Q&A - PSLE Math

[ozora]

Need guidance.

Doris and Annie have each planned a list of words to learn,
If Doris learnt 40 words per day while Annie learnt 20 words per day, Doris would have 70 words left to learn while Annie had completed learning all the words.
If Doris learnt 20 words per day while Annie learnt 40 words per day, Doris would have 130 words left to learn while Annie had completed learning all the words.
How many words do Doris and Annie have to learn respectively?

Is my model correct? and I got stuck.

D [ 40 ][ 70]
A [20][ ]

D [20][ 130 ]
A [20][20][ ]

[MathIzzzFun]

ozora:

Need guidance.

Doris and Annie have each planned a list of words to learn,
If Doris learnt 40 words per day while Annie learnt 20 words per day, Doris would have 70 words left to learn while Annie had completed learning all the words.
If Doris learnt 20 words per day while Annie learnt 40 words per day, Doris would have 130 words left to learn while Annie had completed learning all the words.
How many words do Doris and Annie have to learn respectively?

Is my model correct? and I got stuck.

D [ 40 ][ 70]
A [20][ ]

D [20][ 130 ]
A [20][20][ ]

Hi

MD is as follows:

[] =words learnt

Scenario 1
D [][][][][70]
A [][]

Scenario 2
D [][130]
A [][]

Comparing the models for \"D\"
[][][] = 60
[] = 20

So, number of words to be learnt:
D = 4 x 20 + 70 = 150
A = 2 x 20 = 40

cheers.

[ozora]

MathIzzzFun:

ozora:

Need guidance.

Doris and Annie have each planned a list of words to learn,
If Doris learnt 40 words per day while Annie learnt 20 words per day, Doris would have 70 words left to learn while Annie had completed learning all the words.
If Doris learnt 20 words per day while Annie learnt 40 words per day, Doris would have 130 words left to learn while Annie had completed learning all the words.
How many words do Doris and Annie have to learn respectively?

Is my model correct? and I got stuck.

D [ 40 ][ 70]
A [20][ ]

D [20][ 130 ]
A [20][20][ ]

Hi

MD is as follows:

[] =words learnt

Scenario 1
D [][][][][70]
A [][]

Scenario 2
D [][130]
A [][]

Comparing the models for \"D\"
[][][] = 60
[] = 20

So, number of words to be learnt:
D = 4 x 20 + 70 = 150
A = 2 x 20 = 40

cheers.

can i say that 10 words is [ ]. that's why scenario 1; D has 4 [] and A has 2[]
but why sceanrio 2: D has 1 [] and not 2[]?

[tianzhu]

ozora:

Is my model correct? and I got stuck.

D [ 40 ][ 70]
A [20][ ]

D [20][ 130 ]
A [20][20][ ]

Hi ozora.

Good Morning.

This is a question involving “case1 case 2 scenarios”.

In doing this question, it’s important to note that the number of words to be learnt by Doris and Annie remains the same in both cases.

The first slide shows the thought process. You may use MD or UM to solve this question. In this case, I am using the MD way. As usual, I am drawing more models than necessary to show the flow of events.

Hope this helps.

Best wishes

http://farm6.static.flickr.com/5063/5615048270_0b36426626_z.jpg\">

http://farm6.static.flickr.com/5142/5614468685_555807d62e_z.jpg\">

[tianzhu]

Mum1113:

pixiedust / tianzhu / jiaheng
:oops: :oops: mistake mistake, :spank: DS later so sorrie here ...DS .must work doubly HARD

Hi Mum1113

“Careless mistakes” is something all students in the world are capable of making.

Please do not spank your boy, instead, encourage him to participate more actively in this thread.

We need fresh perspectives, more diverse views from new members in this thread.

Political parties need new candidates to ensure renewal and survival in the long run. This thread also needs renewal and through active participation by young members like your son, we can have a more vibrant forum.

Best wishes

[MathIzzzFun]

ozora:

MathIzzzFun:

[quote=\"ozora\"]Need guidance.

Doris and Annie have each planned a list of words to learn,
If Doris learnt 40 words per day while Annie learnt 20 words per day, Doris would have 70 words left to learn while Annie had completed learning all the words.
If Doris learnt 20 words per day while Annie learnt 40 words per day, Doris would have 130 words left to learn while Annie had completed learning all the words.
How many words do Doris and Annie have to learn respectively?

