Q&A - P5 Math

[mathnoobs]

tianzhu:

mathnoobs:

Hi Tianzhu
how does one know when to use units and parts ? Here the units are assigned to Sally, and parts to Tom. However, since Tom has age in both present time and some other time, how does one tell whether to assign parts/units based on time or individual ? What is the rational for the assignment ?

Hi

I am sorry. I can’t answer in detail at this moment.

If you have a copy of Challenging Maths Made Easy, try to do some reading first.

I’ll try to answer your question at a later time.

Best wishes

Hi Tianzhu
no problem. Thanks for responding first.
I do have the Challenging Maths Made Easy, and here is why I have the confusion.
It is only in Chapter 7, External Transfer with Changed Quantities Concept, that I see both Units and Parts being used.
In the others, ie. Unchanged Total, Unchanged Difference, Unchanged Quantity, only Units are used for the typical Before and After cases. In the unchanged scenarios, the 2 ratios are linked by normalizing them to a common denominator. But before the normalization, I would have thought the After scenario would be labelled as Parts rather than Units.

In the age problem, I see 2 scenarios, the Present age scenario and the some other time scenario. I would have thought that based on the Chapter 7 concept, the label Units, Parts would be assigned based on scenarios (ie. Before, After) in thise case (Present Age, Some Other Time)

[mathnoobs]

after some thinking, I think I see the logic.

The labels Units/Parts are assigned based on the comparison made by the question.
Since the question compared Sally’s age at present time to Tom’s age at some other time, then that comparison should be assigned the same label (ie. either Units or Parts) The second comparision would be assigned another label.

However, I still have this question: in Challenging Maths Made Easy, the chapters on Unchanged Total/Difference/Quantity all used only 1 label for both the Before and After comparision. Should not they have used different labels for the Before and After cases ? I can understand that after normalization (lowest common multiple), all ratios are assigned a single label. But before they are normalized, shouldn’t they have different labels ?

[tianzhu]

mathnoobs:

after some thinking, I think I see the logic.

The labels Units/Parts are assigned based on the comparison made by the question.
Since the question compared Sally's age at present time to Tom's age at some other time, then that comparison should be assigned the same label (ie. either Units or Parts) The second comparision would be assigned another label.

However, I still have this question: in Challenging Maths Made Easy, the chapters on Unchanged Total/Difference/Quantity all used only 1 label for both the Before and After comparision. Should not they have used different labels for the Before and After cases ? I can understand that after normalization (lowest common multiple), all ratios are assigned a single label. But before they are normalized, shouldn't they have different labels ?

Hi

Great, you see the logic. So, there‘s no need for me to draw the MD anymore.

Yes, you may represent them in units and parts to represent before and after ratios. But you still need to change parts into units as you use the concepts of unchanged quantities, unchanged difference or unchanged total quantities. There is more than one way to solve it.

Best wishes

[tianzhu]

mathnoobs:

tianzhu:

[quote=\"mathnoobs\"]
Hi Tianzhu
how does one know when to use units and parts ? Here the units are assigned to Sally, and parts to Tom. However, since Tom has age in both present time and some other time, how does one tell whether to assign parts/units based on time or individual ? What is the rational for the assignment ?

Hi

I am sorry. I can’t answer in detail at this moment.

If you have a copy of Challenging Maths Made Easy, try to do some reading first.

I’ll try to answer your question at a later time.

Best wishes

Hi Tianzhu
no problem. Thanks for responding first.
I do have the Challenging Maths Made Easy, and here is why I have the confusion.
It is only in Chapter 7, External Transfer with Changed Quantities Concept, that I see both Units and Parts being used.
In the others, ie. Unchanged Total, Unchanged Difference, Unchanged Quantity, only Units are used for the typical Before and After cases. In the unchanged scenarios, the 2 ratios are linked by normalizing them to a common denominator. But before the normalization, I would have thought the After scenario would be labelled as Parts rather than Units.

In the age problem, I see 2 scenarios, the Present age scenario and the some other time scenario. I would have thought that based on the Chapter 7 concept, the label Units, Parts would be assigned based on scenarios (ie. Before, After) in thise case (Present Age, Some Other Time)[/quote]Hi

Good Afternoon.

I am trying to recall what my kid did when he was in primary school.

I am an old man; my memory is crowded out by burdens of life, so please bear with me as my recollection might be incomplete.

I think primary school kids start to learn MD as early as the second half of primary one (in my kid’s case).They started off with part whole and comparison model. Later at P5, the topic on ratios was introduced and kids learned the concept of units as in Units Method to solve questions.

The problem solving heuristics one learns in schools as well as books from external sources are important tools to help students to solve questions efficiently. However, the steps or strategies are not cast in concrete which has hardened. These steps or strategies may be adapted to solve future problems. More importantly, students must be able to adopt and adapt suitable strategies and apply them appropriately when faced with unfamiliar questions.

