Q&A - PSLE Math

[small]

speedmaths.com:

small:

This question was extracted from a Maths Heuristic Assessment of my son.

Hi Small,

What was the answer given to your son?

I interpreted the question differently, and got $8500 as her original savings in the bank.

Cheers


Speedmaths.com
.

Hi Speedmaths,

The teacher still have not go thru' with the class, btw I am quite interested in your interpretation on this question, mind to share how did you get $8500 as her original savings in the bank?

TIA..

[mathnoobs]

I'm at a loss on the interpretation here:

Nicole had saved a certain amount of money. In January, she spent 30% of her savings. In February, she managed to save 1/5 of the amount of money she had left. Then she purchased 8 pens at $3.95 each. When she heard heard her parents were going on a tour, she gave them 3/8 of the amount she had left. In March, she managed to save 40% of her savings left. Finally she had $6219.85 in the bank.

In Feb, she managed to save ...Then she purchase 8 pens...

The word \"Then\" came after the statement that she saved 1/5 in Feb. That would indicate that she purchased the 8 pens after Feb, therefore in the month of March. She also gave 3/8 to her parents.
The parent statement came directly after the pen statement, so this would indicate that both are on the same time frame, ie. March.

[speedmaths.012624com]

small:

Hi Speedmaths,

The teacher still have not go thru' with the class, btw I am quite interested in your interpretation on this question, mind to share how did you get $8500 as her original savings in the bank?

TIA..

Hi Small,

Would certainly be most happy to share.

Let the original savings be 100 units (or 100 u in short form)
(100 units would mean 100 boxes, for pupils thinking in terms of the bar models)

Jan:
She spent 30 u
She is left with 100 u - 30 u = 70 u

Feb:
She saved (another) 1/5 of 70 u = 14 u
She now have a new total of 70 u + 14 u = 84 u

She bought 8 pens for 8 x $3.95 = $31.60

She has (84 u - $31.60) left

She gave her parents 3/8 x (84 u - $31.60) = (31.5 u - $11.85)

She now have (84 u - $31.60) - (31.5 u - $11.85)
= (52.5 u - $19.75) left

March:
She save 40% of (52.5 u - $19.75) = (21 u - $7.90)

She now have a new total of
(52.5 u - $19.75) + (21 u - $7.90)
= (73.5 u - $27.65)

73.5 u - $27.65 = $6219.85
73.5 u = $6247.50
1 u = $6247.50 / 73.5 = $85

Original savings = 100 u = $8500

To check, you could start with $8500, and see if you end with $6219.85.

Hope this helps.

Cheers


Speedmaths.com


.

[small]

small:

Nicole had saved a certain amount of money. In January, she spent 30% of her savings. In February, she managed to save 1/5 of the money she had left. Then she purchased 8 pens at $3.95 each. When she heard that her parents were going for a tour, she gave them 3/8 of the amount she had left. In March, she managed to save 40% of her savings and eventually she had $6219.85 in her bank account.

Hi Speedmaths,

Thanks for sharing, I will need some time to digest this solution.

[tianzhu]

mathnoobs:

I'm at a loss on the interpretation here:

Nicole had saved a certain amount of money. In January, she spent 30% of her savings. In February, she managed to save 1/5 of the amount of money she had left. Then she purchased 8 pens at $3.95 each. When she heard heard her parents were going on a tour, she gave them 3/8 of the amount she had left. In March, she managed to save 40% of her savings left. Finally she had $6219.85 in the bank.

In Feb, she managed to save ...Then she purchase 8 pens...

The word \"Then\" came after the statement that she saved 1/5 in Feb. That would indicate that she purchased the 8 pens after Feb, therefore in the month of March. She also gave 3/8 to her parents.
The parent statement came directly after the pen statement, so this would indicate that both are on the same time frame, ie. March.

Hi mathnoobs

Speedmaths's answer of 8500 is correct.

To avoid confusion, I'll remove my original post.

The amount of money she saved later is from new sources, maybe from her salary, and added to the amount she had left in her bank account.

Best wishes

[mathnoobs]

tianzhu:

mathnoobs:

I'm at a loss on the interpretation here:

Nicole had saved a certain amount of money. In January, she spent 30% of her savings. In February, she managed to save 1/5 of the amount of money she had left. Then she purchased 8 pens at $3.95 each. When she heard heard her parents were going on a tour, she gave them 3/8 of the amount she had left. In March, she managed to save 40% of her savings left. Finally she had $6219.85 in the bank.

In Feb, she managed to save ...Then she purchase 8 pens...

The word \"Then\" came after the statement that she saved 1/5 in Feb. That would indicate that she purchased the 8 pens after Feb, therefore in the month of March. She also gave 3/8 to her parents.
The parent statement came directly after the pen statement, so this would indicate that both are on the same time frame, ie. March.

Hi mathnoobs

Speedmaths's answer of 8500 is correct.

To avoid confusion, I'll remove my original post.

The amount of money she saved later is from new sources, maybe from her salary, and added to the amount she had left in her bank account.

Best wishes

I'm afraid I still don't see how the money she spent on pens and the parents came to be under Feb expenses. I would have thought that it belonged to the March expenses, because of the keyword \"then\" , which the problem sum uses to describe the Pen's expenses. If I substitute the word \"after that\" for \"then\" in the problem sum, I would have interpreted the Pens expenses to come in March.

Maybe speedmaths can give his insights as well.
This is all so frustrating. I haven't gotten to solving the problem yet, still figuring out the interpretation of the problem.

