Math workshop slides

Mathematics Workshop for Parents:Model Drawing for P2 Pupils

17 February 20124 to 6 p.m.

part part

whole

B

A

difference

whole

part

ProgrammeProblem Solving With Model Drawing

Why model drawing?What are the models learned in P2?How do I draw a model?Classroom PracticeQ & A

Why Model Drawing?A problem-solving strategy that helps pupils

to better understand fraction, ratio and percentage laterto adopt a plan in solving maths problemsto know a less abstract than the algebraic methodto solve challenging problems

Source: Foong, P.Y. (2008). Problem Solving in Mathematics. Teaching Primary School Mathematics: A Resource Book (2nd ed.). (pp. 54-67). Singapore: McGraw Hill.

4 Steps in Problem Solving1. See (restate problem in own words)

• What is the problem asking you to do?• What are we trying to find out?

2. Plan (explore and select a strategy)• What do we know?• What do we need to know to solve the problem?• What strategies are useful?

3. Do (implement and solve)• Carry out the plan

4. Check (confirm whether answer is reasonable, extend)• Does it make sense?

adapted from Polya, G. (1971).How to solve it. (2nd ed.) Princeton, NJ: Princeton University Press.

R-CUB (Read, Circle, Underline, Box)

Read the question carefully.

Circle (numbers), Underline (key words) & Box (names, if any) the important information in short phrases or sentences.

Transfer information read to model drawing.

Put in ? to represent answer to be found.

What Are The Models Learned in P2?1. Part-whole model

(also known as ‘part-part-whole’ model)


part part

whole

B

A

difference

2. Comparison model

Part-whole Model


part part

wholePoints to noteThe greater the number, the longer its corresponding rectangle (bar).

Questions commonly asked include • looking for the missing part given the other part(s) and the whole• looking for the whole given the parts

Classroom Practice . . .

Part-whole ModelQ1. John has 14 pencils.

Peter has 17 pencils. How many pencils do they have altogether?

Part-whole Model

14 17

?14 + 17 = 31They have 31 pencils altogether.

114+ 17 -------- 31--------

Q1. John has 14 pencils. Peter has 17 pencils. How many pencils do they have altogether?

Part-whole ModelQ2. After using 215 beads to make a chain,

Mary had 116 beads left. How many beads did she have at first?

Part-whole ModelQ2. After using 215 beads to make a chain,

Mary had 116 beads left. How many beads did she have at first?

Part-whole Model

215 used 116 left

? at first215 + 116 = 331

She had 331 beads at first.

Q2. After using 215 beads to make a chain, Mary had 116 beads left. How many beads did she have at first?

1

2 1 5+ 1 1 6

3 3 1

Part-whole ModelQ3. There were 125 pupils in a school.

58 of the pupils were girls. How many boys were there?





125 pupils

125 – 58 = 67There were 67 boys.

0 11 1

1 2 5- 5 8

6 7

58 girls ? boys

Part-whole ModelQ4. There were 854 people at a fun fair.

There were 410 adults and 135 boys. How many girls were there?

Note: The differences of people, adults, men, women, children, boys and girls.





854 people

? girls410 adults

854 – 410 = 444444 – 135 = 309 There were 309 girls.

135 boys

410 + 135 = 545854 – 545 = 309OR

Comparison Model


Questions commonly asked include: • find one of the parts given the whole and the difference.• find the difference given the whole and one of the parts. • how many more or less?

B

A

difference

whole

part

Comparison ModelQ1. John has 14 pencils.

Peter has 17 more pencils than John. How many pencils does Peter have?


Peter has 17 more pencils than John. How many pencils does Peter have?

14 17 more

?14 + 17 = 31Peter has 31 pencils.

J

P

1

1 4+ 1 7

3 1


Peter has 8 fewer pencils than John. How many pencils does Peter have?





14

8 fewer?

14 – 8 = 6Peter has 6 pencils.

J

P

0 1

1 4- 8

6

Comparison ModelQ3. Ramu has 250 stamps.

He has 160 fewer stamps than Jay. How many stamps does Jay have?





250

?

250 + 160 = 410Jay has 410 stamps.

R

J

1

2 5 0+ 1 6 0

4 1 0

160 fewer

Comparison ModelQ4. Ben has 250 marbles.

He has 160 more marbles than Ahmad. How many marbles does Ahmad have?





250

?

250 – 160 = 90Ahmad has 90 marbles.

B

Am

160 more

1 1

2 5 0- 1 6 0

9 0

Comparison ModelQ5. Shirley has 250 crayons.

Wei En has 90 crayons. How many more crayons does Shirley

have than Wei En?

Comparison ModelQ5. Shirley has 250 crayons.

Wei En has 90 crayons. How many more crayons does Shirley

have than Wei En?

Comparison Model

250

90

250 – 90 = 160Shirley has 160 more crayons than Wei En.

S

W

? more

1 1

2 5 0- 9 0

1 6 0

Q5. Shirley has 250 crayons. Wei En has 90 crayons. How many more crayons does Shirley

have than Wei En?

Try these…

Comparison ModelQ1. Beatrice bought 36 candies and chocolates.

If she bought twice as many candies as chocolates, how many candies did she buy?





Candies

Chocolates36

?

3 units -> 361 unit -> 36 ÷ 3 = 122 units -> 12 x 2 = 24 She bought 24 candies.

Comparison ModelQ2. Baker Joe bakes 61 tarts and buns each day. He bakes 15 fewer tarts than buns. How many buns does Baker Joe bake each day?



Buns

Tarts61

15

?

61 – 15 = 4646 ÷ 2 = 23

Baker Joe bakes 38 buns each day.

23 + 15 = 38

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Math workshop slides