Is your child always losing many marks in challenging Maths problems?

Have you ever felt baffled when your child scored 40 out of 45 marks for paper 1 and only a miserable 25 out of 55 marks for paper 2?

To see how challenging our PSLE Math problems can be, download our Challenging PSLE Math Problems for FREE. These are questions compiled from past PSLE Math Paper 2. Click the download button below to download. 

“How could that be?” you ask yourself, and you start to wonder why a child who has a strong command of English and has demonstrated that he or she has a good foundation in maths concepts for Paper 1 could fail to understand the problem sums.

“Did you run out of time before you could complete the paper?” you ask in a concerned tone. Your child shakes his or her head and you automatically strike off “poor time management” in your head and attribute the poor score to your child’s carelessness.

As you flip through Paper 2, your heart sinks when you see that the last five questions are left blank. That is when the bad news hits you — that your child has completely no idea what’s going on in the little scenario set out in the problem sum.

The good news is: your child is not alone. Many other children struggle with challenging Math problems that require them to apply multiple maths concepts in order to solve them.

Your child may not understand the question because he or she could be confused by the maths language, may not know which concept the question is testing on, is unable to figure out which method he or she should use in order to solve the problem sum, or fails to recognise the pattern in maths questions.

Remember, there is no such thing as a “maths person”, it’s whether or not someone has been trained up the right way to tackle Maths. One should always have a growth mindset that constantly evolves to include new effective strategies and processes.

Before we can supply the solution to the problem, we need to conduct a root cause analysis. What exactly is causing your child to feel stumped when he or she is faced with a challenging maths problem?

Here are some tips and tricks we have to help your child in solving challenging maths problems.

Pinpointing the cause

Confused by Maths Language

Like English comprehension questions, Maths also has keywords that students should pick out before they proceed with solving the questions. Not only does this help them to quickly identify the right technique, but it also helps them to reduce the margin for error when they are more conscious of the keywords and are clear about what they are looking for.

Jimmy Maths says:
Your child needs to be trained to identify keywords.

1. Read the problem sum
2. Highlight keywords
3. Read the problem sum again

You will be surprised at how a small trick can do wonders. This enables the child to pay attention to details that he or she might otherwise leave out. Let’s take a look at the following example.

For the first 4 hours of a trip, a plane travelled at an average speed of 520 kilometers per hour. For the remainder of the trip, the plane travelled an average speed of 880 kilometers per hour. If the average speed for the entire trip was 590 kilometers per hour, how many hours did the entire trip take?

Now, reread it again with the keywords underlined. Do you see the difference?

For the first 4 hours of a trip, a plane travelled at an average speed of 520 kilometers per hour. For the remainder of the trip, the plane travelled an average speed of 880 kilometers per hour. If the average speed for the entire trip was 590 kilometers per hour, how many hours did the entire trip take?

To check for comprehension, you may ask your child, “Can you tell me what the question is asking you to do?”

Studying hard, but not smart

Ever wondered how some children can handle certain tasks faster than the rest? Talent aside, skill comes into play as well. At Jimmy Maths and Grade Solution, we teach maths problems by concepts, and not by chapters. We get children to look at the big picture, instead of focusing on the big stepping stone that’s in front of them.

Here are some concepts that your child might be familiar with.

1. Part-whole concept
2. Unit times Value
3. Cut and paste method
4. Repeated identity
5. Equal quantity
6. Unchanged total
7. Unchanged difference
8. Changed quantity
9. Changed gaps
10. Simultaneous concepts

Jimmy Maths says:
Train up your child to have a flexible set of tools that he can use to solve the problem sum in the most efficient way. No longer is doing drills mindlessly a solution to mastering maths problems.

Applying the wrong method

Given enough time, any child should be able to solve a challenging Maths question. The issue is: Do they have the luxury of time during an examination? No.

Let’s attempt to solve this question two ways.
(Don’t forget to identify keywords and highlight them!)

There were 125 sweets to be distributed to 25 children. Each boy received 8 sweets while each girl received 3 sweets. How many girls were there?

If your child is lucky, he or she will get it within the first three tries. But is Maths a game of luck? No. We can’t possibly leave it up to luck when it comes to a major examination.

Jimmy Maths says:
Let’s apply the assumption method instead.

There were 125 sweets to be distributed to 25 children. Each boy received 8 sweets while each girl received 3 sweets. How many girls were there?

Assume that all the sweets were distributed only to boys.

Total → 25 x 8 = 200 (That’s way more than the 125 sweets we have)

Excess → 200 – 125 = 75 (This is what we must reduce the total by)

Difference → 8 – 3 = 5
(For every boy that we substitute with a girl, the total number of sweets decreases by 5)

Opposite → 75 ÷ 5 = 15 (The number of girls needed to replace the boys)
(We assumed that only the boys got the sweets. Hence, this number refers to the girls)

In four simple steps and four simple equations, we have solved the sum. Compare and contrast it with the guess-and-check method. Pay attention to the number of steps required before the student who used the guess-and-check method finally arrived at the answer.

Of course, we always encourage children to use the method that they are most comfortable with. Then again, nobody starts off with being comfortable when they first use chopsticks or when they first put on a pair of rollerblades. It all takes PRACTICE, and it’s a matter of getting used to the most efficient and effective way.

Going too fast, too soon

Some parents might think that a child will do well for Paper 2 as long as he or she can tackle the five most challenging math problems that come at the end of the paper. With that thought in mind, they endlessly force difficult problem sums down their child’s throat, hoping that their child could somehow make sense of the numbers and digest it all.

That’s not how it works.

While we encourage our students to look at the big picture when they are learning new maths concepts, we advocate baby steps when it comes to attempting challenging problem sums. Rome was not built in a day; and neither do people start with scaling Mount Everest on their mountains-to-conquer list.

Jimmy Maths says:
Simplify the problem. Start with smaller numbers.

A challenging 10-step problem sum could be reduced to an 8-step problem sum. A problem sum with huge numbers can seem less daunting if these numbers are substituted with smaller ones that are more familiar to your child.

Take this problem sum as an example.

There were 240 more blue beads than red beads in a box at first. Kimmy added 1850 red beads and removed 290 blue beads from the box. Then, there were 21 times as many red beads as blue beads left. How many red beads were there at first?

What? There were 21 times as many red beads as blue beads left? Children might get scared at the thought of such a big difference. Let’s start with smaller numbers instead.

There were 4 more blue beads than red beads in a box at first. Kimmy added 24 red beads and removed 10 blue beads from the box. Then, there were 3 times as many red beads as blue beads left. How many red beads were there at first?

When we have more than and less than questions, model drawing is useful in helping children to rearrange and make sense of the given information. Let’s see how the model is drawn for this.

2u → 6 + 24 = 30
1u → 30 ÷ 2 = 15
No. of red beads at first → 15 + 6 = 21

Ready? Let’s do the same sum but with the original numbers given.

20u → 50 + 1850 = 1900
1u → 1900 ÷ 20 = 95
No. of red beads at first → 95 + 50 = 145

Check Your Answers by Working Backwards

So, your child has managed to solve the challenging maths problem, then he or she starts to wonder if the answer is correct. We apply the substitution and work-backwards method to see if the numbers fit.

Let’s use the previous question as an example again.

If there are 145 red beads at first, it means that there are (145 + 240) blue beads at the start.

No. of blue beads → 145 + 240 = 385
After Kimmy added red beads → 145 + 1850 = 1995
After Kimmy removed blue beads → 385 – 290 = 95

Now, the question states that in the end, there were 21 times as many red beads as blue beads left.
Does 95 x 21 = 1995?
√ Yes!

We can be sure that our answer is correct. Unlike Science and the languages, it is more possible to score full marks for Maths because it doesn’t have all the complex grammar and vocab rules or oh-so-confusing spelling to handle.

Mastering the technique of checking your work accurately can indeed guarantee you the marks in your maths paper.

Our last tip of the day: Practise with understanding, not quantity

Set aside one or two challenging maths problems for your child to attempt each day. If your child gets it wrong, be sure to go through the solution with your child, and revisit the same question next week, albeit with different figures.

Remember, keep the big picture in mind that maths concepts can be applied across a multitude of questions, but when you are training your child to tackle challenging problem sums, take consistent baby steps.

No child ever did poorly with a little love and patient guidance along the way.  

Before you go, remember to download our Challenging PSLE Math Problems for FREE. These are questions compiled from past PSLE Math Paper 2. Click the download button below to download.