Q&A - P4 Math

[HAPPYH]

Xiao Hu:

jedamum:

[quote=\"Xiao Hu\"]Hi Jedamum,

Thanks for your post.
Glad to know I'm not alone!
Thanks for sharing your boy's experience. I'm hoping to have a chance to check my son's worksheets after being marked by teacher to see what's acceptable for these kind of estimation questions, which did not specify round up to tens or hundreds or thousands.
It's comforting to hear what your son's teacher said about it, because that's what I thought so, no right or wrong.

Thanks,
Xiao Hu.

[/quote]Hi

Could you share your experience with the estimation if it is not specified anything like round off to the nearest ten or hundred? Thank you in advance.

[concerned1970]

Hi, can anyone pls help me to solve the two ques without using algebra and guess and check method. Ty.


1) ABCD is a rectangle with an area of 484 cm2. If its length is 4 times its breadth, find its breadth.

2) PQRS is a rectangle with an area of 576 cm2. If its length is 4 times its breadth, find its perimeter.

Ques were extracted fr Must Know Maths Pb Sums, the ans were given in guess and check method which I discouraged my DS to solve the ques using that.

[MathIzzzFun]

concerned1970:

Hi, can anyone pls help me to solve the two ques without using algebra and guess and check method. Ty.


1) ABCD is a rectangle with an area of 484 cm2. If its length is 4 times its breadth, find its breadth.

2) PQRS is a rectangle with an area of 576 cm2. If its length is 4 times its breadth, find its perimeter.

Ques were extracted fr Must Know Maths Pb Sums, the ans were given in guess and check method which I discouraged my DS to solve the ques using that.

Draw a rectangle. Cut into 4 squares of side = 1 breadth.
Each of these squsres has an area of 484/4 = 121 cm2 = 11 cm x 11 cm

Same for question 2

cheers.

[cimman]

concerned1970:

Hi, can anyone pls help me to solve the two ques without using algebra and guess and check method. Ty.


1) ABCD is a rectangle with an area of 484 cm2. If its length is 4 times its breadth, find its breadth.

2) PQRS is a rectangle with an area of 576 cm2. If its length is 4 times its breadth, find its perimeter.

Ques were extracted fr Must Know Maths Pb Sums, the ans were given in guess and check method which I discouraged my DS to solve the ques using that.

if your child learns algebra, your child is learning to view relationships at a conceptual level. It is a skill set that takes some time, but will reap benefits that will simplify problem sums to a manageable level and aids in application of concepts to actual problems. It is not impossible, in fact, the school teaches this at an sub conscious level, ie. the moon and the stars problems, they just don't call this algebra but it is. To solve the moon and the stars problem types, you need to understand the concept of using a variable, the moon and the stars, and the forming of relationships, ie. the equation.
The model technique, while it is visual, is also algebraic based in it's approach.
When you draw a box, that represents the unknown variable. When you equate the 2 rows of boxes, that represents the relationship, or the equation.
These 2 components form the basis of algebra. All forms of heuristics taught in the market today contains these 2 components, but expressed in different forms. It is just old wine in new bottle. The wine (algebra) remains the same, the presentation differs.

Once your child acquires the skill of thinking conceptually, he or she will find that a lot of problem sums actually have the same solution technique. As one moves from P4 to P6, conceptual thinking is a critical skill to acquire.
A majority of guess and check problems can be solved using algebraic approach. However, the authors of the books assume that algebra is not in syllabus, then your next best approach is guess and check, there is no other way out. All other approaches are just different presentations of the algebraic principles.

I know you're not looking for a solution in algebra, but here is the algebraic solution to your first question:
Breadth x Length = Area (generic equation)
u x 4u = 484
u x u = 484/4 = 121
u = 11, since 11 x 11 = 121 (here is where some guess and check comes in if the child not too well versed with the times table)
or u = square root of 121 (here is where a calculator is useful, since calculators have square root functions, not in P4 though). The concept of square root, while it is not taught in primary school, is a useful and easy concept to understand. The child already know the concept of square root, but might not know the formal name for it.

You'll find that there are multiple representations of the above solution, just expressed differently. The key question you've to ask yourself is this: do I want to be familiar with the multitudes of algebraic representations, or do I want to to be familiar with the root of all the other representations ?

[concerned1970]

Ty MathIzzFun and Cimman. Algebra is way too profound for my DS to comprehend.

[milo-cupcake]

Hello , please help me this question with assumption method.


At a sale, the erasers were priced at 4 for $2 while the markers were priced at 2 for $3 . Miss Macy bought a total of 26 eraser and markers for $23 . Find the number of erasers that Miss Macy bought.

Thank you in advanced. :thankyou:

[MathIzzzFun]

milo-cupcake:

Hello , please help me this question with assumption method.


At a sale, the erasers were priced at 4 for $2 while the markers were priced at 2 for $3 . Miss Macy bought a total of 26 eraser and markers for $23 . Find the number of erasers that Miss Macy bought.

Thank you in advanced. :thankyou:

1 eraser -> $0. 50
1 marker -> $1. 50
price difference -> $ 1. 00

Assume Macy bought all markers, total amount paid = 26 x $1. 50 = $39
amount overpaid for erasers = $ 39 - $ 23 = $16
number of erasers bought = $16 ÷ $1 = 16
number of markers bought = 10

cheers

[peapot]

BigDevil:

snowball:

:thankyou: :please:
for this type of questions, how do we see (beginning) how many units to draw in the model? eg, for the above qn, 6units to draw for the men :?

You will realise what model to draw if you can think of this question in fractions.

At first, there were twice the number of men as women. That's the same as saying number of women is 1/2 of men.

Likewise, at the end, number of women is 1/3 of men.

Changing to same denominator, you get 3/6 at first, and 2/6 at the end.
You can then proceed to solve the problem with fractions (1/6 = 12),
or draw the model with 6 units for men.

You can also draw the following alternate model for this question without realising you need to draw 6 units for men:
http://i48.tinypic.com/iznno9.jpg\">

Big devil!! You are the first person who actually enlighten me. Very clear explanation!! I finally understand how to draw the model. Like many parents I have a problem wondering how many boxes to draw. No one told me to think in fraction, not even my dd's tutor! Thanks!!!
Btw, can we always use fraction to draw box models for all problem sum that has twice as many, 4 times more etc? Can we also find out man first instead of starting to find woman first?

[peapot]

HAPPYH:

I need help to understand the following (Pardon me if this is a very basic question; Obviously I am not sure)


Estimate the answer

535 + 320 = ?

567+341 = ?

They never say round off to the nearest tens or hundreds. Then how do we know for sure?

For eg:
535 + 320 = 540 + 320 = 860
535 + 320 = 500 + 300 = 800

Which one is correct? And why?

Thank you in advance.

I would think 860 should be the ans. we are asked to estimate the ans so the ans must be the closest to the real ans. this means u should round to nearest 10s.

[milo-cupcake]

Hi , please help me this question with assumption method.


Doreen paid $25 for 35 pens and pencils altogether.The pen were sold at $2 each and the pencils were sold at 3 for $1. How many pencil did she buy?

Thank you