Q&A - PSLE Math

[bookwormkids]

tianzhu:

bookwormkids:

2)
Catherine has a box containing some black and white counters. When she adds in 15 white counters, 65% of the counters in the box are black. If she adds in another 40 black counters, 75% of the counters in the box are black. How many white counters are there in the box at first?

Hi

Scenario 1

When she adds in 15 white counters, 65% of the counters in the box are black.

White:Black ------ 7:13

Scenario 2

If she adds in another 40 black counters, 75% of the counters in the box are black.

Make the units for white counters for both scenarios the same.

White:Black ------ 1:3 -----7:21

21 – 13 ----- 8

8 units ---- 40

1 unit ----- 5

7 units ----- 35

35 – 15 ----- 20 (white counters@first)

Best wishes

Hi Tianzhu, my son would like to know:

When 40 black counters are added, the number of white counters remain unchanged. So when 15 white counters are added,did the number of black counters remain the same?

Thanks for your time.

[bookwormkids]

MathIzzzFun:

bookwormkids:

Need help on the following questions.


1)
Log A and Log B are of different lengths. A carpenter wants to saw them into equal number of shorter pieces. The length of each piece from Log A need not be the same as that of each piece from Log B. If he saw Log A into 1.2m pieces and log B into 0.9m pieces, he has no leftover from log A but there will be 0.6m of log B left. If he saw Log A into 1.6m pieces and log B into 1.25m pieces, he has no leftover from log A but there will be 0.6m of log B left. Find the length of log A.


Thanks.

Original question discussed at pg 801


http://www.kiasuparents.com/kiasu/forum/viewtopic.php?f=69&t=280&p=844766#p844766


cheers.

Thank you MathIzzzFun and Tianzhu fpr your help.

[Beikiasu]

Hi, can someone help me to solve these problem sum?


1) A rectangular tank A, 180 cm by 60 cm by 80 cm, is 5/8 filled with water. When some water from tank A is pumped into another rectangular tank B, tank A is left with 15% of its water.
(a)How many litres of water is pumped into tank B? Ans:459 litres
(b)Given that tank B has a square base of sides 50 cm, what is the height of water in tank B? Ans:183.6 cm.SCG, 2011,SA1, Question 13, 4 mark.

2) Tina paid a total of $336 for 2 similar dresses and a skirt after a discount of 20% was given on the price of each item. If the original of each dress was 25% more than that of the original price the skirt, find the price of each dress before the discount. SCG, 2011, SA1, Question 12, 4 mark, Ans: $150.

3) Bemie and Ahmad shared the cost of a meal.Bemie paid $15. If Bermie paid $2 less, Ahmad would have had to pay 20% more. What was the cost of the meal? MGS, 2011, SA1, Question 3, 2 mark, Ans: $25.

Thanks

[tianzhu]

Beikiasu:

2) Tina paid a total of $336 for 2 similar dresses and a skirt after a discount of 20% was given on the price of each item. If the original of each dress was 25% more than that of the original price the skirt, find the price of each dress before the discount. SCG, 2011, SA1, Question 12, 4 mark, Ans: $150.

Hi

This question was discussed earlier in this thread.

This was my response.

You may use MD or work using units.

Original price of 2 similar dresses and a skirt ------- 420

1 dress ------ 5 units
1 skirt ------- 4 units

14 units ------- 420
1 unit ------- 30

Original price of dress ------- 5*30 -------150

Best wishes

[tianzhu]

Beikiasu:

3) Bemie and Ahmad shared the cost of a meal.Bemie paid $15. If Bermie paid $2 less, Ahmad would have had to pay 20% more. What was the cost of the meal? MGS, 2011, SA1, Question 3, 2 mark, Ans: $25.

Hi

Bernie ----- 15

If Bernie paid $2 less, Ahmad would have had to pay 20% more.

20% ----- 2

100% ------- 10

Cost of meal ----- 10+15 ----- 25

Actually, the numbers are pretty neat, students can easily arrive at the answer using GC.

Best answer.

[tianzhu]

bookwormkids:

Hi Tianzhu, my son would like to know:

When 40 black counters are added, the number of white counters remain unchanged. So when 15 white counters are added,did the number of black counters remain the same?

Thanks for your time.

Hi

I'll prepare the slide and give you the answer tomorrow.

Best wishes

[tianzhu]

Beikiasu:

Hi, can someone help me to solve these problem sum?

1) A rectangular tank A, 180 cm by 60 cm by 80 cm, is 5/8 filled with water. When some water from tank A is pumped into another rectangular tank B, tank A is left with 15% of its water.
(a)How many litres of water is pumped into tank B? Ans:459 litres
(b)Given that tank B has a square base of sides 50 cm, what is the height of water in tank B? Ans:183.6 cm.SCG, 2011,SA1, Question 13, 4 mark.

Hi

A rectangular tank A, 180 cm by 60 cm by 80 cm, is 5/8 filled with water.

