards as Melissa.
How many more postcards does Sally have than Melissa?

 Melissa’s
              6
 postcards

             1x    2x        3x
 Sally’s
 postcards   (6)   (6)       (6)

                         ?


                     By Linda King, Windsor C-1
 Problem 7 Solution:
7. Melissa has 6 postcards.
Sally has 3 times as many postcards as Melissa.
How many more postcards does Sally have than Melissa?

 Melissa’s
                 6
 postcards
                                                     6 + 6 = 12
                1x    2x        3x
 Sally’s
 postcards      (6)   (6)       (6)

                            ?    12

             Sally has 12 more postcards than Melissa.

                        By Linda King, Windsor C-1
                      Problem 8
8. Brian has 6 goldfish.                     Work through
He has 5 times as many                          Step 5:
  guppies as goldfish.                        sentence 2.
STOP                                            THEN,
If he puts his guppies
   equally into 3 tanks, how
   many guppies are in each
   tank?
(3rd grade problem)




                         By Linda King, Windsor C-1
 Problem 8: Step 5, sentence 3
 8. Brian has 6 goldfish.
 He has 5 times as many guppies as goldfish.
 If he puts his guppies equally into 3 tanks, how many guppies
       are in each tank?


Brian’s
goldfish     6

            x1      x2      x3         x4         x5
Brian’s
guppies




                          By Linda King, Windsor C-1
 Problem 8: Step 5, sentence 3
  8. Brian has 6 goldfish.
  He has 5 times as many guppies as goldfish.
  If he puts his guppies equally into 3 tanks, how many guppies
        are in each tank?
                                           Pull down the bar.
Brian’s                               Too confusing to divide the
                6                           guppie bar again.
goldfish

Brian’s      x1      x2      x3         x4         x5
guppies




                           By Linda King, Windsor C-1
 Problem 8: Step 5, sentence 3
  8. Brian has 6 goldfish.
  He has 5 times as many guppies as goldfish.
  If he puts his guppies equally into 3 tanks, how many guppies
        are in each tank?
                                      NOW, divide the “pull-down”
Brian’s
                6                      bar into 3 parts and label.
goldfish

Brian’s      x1     x2      x3         x4         x5
guppies



             tank 1        tank 2           tank 3


                          By Linda King, Windsor C-1
 Problem 8: Step 5, sentence 3
 8. Brian has 6 goldfish.
 He has 5 times as many guppies as goldfish.
 If he puts his guppies equally into 3 tanks, how many guppies
       are in each tank?

Brian’s                                   Complete the problem.
             6
goldfish

Brian’s     x1      x2      x3         x4         x5
guppies



             tank 1        tank 2           tank 3


                          By Linda King, Windsor C-1
 Problem 8 Drawing:
 8. Brian has 6 goldfish.
 He has 5 times as many guppies as goldfish.
 If he puts his guppies equally into 3 tanks, how many guppies
       are in each tank?

Brian’s
             6
goldfish

Brian’s     x1      x2      x3         x4         x5
guppies     (6)     (6)     (6)        (6)        (6)   (30)

                                   (30)

            tank 1 ?       tank 2            tank 3


                          By Linda King, Windsor C-1
 Problem 8 Solution:
 8. Brian has 6 goldfish.
 He has 5 times as many guppies as goldfish.
 If he puts his guppies equally into 3 tanks, how many guppies
       are in each tank?

Brian’s
             6
goldfish

Brian’s     x1        x2      x3         x4         x5
guppies     (6)       (6)     (6)        (6)        (6)   (30)

                                     (30)
                                                            5 x 6 = 30
            tank 1 ?        tank 2             tank 3       30 ÷ 3 = 10
                 10
                        Brian has 10 guppies in each tank.
                            By Linda King, Windsor C-1
Problem 9:

9. The capacity of a bucket is 6 liters.
5 buckets of water are needed to fill up a tank.
What is the capacity of the tank?
(3rd grade problem)


Try this one on your own using the 8 Steps
   for Model Drawing.



                      By Linda King, Windsor C-1
Problem 9 Drawing:
9. The capacity of a bucket is 6 liters.
5 buckets of water are needed to fill up a tank.
What is the capacity of the tank?

           Bkt 1   Bkt 2   Bkt 3      Bkt 4        Bkt 5
 Tank’s
capacity     6     (6)      (6)        (6)         (6)

                             ?




                      By Linda King, Windsor C-1
Problem 9 Solution:
9. The capacity of a bucket is 6 liters.
5 buckets of water are needed to fill up a tank.
What is the capacity of the tank?

           Bkt 1    Bkt 2   Bkt 3      Bkt 4        Bkt 5
 Tank’s
capacity     6      (6)      (6)        (6)         (6)

                              ? 30
       5 x 6 = 30

            The capacity of the tank is 30 liters.


                       By Linda King, Windsor C-1
Contact Linda King: lking@windsor.k12.mo.us
          (636) 464 – 4400, extension 4399




                 By Linda King, Windsor C-1

								
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