Read the book with an open mind, there is more than one way to solve a question. Model Drawing can be drawn in different ways; students may stretch their imagination to visualise the solutions as long as they help to solve the problems. Units and Parts may be presented in different forms.

Enjoy the maths journey with your kid.

Best wishes

[mathnoobs]

tianzhu:

mathnoobs:

after some thinking, I think I see the logic.

The labels Units/Parts are assigned based on the comparison made by the question.
Since the question compared Sally's age at present time to Tom's age at some other time, then that comparison should be assigned the same label (ie. either Units or Parts) The second comparision would be assigned another label.

However, I still have this question: in Challenging Maths Made Easy, the chapters on Unchanged Total/Difference/Quantity all used only 1 label for both the Before and After comparision. Should not they have used different labels for the Before and After cases ? I can understand that after normalization (lowest common multiple), all ratios are assigned a single label. But before they are normalized, shouldn't they have different labels ?

Hi

Great, you see the logic. So, there‘s no need for me to draw the MD anymore.

Yes, you may represent them in units and parts to represent before and after ratios. But you still need to change parts into units as you use the concepts of unchanged quantities, unchanged difference or unchanged total quantities. There is more than one way to solve it.

Best wishes

yes, I understand that one needs to change parts into units for unchanged stuff. However, in Ammiel Wan's book, both ratios were presented as units before the common multiple operation was done. Is this correct ? or one of the ratio should be labelled as parts ?

[tianzhu]

mathnoobs:

yes, I understand that one needs to change parts into units for unchanged stuff. However, in Ammiel Wan's book, both ratios were presented as units before the common multiple operation was done. Is this correct ? or one of the ratio should be labelled as parts ?

Hi

There is more than one way to solve a question.

There are many assessment and guide books in the market and their way of presentation may differ.

Best wishes

[tianzhu]

Hi


I’ve intentionally labelled the boxes as unit and part so that students can have an option if they choose to work using Units and Parts.

As usual, I’ve done more MD than necessary, once students understand the logic, they may consodilate the steps.

Hope this helps.

Best wishes

http://farm8.staticflickr.com/7035/6812082325_7bb0b1b14f_z.jpg\">

[mathnoobs]

tianzhu:

Hi


I’ve intentionally labelled the boxes as unit and part so that students can have an option if they choose to work using Units and Parts.

As usual, I’ve done more MD than necessary, once students understand the logic, they may consodilate the steps.

Hope this helps.

Best wishes

http://farm8.staticflickr.com/7035/6812082325_7bb0b1b14f_z.jpg\">

Hi Tianzhu
thank you very much again for taking the time to come up with an excellent diagram. It very clearly illustrate the concept involved.

I find that while modelling is very good for understanding the concept, when it comes to answering exam questions, the unit transfer method is faster, since there is no drawing involved. Drawing takes up more time, compared to writing out a few numbers. More so if the child's motor skills isn't that good and drawing a straight line freehand, is going to be cumbersome.

[tianzhu]

mathnoobs:

Hi Tianzhu
thank you very much again for taking the time to come up with an excellent diagram. It very clearly illustrate the concept involved.

I find that while modelling is very good for understanding the concept, when it comes to answering exam questions, the unit transfer method is faster, since there is no drawing involved. Drawing takes up more time, compared to writing out a few numbers. More so if the child's motor skills isn't that good and drawing a straight line freehand, is going to be cumbersome.

Hi

You’re welcome.

First thing first, I think the schools will expose students to a range of problem solving heuristics in their journey towards PSLE maths.

When it comes to examination, let the child decides on whichever method he/she is comfortable with.

MD creates pictures from abstract statement and help students to visualise solutions better. One needs not draw boxes in precision scaled shapes with perfectly right angled corners. As long as MD is drawn in good proportion to see the relationships in a solution, it’s good enough.

Finally, take note that MD is not the only way to solve primary school questions. As stated in MOE syllabus, there are many other strategies as well.

Best wishes

[YumYum]

Hi, my dd needs help with the folk Qns:


1. Lorraine has 5/6 as many red balloons as blue balloons. If she buys another 25 red balloons, there will be 3/5 as many blue balloons as red balloons. How many balloons does she have altogether?

2. Amelia gave some crayons to her students. If each student receives 18 crayons, she will be short of 20 crayons. If she receives 15 crayons, she will be left with 49 crayons.

A. How many students were there in the class?

B. How many crayons did she have?


3. Thomas spent 2/7 of his salary.
He gave 7/8 of the remaining to his wife and two children in the ratio of 16:2:3 and saved the rest.
He saved $420.
What fraction of his salary did he give to his children?


4. Darren placed 263 books on 3 shelves, labeled X, Y and Z.
After more books were placed onto shelf X and shelf Y, the number of books on shelf X increased by 27 and the number of books on shelf Y quadrupled.
20 books were then taken down from shelf Z.
As a result, there are now an equal number of books on each shelf.
Find the number of books on shelf x at first.

Many Thanks!