5 units ----- 540 litres (180*80*60*5/8) (convert from cm3 to litres)

15% of 540 litres ------ 81 litres

Amount of water transferred to tank B ------ 540 – 81 ------ 459 litres

Height of water in tank B ------ 459000/50*50 ------ 183.6cm

Best wishes

[cimman]

bookwormkids:

tianzhu:

[quote=\"bookwormkids\"]
2)
Catherine has a box containing some black and white counters. When she adds in 15 white counters, 65% of the counters in the box are black. If she adds in another 40 black counters, 75% of the counters in the box are black. How many white counters are there in the box at first?

Hi Tianzhu, my son would like to know:

When 40 black counters are added, the number of white counters remain unchanged. So when 15 white counters are added,did the number of black counters remain the same?

Thanks for your time.

[/quote]this is a query on problem interpretation. In the context of Singapore Maths Problem sums (regardless of Maths topic), whenever something is not mentioned, it has a value of 0. eg. Tom and Mary each brought $10 to school. During recess time, Tom spent $5 on food and $2 on stationary. How much did Mary have in the end ?

Notice that the problem sum gave information on how much Tom spent but no information on how Mary spent her money. If nothing was mentioned about Mary, we must assume Mary spent nothing.
Of course, in the real world, if you boss never mentioned anything about your bonus for the year, we just say the bonus is unknown and not assume there's no bonus. The language of Maths problem sum does not reflect how we normally express ourselves. Because of this, we must learn how Maths problem sums are typically structured (from a language viewpoint) and what needs to be inferred.

This problem belongs to a category of problems I call \"Double If\" problems. The word \"when\" can be substituted for \"if\".
In most Double If questions, the 2 If scenarios are not linked, except at the initial conditions (Before values). ie. if something happened to the white counters in the first scenario, then in the second scenario, we start off with a clean slate, ie. assume nothing happened to the white counters. Nothing is carried over from the 1st If scenario to the 2nd If scenario.

This is an unusual question because it carried information from the 1st If scenario to the 2nd If scenario. The clue to this lies in the keyword \"another\", \"...adds in another 40 black counters\". If the word \"another\" is used, it means there is a precedent, or a prior condition. The next question to ask is, what does the precedent refers to ? It refers to conditions in the 1st If scenario.

Which leads to the next question: What are the conditions for the 1st If scenario ? - no information was given about any activities on the black counters, and 15 white counters were added. This means that we must assume that 0 Black counters were added or removed, and 15 white counters were added.

In the 2nd If scenario, because of the word \"another\", we must provide the initial condition of 0 change in Black counters and 15 white counters added. On top of this, we have to add in 40 black counters.
http://i49.tinypic.com/iwjdjo.png\">

Contrast this to how the problem is normally worded:
Catherine has a box containing some black and white counters. When she adds in 15 white counters, 65% of the counters in the box are black. If she adds in 40 black counters, 75% of the counters in the box are black. How many white counters are there in the box at first?

in this case, because there is no keyword \"another\", the 2nd scenario is decoupled from the 1st scenario. We start off the 2nd IF scenario with a clean slate. 40 Black counters are added, and no White counters are added or removed. Notice the zero values in the boxes. There is no prior condition.
http://i47.tinypic.com/jqtijt.png\">

I call this concept, the \"Zero Assumption\" concept - if nothing is mentioned, assume 0 Change value. Problem interpretation concepts are an important component in my workshops.

[Barley Tower]

A coin box contained only twenty-cent and fifty-cent coins in the ratio of 4:5. When 16 fifty-cent coins were taken out and replaced by some twenty-cent coins, the number of fifty-cent coins left in the box was 7/8 of the twenty-cent coins. The total value of all the coins remained the same. Find the sum of money in the coin box.


Hi nnchia, you might want to consider this method without using algebra which some children may find too abstract and may not understand.


16 50-cent coins = $ 8.00 which is 40 20-cents coins.\t\t
\t\t
Now:\t\t
Since the Ratio of 20 cents coins to 50-cents coins is 8:7\t\t

20-cents coins: \t8 Units + 40\t
50-cents coins: \t7 Units + 35 \t
\t\t
At First:\t\t
To work backward to the At-First situation, deduct 40 20-cents coins and add back 16 50-cents coints\t\t

20-cents coins: \t8 Units\t
50-cents coins: \t7 Units + 35 + 16\t
\t\t
We are also given that At First, the ratio of 20-cent coins to 50-cents coins is 4:5
\t\t
Hence, if there are 8 units of 20-cent coins, there must be 10 units of 50-cents coins.
\t\t
20-cents coins: \t8 Units\t
50-cents coins: \t10 Units\t
\t\t
Compare the 50-cents coins:

10 Units = 7 Units + 51\t\t
3 units = 51 coins\t\t
1 unit = 17 coins\t\t
\t\t
At first, there are 17 X 8 = 136 20-cents coins and 17 X 10 = 170 50-cents coins.
\t\t
Total value of the coins is $ 27.20 + $ 85.00 = $ 112.20.

[marstolive]

Hi MathIzzzFun,

Thanks for all the help!