pirate:

numeric:

[quote=\"pirate\"]To understand why the number of friends is shortage + excess would actually involve a logical operation with multiple steps:


Step 1: 4 muffins = 3 muffins + 1 muffin
Step 2: Distribute the 12 muffins among the friends evenly -> number of friends with 4 muffins = 12
Step 3: 3 muffins = 4 muffins - 1 muffin
Step 4: Take the 4 imaginary muffins from the friends ( :scared: ) -> number of friends with 3 muffins = 4
Step 5: Total number of friends = those with 4 muffins + those with 3 muffins = 12 + 4 = 16

Mathematically, the logical operation is: (12 / (4 -3)) + (4 / (4-3))

No way is this anywhere near a 2 step problem.

Alternatively, just teach them to memorize shortage + excess and do by rote. But no guarantee they actually understand why number of friends is (shortage + excess) / difference in muffins.

It's easier to understand by drawing. It may look unsophisticated, but it's certainly more do-able and the answer can be interpreted from the drawing.
http://i58.tinypic.com/2yll36t.jpg\">

That's what I did to explain to explain to dd:

Step 1:

③③③③...

(Actually I drew them vertically, but it is a bit tedious to do it here. :faint: )

Step 2:

③③③③③③③③③③③③...
①①①①①①①①①①①①

(Filling up the ③s as I drew each ① was initially necessary for dd to enable her to picture it, but maybe your dc are smarter than dd. )

Step 3:

③③③③③③③③③③③③❹❹❹❹
①①①①①①①①①①①①

Step 4:

③③③③③③③③③③③③③③③③
①①①①①①①①①①①①❶❶❶❶

(It sinks in better if you draw the ① and then strike it off to show the shortage, but I can't seem to be able to do a strike-through here.)

Step 5:

Count or do 12 + 4 = 16

And I came to the conclusion that it takes 5 steps to arrive at 16 friends!

Now dd can do it mentally and make up her own questions. :boogie:[/quote]I thought only workings are counted as steps, but drawing diagrams, thinking and analysing it aren't counted as steps? If so, then there will be a lot of steps because the thinking takes time.
But the point is not about the number of steps. It's about the discipline and thinking put into it. I always tell my dd to start drawing if she doesn't understand or can't interpret the question; it's better than staying stuck with the question. Only then will she be forced to act, observe and think about it, and the question will look less daunting.

If the diagram is correct and clearly drawn, they should be able to deduce the answer in a few steps. I'm not as inclined for my dd to go for methods at this stage as they are \"packaged\" from raw concepts and takes the rigour out of the thinking process, although these save a lot of time. The idea is to cultivate analysis skills early in life, have enough good practises and not learn to blindly apply (like our time). Of course, the rigour needs confidence and concentration, consumes energy and generates a lot of stress

pirate:

lovinglife:

[quote=\"lee_yl\"]P3 Topical Test for Multiplication and Division:


Mindy baked some muffins for her friends. If she gave each friend 3 muffins, she would have 12 muffins left. If she gave each friend 4 muffins, she would need to bake 4 more muffins.

a) How many friends did Mindy give the muffins to?
b) How many muffins did Mindy have at first?

(Shortage + Excess) / Difference of muffins = No. of friends
Excess: 12
Shortage: 4
Diff: 1
No. of friends: 16/1 = 16
No. of muffins: (16*3)+12 = 60
check: (16*4)-4 = 60

To understand why the number of friends is shortage + excess would actually involve a logical operation with multiple steps:

Step 1: 4 muffins = 3 muffins + 1 muffin
Step 2: Distribute the 12 muffins among the friends evenly -> number of friends with 4 muffins = 12
Step 3: 3 muffins = 4 muffins - 1 muffin
Step 4: Take the 4 imaginary muffins from the friends ( :scared: ) -> number of friends with 3 muffins = 4
Step 5: Total number of friends = those with 4 muffins + those with 3 muffins = 12 + 4 = 16

Mathematically, the logical operation is: (12 / (4 -3)) + (4 / (4-3))

No way is this anywhere near a 2 step problem.

Alternatively, just teach them to memorize shortage + excess and do by rote. But no guarantee they actually understand why number of friends is (shortage + excess) / difference in muffins. [/quote]
It's easier to understand by drawing. It may look unsophisticated, but it's certainly more do-able and the answer can be interpreted from the drawing.
http://i58.tinypic.com/2yll36t.jpg\">

tianzhu:

6race0ng:

Thanks for solving but what is the method to find how many groups of teacher and pupils?

Hi 6race0ng

Good Evening

Start with assuming all were teachers, number of trees planted ----- 360*3 ----- 1080

Total difference ----- 1080 – 520 ----- 560

A group of 3 teachers will plant (3*3) ----- 9 trees

A group of 3 pupils will plant 2 trees.

Difference in number of trees per group ----- 9 - 2 ----- 7

Number of groups ----- 560/7 ----- 80

Number of pupils ----- 80*3 ----- 240

Hope this helps.

Best wishes

Hi 6race0ng, if a pictorial representation helps, here it is:
http://i60.tinypic.com/1zl57c4.jpg\">

fav_giraffe:

hi hi, I need some help on this question.


Mr Wong has some marbles. If he gives 6 marbles to each of his children, he will be left with 3 marbles. If he gives 8 marbles to each of his children, he will need 5 more marbles.
a) how many children does Mr Wong have?
b) how many marbles does Mr Wong have?

How to solve this question short of using algebra? Thanks!

Another approach:
http://i60.tinypic.com/2moz88j.jpg\">

6race0ng:

Hi, can someone help me with this qns? TIA!

A total of 360 teachers and pupils participated in tree planting. Each teacher planted 3 trees and each group of 3 pupils planted 2 trees. If 520 trees were planted altogether, how many pupils were there? 

360 people -> 520 trees
Divide by 40,
9 people -> 13 trees

1 teacher -> 3 trees
3 teachers -> 9 trees

3 pupils -> 2 trees
6 pupils -> 4 trees

3 teachers + 6 pupils -> 13 trees
Multiply by 40,
120 teachers + 240 pupils -> 520 trees

ss2:

From my understanding,


34 girls had to make 3 more necklaces each since 1 girl was absent.

so 3*34= 102

so each gal supposed to make 102 necklaces.

so total no neckalces done by 35 students - 102*35 = 3570

Is that correct>?

Yes.

Beautyful Minds:

angel:

Alice had some boxes of fruits for sale. She sold 35 boxes on Monday. She sold 1/5 of the remaining boxes of fruits on Tuesday. Then she had 1/3 of the total number of boxes of fruits left. How many boxes of fruits did she have at first?

Hi Angel,

Please refer to the link below for the detailed solution.

http://geniebookapp.com/public_question ... a5b02bfcfa

Let us know if you have any doubts.

Beautyful Minds

http://i62.tinypic.com/20arszq.jpg\">

lynn01sg:

Pls help!


Ahmad had thrice as many marbles as Ian. Ian had twice as many marbles as Jeffrey. Given that Ahmad had 1605 marbles more than Jeffrey, how many marbles do they have althogether?

http://i60.tinypic.com/aayvcj.jpg\">

SOS mum:

Hi..ps help..Many tks n God Bless:)


The total cost of a calculator and a watch was $94. John bought 5 such calculators, 3 such watches and a camera for $1242. The total cost of a camera and a calculator was $924. How much did he pay for the watches?

http://i62.tinypic.com/k0oitw.jpg\">

Brownbear:

Actually it can be very easy to solve it by drawing model. Numeric, you are GOOD! Thanks.

Thanks for your compliments. It took me a while to solve this :oops: