stack keenan

7/27/2019 Stack Keenan

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October 20

Mathematical Thinking

Barb Stack

Grade Six Math TeacherMoorhead Public Schools

Moorhead, MN

[email protected]

Cheryl KeenanGrade Six Math Teacher

(Retired)[email protected]

The Five Stages ofSingapore Bar Model Development

Concrete Pictorial Abstract


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October 20

Stage 1: Children Draw Objects

.more bear. How many bears does Sally have

now ?

4


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October 20

Stage 3. Dots Replace Objects

Arrows Appeare er p c e ree owers. y p c e wo

flowers. How many flowers did thechildren pick?

?

Jimm has 6 to cars. His brother ives him

Stage 4: Numbers Replace Dots

3 more cars. How many toy cars does

Jimmy have now?

?


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Juan has 36 baseball cards. Sue has 15

Stage 5: Numbers Move Outside

of the Bars and Bars are Labeled

baseball cards. How many more cards doesJuan have than Sue?

36

Sues15

?

Difficult Missing Start Problems

Allys sister, Lee, gave her 7 chocolate kisses. Now,.

Ally have before her sister gave her the 7?

12

7 ?


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Mias class sold 128 rolls of gift wrap.This is 21 more rolls than Makotos

Compare and Equalize Problems

.wrap did Makotos class sell?

Miasclass

128

Makotosclass ? 21

1. Jims Car1. Jims Car

Jim had $67 in hispoc e a er ebought a radiocontrolled car. Hewent to the storewith $142. How

67 ?

much did Jimspend on the car?

142 67 = ?67 + ? = 142

? + 67 = 142


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2. T2. T--ballball

A group of 8787

c ren a en aT-ball game.There are 32more adults at thegame than

C

A 32

children. What is

the totalattendance for the

T-ball game?

2(87) + 32

3. Shell Collecting3. Shell Collecting

Rosa has 336 R 336s e s. e eeps72 shells andshares theremaining shellsevenly between 6

72

F

friends. How manyshells does eachfriend receive?

336 72 = 264

264 6 = 44

Facilitates multi-step think ing


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October 20

4. Computer Purchase4. Computer Purchase

?

ara uys a pr n erfor $120. She buysa computer thatcosts 4 times asmuch as the

P ?$120

printer. What is the

cost of the entirepurchase?

c = 4 x p

c = 4 x $120 = 480c + p = 120 + 480 = $600

Reasoning with a Bar ModelTogether the gir ls spent $250.

.

did each gir l spend?

Jenny

250

Maria

5 unit s = $250

1 unit = $250 5 = $503 uni ts = 3 x $50 = $150

2 uni ts = 2 x $50 = $100

Jenny spent $150. Maria spent $100


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Your Turn

Work with someone at your table to try torepresent all 4 problems with the bar model, andthen solve.

Start with your focus problem first.

Remember that the bar model will NOT solve,

represent the problem and decide which solution

strategy will be most appropriate.

Be ready to share!

Buying Costumes

1. Melissa is buying two costumes. One costs. . .

will she get from $20?


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October 20

Trick or Treating

2. Robin trick or treated at 36 houses, which is12 less than Kathy but twice as many as

Sandy. How many houses did each girl visit?

Halloween Candy

3. Tommy has four times as many pieces ofcan y as y an a as many as m y.Together the three children have 676 pieces ofHalloween candy. How many more pieces ofcandy does Emily have than Billy?


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Spider Rings

4. There are 3 times as many orange spider

collection. If there are 3642 orange spiderrings, how many black spider rings arethere? How many spider rings are therealtogether?

Benefits to Bar ModelsBenefits to Bar Models Help focus students on comprehension of the

problems situation, rather than just finding numbersto crunch or just looking for an isolated key word orphrase.

Shows explicitly the problem structure along with theknown and unknown quantities

Visual tool to help students determine the operationneeded to solve


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Additional Resources

AVMR - Math Recovery


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Ten Principles of Thinking MathematicsAFT Educat ional Research and Dissemination Program 1993,2003

1.) Build from intuitive knowledge.

2.) Establish a strong number sense throughcounting, estimation, mental computation skills,and use of benchmarks.

3.) Base instruction on situational story problems.

4.) Use manipulatives and other representations torepresent problem situations; then link concreteto symbolic.

5.) Require students to describe and justify theirmathematical thinking.

6.) Accept multiple correct solutions and whenappropriate more than one answer.

7.) Balance conceptual and procedural learning.

8.) Use a variety of teaching strategies.

9.) Use ongoing assessment to guide instruction.

10.) Adjust the curriculum timeline.

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