heuristics

Stacking Models 1

Level 1

Heuristics & Key Concepts

Stacking models

Tips :

1)Question has 2 or more items. At least there are more than 1 copy of each item. Eg : 2 chairs and 3 tables

1) A table and 2 chairs cost $215. The table costs 3 times as much as a chair. Find the cost of the table.

table

chair $215

?

Stacking Models 1

chair

(Total) 5 units → $2151 unit → $215 ÷ 5 = $43(Table) 3 units → 3 X $43 = $129 Ans : $129

1) Rani paid $224 for 2 boxes of mangoes and 3 boxes of apples. A box of mangoes cost twice as much as a box of apples. Find the cost of each box of apples?

mangoes

apples $224?

Stacking Models 1

apples

(Total) 7 units → $2241 unit (apples) → $224 ÷ 7 = $32

Ans : $32

Practice 2

mangoes

apples

2) Edward paid $520 for 3 ties and 8 shirts. A tie cost 4 times as much as a shirt. Find the cost of each tie.

tie

shirt $520

?

Stacking Models 1

(Total) 20 units→ $5201 unit (shirt)→ $520 ÷ 20 = $264 units (shirt)→ $26 x 4 = $104 Ans : $104

Practice 2

tietie

shirtshirtshirtshirtshirtshirtshirt

3) Mr Teo bought a visualiser and 2 cameras for $7 500. The visualiser cost half as much as camera.Find the cost of each visualiser.

visualiser

camera $7 500

?

Stacking Models 1

camera

(Total) 5 units → $7 5001 unit (visualiser) → $7 500 ÷ 5 = $1 500

Ans : $1 500

Practice 2

4) Jane has enough money to buy either 6 markers or 12 pens. If she buys 8 pens, how many markers can she buy with the remaining money?

markers

pens

Stacking Models 1

4 pens 2 markers Ans : 2

Practice 2

Remaining money

5) Daniel could buy 8 apples and 5 peaches with $8.He could buy 16 such apples with the same amount of money. If he decided to buy peaches only, how many peaches could he buy with $100?

Stacking Models 1

16 apples $ 8 8 apples $ 4 (5 peaches) $4 5 peaches$100 100 x 5 = 125 Ans : 125 4

Practice 2

$ 8

$ 4 $ 4

Multiples & Comparison Models 1

Level 2


Tips :

1) Look for comparison terms such as‘more than’, ‘less than’, ‘shorter than’, ‘longer than’, ‘taller than’, ‘heavier than’, ‘lighter than’ etc.

2) Look for terms such as‘twice as much as’, 3 times as many as’ etc.

3) All the bars will be of different no. of units. But each unit is of the same size. Hence solving multiples model is easier than solving comparison model.

4) Start labelling first and then draw the bars in different lengths.


Harry has 2 times as much savings as Aaron. Mike has $3087 more than Aaron. They have a total savings of $13 259. How much savings does Mike have?


Harry

Aaron$13 259

?$3087Mike

4 units → $13 259 - $3087 = $10 1721 unit → $10 172 ÷ 4 = $2543Mike → $2543 + $3087 = $5630 Ans : $5630

1) Jason, William and Joyce share $120. William gets $16 more than Jason. Joyce gets twice as much money as William. How much money does William get?


Joyce

William $120?

Jason

$120 + $16 = $1364 units → $136 (total)1 unit → $136 ÷ 4 = $34 (William)

Ans : $34

Practice 4

$16

2) A hawker sold 1 090 cans of drinks in 3 days. He sold 110 more cans on Day 1 than on Day 2.On Day 3, he sold thrice as many cans as Day 1.How many cans of drinks did he sell on Day 1?


Day 3

Day 1 1 090 cans

?

Day 2

1 090 + 110 = 1 2005 units → 1 200 (total)1 unit → 1 200 ÷ 5 = 240 (Day 1) Ans : 240

Practice 4

110

3) Ann, Jane and Nelson have a total of 188 comic books. Ann has twice as many as comic books as Jane. Nelson has 24 fewer comic books than Jane. How many comic books does Nelson have?


Ann

Jane 188 books?Nelson

188 + 24 = 2124 units → 212 (total)1 unit → 212 ÷ 4 = 53 (Jane)53 – 24 = 29 (Nelson) Ans : 29

Practice 4

24


Gena

Jessie 72 dollsPrema72 - 7 = 655 units → 65 (total)1 unit → 65 ÷ 5 = 13 (Jessie)13 + 7 = 20 (Prema) Ans : 20

Practice 4

7

?

4) Three girls have a total of 72 dolls. Gena has 3 times as many dolls as Jessie. Prema has 7 more dolls than Jessie. How many dolls does Prema have?


Ian

Thomas 264 dollsJosh264 + 30 = 2947 units → 294 (total)1 unit → 294 ÷ 7 = 42 (Thomas)3 units → 42 x 3 = 126 (Ian) 126 – 30 = 96 Ans : 96

Practice 4

30?

5) Ian, Thomas and Josh have a total of 264 phone cards. Ian has thrice as many phone cards as Thomas. Josh has 30 fewer phone cards than Ian. How many phone cards does Josh have?

Before & after model – equal stage Tips :For Equal stage, normally we start drawing model from the equal stage. However, for internal transfer, we should start drawing from the ‘Before’.

Internal transferTips :In internal transfer, both quantities change in before and after scenarios, but the total is unchanged.

Before & after model – equal stage 1 (1 quantity unchanged)


Before & after model – equal stage Tips :

For Equal stage, always start drawing model from the equal stage, except for internal transfer where we should start drawing from the ‘Before’.

1 quantity unchangedTips :Identify the quantity that is unchanged.


1) Harry and Calvin had the same amount of money. Calvin spent $96. In the end, Harry had 4 times as much as Calvin. How much did Harry have?

Harry

Calvin

Note : Harry’s $ is unchanged.

4 units

1 unit

Spent $96

3 units

3 units → $961 unit → $96 ÷3 = $32(Harry) 4 units → 4 X $32 = $128 Ans : $128

= $?


2) Ben and Ken had the same amount of money. Ken spent $146. In the end, Ben had 3 times as much as Ken. How much did Ben have?

Ben

Ken

Note : Ben’s $ is unchanged.

3 units

1 unit

Spent $146

2 units

2 units → $1461 unit → $146 ÷ 2 = $73(Ben) 3 units → 3 X $73 = $219 Ans : $219

= $?


3) Rick and Stan had the same amount of money. Stan spent $308. In the end, Rick had 8 times as much as Stan. How much did Rick have?

Rick

Stan

Note : Rick’s $ is unchanged.

8 units

1 unit

Spent $308

7 units

7 units → $3081 unit → $308 ÷7 = $44(Rick) 8 units → 8 X $44 = $352 Ans : $352

= $?

Before & after model – equal stage 2 (internal transfer)

P4 Heuristics & Key Concepts

Before & after model – equal stage Tips :For Equal stage, normally we start drawing model from the equal stage. However, for internal transfer, we should start drawing from the ‘Before’.

Internal transferTips :In internal transfer, both quantities change in before and after scenarios, but the total is unchanged.


1) Jack and Rick had the same amount of money. After Jack gave $49 to Rick, Rick had 3 times as much as Jack. How much did Rick have in the end?

Internal transfer – total is unchanged

Internal transfer – Start drawing from ‘before’

$49

$49

$49 $49

1 unit

3 units

2 units2 units → $49 x 2 = $981 unit → $98 ÷ 2 = $49(Rick in the end) 3 units → 3 X $49 = $147 Ans : $147

J

R

J

R

1 unit


2) Vince and Stan had the same amount of money. After Vince gave $90 to Stan, Stan had 7 times as much as Vince. How much did Stan have in the end?

Internal transfer – total is unchanged

Internal transfer – Start drawing from ‘before’

$90

$90

$90 $90

1 unit

7 units

6 units6 units → $90 x 2 = $1801 unit → $180 ÷ 6 = $30(Stan in the end) 7 units → 7 X $30 = $210 Ans : $210

V

S

V

S

1 unit


3) Stan and Aaron had the same amount of money. After Stan gave $36 to Aaron, Aaron had 5 times as much as Stan. How much did Aaron have in the end?

Internal transfer – total is unchangedInternal transfer – Start drawing from ‘before’

$36

$36

$36 $36

1 unit

5 units

4 units4 units → $36 x 2 = $721 unit → $72 ÷ 4 = $18(Aaron in the end) 7 units → 5 X $18 = $90 Ans : $90

S

A

S

A

1 unit

heuristics

Documents

stacking models

unit apples

multiples comparison

thomas3 units

shirt4 units shirt

apples apples total

unit visualiser

total1 unit