Is my model correct? and I got stuck.

D [ 40 ][ 70]
A [20][ ]

D [20][ 130 ]
A [20][20][ ]

Hi

MD is as follows:

[] =words learnt

Scenario 1
D [][][][][70]
A [][]

Scenario 2
D [][130]
A [][]

Comparing the models for \"D\"
[][][] = 60
[] = 20

So, number of words to be learnt:
D = 4 x 20 + 70 = 150
A = 2 x 20 = 40

cheers.

can i say that 10 words is [ ]. that's why scenario 1; D has 4 [] and A has 2[]
but why sceanrio 2: D has 1 [] and not 2[]?[/quote]Hi

For questions like this, the key is to use the \"constants\" - in this case
1) the total number of words to be learned remains the same,
2) the total number of words learned per day by both persons remain the same,
3) Annie completed learning all her words in both scenarios.

Using fact 3) above, same number of blocks will be used for words learned by Annie in scenario 1 & 2. For scenario 2, words learned by Doris will be half of Annie's - that's why 2 blocks are used to represent Annie's words so that 1 block can be used to represent Doris's in scenario 2. Working back to scenario 1, Doris's words will be twice Annie's - so 4 blocks are used.

We can also use fact 2) and 3) above to solve the problem. From 3), number of days in scenario 1 will be twice that in scenario 2, which means that the total number of words learned by both Doris & Annie in scenario 1 will be twice that in scenario 2. So the MD is as follows:

scenario 1 - [][][70]
scenario 2 - [][130]

where [] represent the total number of words learned by both Doris and Annie

solving using fact 1), [] = 130 - 70 = 60
since the total number of words learned by Doris and Annie per day is 40 + 20 = 60,
number of days to learn in scenario 2 = 60/60 = 1
number of days to learn in scenario 1 = 2 x 1 = 2

Number of words Doris has to learn = 40 x 2 (scenario 1) + 70 = 20 x 1 (scenario 2) + 130 = 150
Number of words Annie has to learn = 20 x 2 (scenario 1) = 40 x 1 (scenario 2) = 40

hope this helps.

cheers.

[Mum1113]

tianzhu:

Mum1113:

pixiedust / tianzhu / jiaheng
:oops: :oops: mistake mistake, :spank: DS later so sorrie here ...DS .must work doubly HARD

Hi Mum1113

“Careless mistakes” is something all students in the world are capable of making.

Please do not spank your boy, instead, encourage him to participate more actively in this thread.

We need fresh perspectives, more diverse views from new members in this thread.

Political parties need new candidates to ensure renewal and survival in the long run. This thread also needs renewal and through active participation by young members like your son, we can have a more vibrant forum.

Best wishes

tianzhu, thanks for your encouraging words, you make me feel better now, actually I didnt :spank: .....but I :heresmyfish: .....cos first attempt by DS in this forum and kena :booboo: ...... :imsorry: the emoticons are too tempting for use here.... ...

Anyway seriously, DS is one who thinks too fast (from his MA T) and solve problems too quickly BUT tends to lose marks for little mistakes. This little mistakes can add up to huge sacrifice and the marks are lost unnecessarily. Carefulness, detail checking and slow and steady is the way to go. This is to encourage all students to be EXTRA careful irregardless of which subjects or papers they are doing. It pays off in the end

[pixiedust]

Yes,mum1113, please thank your boy for taking time to help this aunty. His solution would have gotten some marks but this aunty got zero!


Tianzhu, your illustrations are really really nice!

[Mum1113]

pixiedust:

Yes,mum1113, please thank your boy for taking time to help this aunty. His solution would have gotten some marks but this aunty got zero!


Tianzhu, your illustrations are really really nice!

pixiedust , I will definitely tell him so, and we parents are all here to learn too. The forumers here are indeed very helpful and creative in their drawings. It is always a pleasure to look at the colorful illustrations

[pixiedust]

This is not a maths problem but I need help to understand/explain the equal concept, units method :


The method is to find a common multiple by making the numerators of both fractions the same. why ? Instead of just memorizing the steps, I want to know why is it if the numerator are the same, the denominators are the total units?

1/2 of apples = 3/4 of pears
3/6 of apples = 3/4 of pears
Total fruits 4+6=10 units <---- why ?