$2 x 83 = $166 $226 - $166 = $60 $5 - $2 = $3 60 / 3 = 20 (answer)

Hi, I just did this with my daughter too. Guess and check will be easier to understand for them, I think.

Yes, it is a guess n check qn for a p3 kid.

Must usually start off with nearly equal number of pens and pencils and hence 40 pens and 43 pencils. Must gradually increase or decrease the number of pens and pencils till you get the answer

question would be pretty hard if there are 2 big prime numbers.

Thank you all for taking the time to comment and help out! It really is very useful for me. Thanks for showing the diff methods to get there and tips on where to "start". My child's difficulty is even to design the table for guess and check.

Always good to try and solve in more than one way to sharpen our problem solving skills. Besides guess and check, try the method of supposition:

Pens + pencils = 83 $5 Pens + $2 pencils = $226 Pens = 20

Problem solving shouldn't be only about getting the answer but about the thinking and reasoning so even if the student can get the answer, we should ask if there is another way. Guess and check might be difficult if decimals are involved.

Another consideration when doing guess and check: Looking at the total cost of $226 (unit digit is 6), and the costs of each pen ($5) and pencil ($2), we can make an educated guess that the number of pencils must have a unit digit of 3 (3, 13, 23, etc). Thinking in this way, students won't choose any random numbers to start their guess.

For P3, probably has to teach them the guess and check (trial and error) method by drawing table, pretty hard to explain to them. Alternatively you can experiment with teaching them about graphs with Pens on the x-axis and Pencils on the y-axis which is the result or outcome of the guess and check method.

At P3, the heuristic: "guess and check" is more appropriate. If we guess say 80 pens and 3 pencils, the total cost is $406. Ask, "why the total cost is not $226?" (Too many pens). So we should have fewer pens and more pencils. Ask, "how many pens do we have to change for pencils do that the total cost is $226?" (180/3=60). There are 80-60=20 pens.

Hi Vei Li Soo, for third part working how do you get 18 and divide by three? very confuse???

I take $226 - 6 =$220 ÷ 2 (pen and pencils) =$110 ÷ $5=22 pens =$110 ÷ $2=58 pencils balance $6 ÷ $2=3 (pencils) 22 pens, does my guess make sense?

Ow Yong, something must have happened when I wrote the working and the numbers got erased... It's meant to be $189/3 = 63. That's why it's 83-63=20. Sorry about that...

Thanks for the clarification, Vei Li

Hi, I am trying to understand the supposition method. How do we know which item to suppose first? Also, how to explain part 4 on converting pens to pencils? How do we know the final answer is for pens or pencils? Thanks.

It is ok to suppose any of the pbjects whether it is pen or pencil. but usually we use the pne that leads to more simple calculation.

Idy Tan, it doesn't matter which one to 'suppose' first. E.g. if we suppose that all 83 items bought are pencils, then the cost would be $2x83=166. Then 226-166=$60 (shortfall of $60). Since the difference between the costs of pencil and pen is $3 and $60/$3=20, we know that the shortfall of $60 is because of the 20 pens (at first supposed to be 0 pens, so now 20 pens).

Actually there are some logical reasons to choose one or the other. In this particular question it is asking for pens, so we suppose pencils first and the solution will lead us to pens. If asking pencils we start with pens and the solution will bring us to pencils. This is when using supposition

In fact, we can also let there be 10 pens and 73 pencils. Cost = 50+146=$196. 226-196=$30 (shortfall), and $30//$3=10, so change 10 of the pencils to pens (to increase the total cost by $30) and it now becomes 20 pens and 63 pencils. You can try with a few other combinations of pens and pencils to process the ideas in this method. An important thing to do is to write your steps and statements clearly so that you can track your thinking process.

And when working with children, it is helpful to get them to explain their thinking -- why they take a certain step, why divide by 3, why add, etc.

For Guess and Check, one of the problems is that kids guess and guess and guess because they do not understand the logic beyond the guesses. As a result many kids end up with solutions having 5, 8, or even 12 guesses. While the answer is eventually found, it is not using the tool appropriately nor does it help them with efficiency. After the first guess, kids should be able to intelligently know which 'guess' to choose next based on the given numbers and whether they total is too high or too small. I have attached a pic which shows demonstrates the logic beyond the guesses. You can see that this is actually a pattern ie a linear gap increasing by $3 each 'step'.

For Primary 3, students may simply guess say 40 pens and 43 pencils. Check: Total cost = $200+$86 = $286 Too much. So need to have fewer pens. Next guess: 30 pens and 53 pencils. Check: Total cost=$150+$106 = $256 Still too much. Guess again: 20 pens and 63 pencils. Check: Total cost=$100+$126 = $226 Just right. The answer is 20 pens and 63 pencils.

Students may learn to present the guess and check process in tabulation form: Pens Pencils Total cost

Apply Guess and Check Method

I would assume all are pencils. So 83x2=166. Which means the extra amount of $60 would have to come from the pens . Then 60 divide by $3 to give 20 pens. $3 being the difference in the cost .

This method can be used to solve all similar questions. Like the no of legs of 2 legged animals or the number of car and motorcycles.

It is guess and check because you don't know the amount of pens and pencils. But thanks because this came out for my Maths exam. :)

This can be done without guess n check at p3 level

yup. All comes down to logical thinking and processing.

9yr

May I ask why you take 3 units for 9 under Men instead of 4 units for 9 under Women? This will help me understand your answer better.

Difference between men and women is the same for both ratios. Both men and women increase by 3 units each, hence 3 units= 9.

This qn is the silimar concept as 'age qn'. Difference bet ages of any 2 persons is always the same.

Chee Weng Tang yes

Tan SUnny Do you use that illustration to explain to kids?

this is from an extract of a book I wrote for parents and educators. Kids can be explain in simplified manner.

A more generic question students may ask when faced with such problem is to ask "what remains unchanged? ". Might be too much for students to remember the different scenarios.

Thanks so much for ur help Adrian. Nowadays parents also learn together with our children. Brains got to put some lubricants to prevent rusting.. hehe..

Hi, thanks for the reply.. may i ask why 5u -> 3/5 + 105?

5 units in the first row= 3/5 of the money + $105

My answer base on logic. Find the fraction of original equivalent to $105

Thanks Mike & Aline 👏

This is addictive.

Aline Ang yes, I do it as a pastime lol

I would like to join this as much as i could after my work and duties.

Aw, I feel noob, I taught the kid to draw 63 units, coz 7 x 9 = 63 which is the denominator and from it did it slowly, by drawing alot alot of diagrams. The issue is for the kid to see how to solve it, although the easiest is to teach them to Let x be the initial amount. The main aim is to give the kids confidence in solving problem imo.