Transcript Slide 1

Strategy 1: Guess and Check
Q1. Peter keeps some chickens and goats on his farm. There are altogether 16
heads and 44 legs of the animals. How many chickens and goats are there?
1st Guess: Use half of them as chicken and half of them goats
Heads Legs
8 chickens
8
8x2 = 16
8 goats
8
8x4 = 32
----------16
48 (X)
2nd Guess: Use more chickens and less goats as there are too many legs
Heads Legs
9 chickens
9
9x2 = 18
7 goats
7
7x4 = 28
---------------16
46 (X)
3rd Guess: Use more chickens and less goats again as there are still too many legs
Heads
Legs
10 chickens
10
10x2 = 20
6 goats
6
6x4 = 24
-------------16
44 (Correct)
Answer: There are 10 chickens and 6 goats.
Strategy 2 :Work From
Behind( Work Backwards)
Q2. Stacy and Huiyu had 400 stickers between them. Stacy gave 3/7 of her
stickers to Huiyu. Huiyu then gave 3/8 of her stickers to Stacy. After that, they
had an equal number of stickers. How many stickers did Stacy had at first?
Working out the question from backwards,
400 divided by 2 = 200 stickers
5 units -> 200 stickers (Huiyu)
1 unit -> 40 stickers
3 units -> 40 x 3 = 120 stickers
Therefore Huiyu gave 120 stickers to Stacy
200 - 120 = 80 stickers
4 units -> 80 stickers (Stacy)
1 unit -> 20 stickers
7 units -> 20 x 7 = 140 stickers
Answer: Stacy had 140 stickers at first. (Huiyu had 260 stickers at first)
Strategy 3 : Simplify the problem
Q3. A shopkeeper had a total of 120 blue and black bags in the ratio 3:5. After he
sold an equal number of each colour of bag, the ratio of blue to black bags was
3:8. How many bags did he sell altogether.
Total: 3 + 5 = 8 units
120 bags divided by 8 units = 15 bags
15 x 3 = 45 blue bags, 15 x 5 = 75 black bags
Difference in number of bags = 75 - 45 = 30 bags
After selling an equal number bags of each colour, the difference is the same at 30 bags.
8 - 3 = 5 units
There are 5 more units of black bags than blue bags
5 units -> 30 bags
1 unit -> 6 bags
11 units -> 66 bags (both blue and black)
120 - 66 = 54 bags
Answer: The shopkeeper sold 54 bags. (27 blue and 27 black bags)
Strategy 4: Trial & Error, Act it Out
Q4. John is given a large container filled with 2.4 litres of orange juice. He has 3
empty containers whose capacities are 1.3 litres, 1.1 litres and 0.5 litres. What
can John do to get 3 equal portions of 0.8 litres of orange juice each
Answer:
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Step 1. Pour 2.4 litres container of juice into 1.1 litres and 0.5 litres container
2.4 - 1.1 - 0.5 = 0.8 litres (in 2.4 litres container)
Step 2. Pour 0.5 litres container of juice completely into 1.3 litres container. Fill up 1.3 litres
container completely with juice from 1.1 litres container. There will be 0.3 litres of juice left in 1.1
litres container.
Step 3. Next, pour 1.3 litres container of juice into the empty 0.5 litres container.
1.3 - 0.5 = 0.8 litres (in 1.3 litres container)
2.4 - 0.8 - 0.8 = 0.8 litres. (in the other 2 containers)
Strategy 5: Draw A Model
Q5. Mrs Ang has some children. Each of her daughters has twice as many brothers
as sisters. Each of her sons has the same number of brothers as sisters. How
many daughters does Mrs Ang have ?
Answer: Mrs Ang has 3 daughters (and 4 sons)
Strategy 6: Make an organised list
Q6. When a number is divided by 3, the remainder is 1. When the same number is
divided by 5, the remainder is 3. What is the number if it is between 20 and 30?
Make a list which is a multiple of 3 and then add 1
3+1= 4, 6+1 = 7, 9+1 = 10....
=> 4, 7, 10, 13, 16, 19, 22, 25, 28, (stop at 30)
Make a list which is a multiple of 5 and then add 3
5+3= 8, 10+3 = 13, 15+3= 18....
=> 8, 13, 18, 23, 28 (stop at 30)
There are two answers, 13 and 28. But the number is between 20 and 30, therefore the
correct answer is 28.
Answer: The number is 28.
Strategy 7: Ratio Method
Q7. 3 children can carry 21 books. How many books can 8 children carry if each
child can carry the same number of books?
Using ratio method, put the unknown to be solved on the right hand side (RHS). Put the
known item on the left hand side (LHS).
LHS
RHS
3 children -> 21 books
8 children -> (21/3) x8 (RHS divided LHS x below LHS)
=7x8
= 56
The number of books that 8 children can carry is 56 books.
(Notice that this ratio method allows you to skip one step to find how many books one
child carries)
Answer: The number of books that 8 children can carry is 56 books.
Strategy 8: Total Amount (Quantity)
of Work Rule.
Q8. It takes 2 men 6 days to paint 3 houses. How long does it take 3 men to paint 6
houses?
Calculate the total amount of work the two men does = 2 x 6 = 12 mandays
Use the ratio method,
3 houses -> 12 mandays
6 houses -> 12/3 x 6 = 24 mandays
24 mandays divided by 3 men = 24/3 = 8 days.
It takes 8 days for 3 men to paint 6 houses.
(this is the concept of "more hands make the work lighter")
Answer: It takes 8 days for 3 men to paint 6 houses.
Strategy 9: Compare and Eliminate
method
Q9. 3 diamond rings and 2 gold rings cost $1900. A diamond ring and a gold ring
cost $700. How much does a gold ring cost?
(A) DR DR DR + GR GR = $1900
(B) DR + GR = $ 700
(C) DR + GR +
DR + GR
= $700 x 2 sets = $1400
compare (A) and (C), (A) has one more DR than (C)
1 DR = $1900 - $1400 = $500
Therefore 1 GR = $700- $500 = $200
Answer: A gold ring cost $200.
Strategy 10: Substitution method
Q10. A box with 50 rubber balls in it weighs 1150 g. Another identical box with 30
rubber balls weighs 750 g. Find the weight of each rubber ball.
1 Box + 50 rubber balls -> 1150 g
1 Box + 30 rubber balls -> 750 g
1 box + 30 balls + 20 balls -> 750 g + 20 rubber balls = 1150 g
20 rubber balls weighs 1150 -750 = 400 g
1 rubber ball weighs 400/ 20 = 20 g.
Each rubber ball weighs 20 g.
Answer: The weight of each rubber ball is 20g.
Strategy 11. Simplify the Problem
by finding a pattern.
Q11. Add up the even numbers from 2 to 100.
Write out the number sequence given in the question;
2 + 4 + 6 + ... + 96 + 98 + 100
Notice the pattern;
2 + 100 = 102
4+ 98 = 102
6 + 96 = 102 and so on...
There are 100/2 = 50 even number from 2 to 100.
There are 50/2 = 25 pairs of even numbers which adds up to 102.
102 x 25 = 2550.
Answer: The answer is 2550.
Strategy 12. Simplify the Problem
(Challenging).
Q12. There are 1000 lockers in a school with 1000 students. The first student
opens all the lockers. The second one closes lockers 2,4,6,8,10 till 1000. The
third one changes the state (close opened one and open closed one) of lockers
3,6,9,12,till 1000. The fourth one changes the state of lockers 4,8,12,16 till 1000.
How many lockers are opened at the end?
1st student open 1000 lockers
2nd student closed the even number lockers, so only odd number left open.
1, 3, 5, 7, ...999 => there are 500 odd number lockers left open
3rd student change state for:
3, 6, 9, 12, 15... 999 => multiples of 3 (total 333 numbers, 167 odd and 166 even numbers)
500 - 167 (odd) + 166 (even) = 499 lockers left open
4th student change the state for:
4, 8, 12, 16, 20... 1000 => multiple of 4 (total 250 numbers)
since 499 locker included some even number lockers which are multiple of 3 and 4 =>
these even number lockers are multiple of 12. (4x3=12)
12, 24, 36, ...996 => 83 multiples of 12.
250-83 = 167 (multiple of 4 but not multiple of 12)
499 + 167 - 83 = 583 lockers left open
Answer: There are 583 lockers left open in the end