[tianzhu]

mathnoobs:

I'm afraid I still don't see how the money she spent on pens and the parents came to be under Feb expenses. I would have thought that it belonged to the March expenses, because of the keyword \"then\" , which the problem sum uses to describe the Pen's expenses. If I substitute the word \"after that\" for \"then\" in the problem sum, I would have interpreted the Pens expenses to come in March.

Maybe speedmaths can give his insights as well.
This is all so frustrating. I haven't gotten to solving the problem yet, still figuring out the interpretation of the problem.

Hi

First, I must say I like your attitude in pursuing knowledge. You’re a very enthusiastic maths mummy.

But, please do not get frustrated; it’s not worth it at all. This minor issue can always be clarified.

Yes, you’re right to say that the expenses are incurred during the month of March. That’s a possible scenario.

Scenario1
Nicole saved an amount equivalent to 1/5 of her savings in her bank (70%) on 28 Feb.
Then she started to spend on the pens and parents’ tour expenses from 1 March.

Scenario 2
Nicole saved an amount equivalent to 1/5 of her savings in her bank (70%) on 25 Feb
Then she started to spend on the pens and parents’ tour expenses on 26 Feb.

But, it’s important to note that expenses whether incurred in Feb or March does not affect the calculations much. The key point is expenses are incurred after her savings in Feb.

To get the answer of 8500, the starting point is to see that Nicole had a certain amount of money in her bank account at first.

In Jan, she spent 30%, this means she had 70% of her initial amount remaining.

In Feb, she managed to save 1/5 of the remaining amount she had left. One may ask,” Where does this amount come from? A logical explanation is from her salary, perhaps.

The amount of money she saved (1/5) is then added to her remaining saving in her bank (70%).

Then she went go to purchase 8 pens and gave 3/8 (3 parts) of the amount left to her parents for their holidays.

She had 5 parts remaining. From here, she added another (40%) or 2 parts .This means she had 7 parts or 140% which is equal to 6219.85.

A neat way to do this problem is to breakdown the question into smaller successive sub problems and use “Work backwards”.

Draw out some pictorial representation and you’re on the way to the solution.

Best wishes

[small]

tianzhu:

Hi

First, I must say I like your attitude in pursuing knowledge. You’re a very enthusiastic maths mummy.

But, please do not get frustrated; it’s not worth it at all. This minor issue can always be clarified.

Yes, you’re right to say that the expenses are incurred during the month of March. That’s a possible scenario.

Scenario1
Nicole saved an amount equivalent to 1/5 of her savings in her bank (70%) on 28 Feb.
Then she started to spend on the pens and parents’ tour expenses from 1 March.

Scenario 2
Nicole saved an amount equivalent to 1/5 of her savings in her bank (70%) on 25 Feb
Then she started to spend on the pens and parents’ tour expenses on 26 Feb.

But, it’s important to note that expenses whether incurred in Feb or March does not affect the calculations much. The key point is expenses are incurred after her savings in Feb.

To get the answer of 8500, the starting point is to see that Nicole had a certain amount of money in her bank account at first.

In Jan, she spent 30%, this means she had 70% of her initial amount remaining.

In Feb, she managed to save 1/5 of the remaining amount she had left. One may ask,” Where does this amount come from? A logical explanation is from her salary, perhaps.

The amount of money she saved (1/5) is then added to her remaining saving in her bank (70%).

Then she went go to purchase 8 pens and gave 3/8 (3 parts) of the amount left to her parents for their holidays.

She had 5 parts remaining. From here, she added another (40%) or 2 parts .This means she had 7 parts or 140% which is equal to 6219.85.

A neat way to do this problem is to breakdown the question into smaller successive sub problems and use “Work backwards”.

Draw out some pictorial representation and you’re on the way to the solution.

Best wishes

Hi Tianzhu,

Big thanks for your explanation. :udaman: :udaman:

[mathnoobs]

a big thank you to Tianzhu for your very detailed explanation.

After going through the solution very carefully, I finally understood the whole long sequence, and I really mean the sequence. A lot of information are linked sequentially. I realised what \"then\" meant. It didn't mean the next month, it meant the remaining amount for Feb, and then she spent the money on pens, and then she spent the money on her parents. Each new expenditure is based on the amount remaining from the previous expenditure.

All those \"... amount of money she had left\" did not refer to the amount of money saved in Feb, but the subsequent amount after each expenditure.

This is one of the most convoluted question I've ever encountered in Primary school maths. I don't think primary school children can decipher it's meaning under exam conditions. Not because it is difficult but rather, it is so vaguely phrased. If the question had phrase it \".. the amount of money left after buying the pens\" or \"... the amount of money left after saving 1/5 of ...\", it would have been a lot clearer.

Sigh..... can't they just test our children on maths in a Maths exam rather than English comprehension ?

[mathnoobs]

mathnoobs:

I realized where my mistake in interpretation was. I interpret \"In February, she managed to save 1/5 of the amount of money she had left.\" as out of the 5 parts that she had left from Jan's savings, she spent some money, and what's left is 1 part. I did not see that as a fresh injection of funds into her account. Rather, I saw it that from her initial savings, the amount kept dwindling every month.

sorry if I'm a bit long winded. But \"In February, she managed to save 1/5 of the amount of money she had left.\", why can't we interpret that to mean say, out of $1,000 in the bank, she saved 1/5 or $200? How would one phrase \"Out of $1,000 in the bank, Peter saved $200 in Feb ?\" , ie. no injection of funds into bank account.