lower primary heuristics model drawing

Lower PrimaryLower PrimaryModel Drawing Model Drawing

WorkshopWorkshopFor ParentsFor Parents

Endeavour Primary SchoolMathematics Department

Rationale for Model Rationale for Model DrawingDrawing

•Visual representation of details

•Helps children with problem solving

•Helps children logically think using visual models to determine their computations

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•Teaches mathematical language

•Provides foundation for algebraic understanding

•Empowers students to think systematically and master more difficult problems

Rationale for Model Rationale for Model DrawingDrawing

Endeavour Primary SchoolMathematics Department

•Makes multi-step and multi-concept problems easy to work

Rationale for Model Rationale for Model DrawingDrawing

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Model Drawing does Model Drawing does NOTNOT

• Work on every problem

• Specify ONE RIGHT model

• Specify ONE RIGHT operation

Endeavour Primary SchoolMathematics Department

Concrete-Pictorial-Abstract Approach

Concrete• Modeling each mathematical concept with concrete materials: base-ten blocks- Fraction bars- Geometric figures etc.

Pictorial• Transforming the concrete model into a pictorial (semiconcrete) level which involves:- Drawing pictures- Drawing models etc.

Abstract • Modeling the mathematics concept at a symbolic level using: - Numbers- Mathematical symbols etc.

Illustration of CPA

Concrete – Manipulative

s:

Base-Ten Blocks

Pictorial - Models:

100

30 ?

Abstract – Symbols:

100 – 30 = 70

1. Main Item• Read the problem.• Identify the main item.• Draw a unit bar for the main item.2. Details• Identify other key details.• Draw in other details with the unit bar as a

guide.

• Re-read the problem one sentence at a time adjusting the unit bars to match the story.

3. Strategy• Write the number sentence and the answer.

Model DrawingModel Drawing

Endeavour Primary SchoolMathematics Department

4 Types of Models4 Types of Models

1. Part-Whole Model

2. Comparison Model

3. Multiplication Model

4. Division ModelEndeavour Primary SchoolMathematics Department

Calvin spent $135 on a shirt and$75 on a blouse.

How much did he spend altogether?

Part-Whole ModelsPart-Whole Models

$135

shirt

$75

blouse

?

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$135

shirt

$75

blouse

?

Altogether $135 + $75= $210

Ans: He spent $210 altogether.

Endeavour Primary SchoolMathematics Department

Calvin earns $2000 every month. He pays $300 for food. He also spends $200 on his car, $500 on housing and saves the rest. How much does he save every month?

Part-Whole ModelsPart-Whole Models

$300 $200

car(c)

$500

food(f)

housing(h)

?

saving(s)

$2000

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$300 $200

car

$500

food housing

?

$2000

saving

Used $300 + $200 + $500= $1000

Ans: He saves $1000 every month.

Saving $2000 - $1000= $1000

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Aloysius collected 3426 stamps. He collected 841 fewer stamps than Ben. How many stamps did Ben collect?

Comparison ModelsComparison Models

3426A

841

fewer

?

fewer

B

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Who has

more?

Whose bar is

longer?

3426A

B 841

fewer

?

Ben 3426 + 841= 4267

Ans: Ben collected 4267 stamps.

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Same quantity so same length

Peter had 789 cards. He had 58 more cards than Sam. How many cards did they collect altogether?

Comparison ModelsComparison Models

789P

S 58 fewer?

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Who has

more?

Whose is

longer?

789P

S 58 fewer?

Sam 789 – 58= 731

Ans: They collected 1520 cards altogether.

Altogether 789 + 731= 1520

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“More” does not always

mean add

Carl has $90. David has twice as much money as Carl. How much money does David have?

Comparison ModelsComparison Models

$90C

D $90 $90

?Endeavour Primary SchoolMathematics Department

Same quantity so same length

$90C

D $90 $90

?

David 2 x $90= $180

Ans: David has $180.

Endeavour Primary SchoolMathematics Department

Ali ran 170m. Ben ran twice as far as Ali. Claire ran 20m more than Ben.How far did Claire run?

Combined ModelsCombined Models

170mA

B

?

C

20m

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170m 170m

Ben 2 x 170m= 340m

Ans: Claire ran 360m.

Claire 340m + 20m= 360m

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170mA

B

C

20m170m 170m

?

Cindy gave 10 sweets to 5 friends.How many sweets did she give in all?

Multiplication ModelsMultiplication Models

10 10 10 10 10

?

10 10

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10 10 10 10 10

?

10 10

No. of sweets given 5 x 10

= 50

Ans: Cindy gave away 50 sweets.

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Same quantity so same

sized

Jody gave 5 sweets to 20 friends.How many sweets did she give in all?

Multiplication ModelsMultiplication Models

5 5 . . . . 5

?

1st 2nd 20th

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5 5 . . . . 5

?

1st1st 2nd 10th

No. of sweets given 10 x 5

= 50

Ans: Jody gave away 50 sweets.

Endeavour Primary SchoolMathematics Department

Wendy has 200kg of rice. She packs the rice into bags of 5kg.How many bags of rice does she have?

Division ModelsDivision Models

5kg5kg . . . . 5kg

1st 2nd ?th

?

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5kg 5kg . . . . 5kg

200kg

1st1st 2nd ?th

No. of bags 200kg ÷ 5kg= 40

Ans: She has 40 bags of rice.

Endeavour Primary SchoolMathematics Department

Part-Whole ModelsPart-Whole ModelsWhat to look out for?What to look out for?

1. Draw the bar with the 1. Draw the bar with the larger value longer.larger value longer.

2. Start drawing the curly 2. Start drawing the curly bracket at the start of bar.bracket at the start of bar. ((Enclose the number with Enclose the number with 2 lines to show where it 2 lines to show where it starts and ends.)starts and ends.)

Comparison ModelsComparison ModelsWhat to look out for?What to look out for?

1.1. Alignment and thickness ofAlignment and thickness of the bars.the bars.

2. Bars which have the same 2. Bars which have the same quantity must be of same quantity must be of same length.length.

Combined ModelsCombined ModelsWhat to look out for?What to look out for?

1.1. Bars must be relatively sized. Bars must be relatively sized.

Multiplication/Division ModelsMultiplication/Division ModelsWhat to look out for?What to look out for?

1.1. Bars must be relatively sized.Bars must be relatively sized.

2. Bars of equal quantity must be2. Bars of equal quantity must be of same size.of same size.

In General:In General:

1.1. Naming of bars must match Naming of bars must match

correctly.correctly.

2. Place a question mark on the2. Place a question mark on the

part of model where answer part of model where answer

is.is.

Thank you for your attention.

The End.

Question and Answer Session

Endeavour Primary SchoolMathematics Department