Q&A - PSLE Math

[tianzhu]

Hi pixiedust


Mum1113 is using a method known as the “Units Method”.It’s an alternative to MD. Unlike MD which is more visual in nature, UM is usually presented in tabulated form. There are many examples of solutions using UM in this thread.

It’s described in greater details in this book which is available in Popular.

Challenging Maths Made Easy by Ammiel Wan.

If you use MD, the first step is to find the total number of marbles.

1 unit ----- 63
4 units or the total number of marbles ------- 252

The second part is to divide 252 by 7

1 part ----- 36
Mary ------ 3 parts ------- 108

108 – 63 ------45

Best wishes

[jieheng]

pixiedust:

Thank you Mum1113 and jieheng.


I use back-check, ans is 45 marbles.

However, I don't understand :
1 : 3 (4)
+63 -63
___________
1 : 1 (2)
2 : 2 (4)

Is this the notation taught in school (our school haven't cover ratio yet/P5) ? Is there a solution using model ? I use model method to arrive at ans 45 but I split the problem into 2 parts and took many steps.

Thanks in advance for any help.

At First ,
M 1u

J 3u

Total 4u

1u -----> 63

total -----> 4u = 4*63 = 252

After John gave Mary some marbles ,
M 3u

J 4u

Total 7u

Since total units should be the same , changed the total units to the common multiples 4u*7 = 7u*4 = 28u

At First ,
M 7u (1u*7)

J 21u (3u*7)

Total 28u (4u*7)

After John gave Mary some marbles ,
M 12u (3u*4)

J 16u (4u*4)

Total 28u (7u*4)

28u -----> 252

1u -----> 9


Number of marbles that John must give to Mary = 21u - 16u = 5u = 5*9 = 45 (Ans)

[pixiedust]

Thank you for your patience everyone. Got it !

[Mum1113]

pixiedust:

Thank you for your patience everyone. Got it !

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

[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.