 ## Useful tips for PSLE Math Paper 2

Some adults would find PSLE Math Paper 2 questions with two lines daunting, what more children when they are faced with a question and a large amount of space. How do they dissect the question and work towards reaching the correct answer? At Grade Solution, topics are taught according to Concepts. Your child would be able to read the question at a glance, pick out the keywords, and decide which method they are being tested on. Is it the assumption method, the group × number value method, the excess and shortage method, internal transfer (constant total) method, etc.  There will be topics that are easier for some students, and more difficult for others. Each child would grasp each concept differently, and this is understandable. With a firm foundation in the problem-solving concepts, your child will be able to tackle the questions in a clever manner.

Here are some tips for conquering the PSLE Math Paper 2. ### Time management – skip hard ones first

Read, analyse, and identify. In 30 seconds, students should be able to read and analyse the question, then identify which method the question is testing him or her on. Once your child is able to identify which method to use in solve the question, he or she will be able to estimate the number of steps required, the complicacy of the model involved, and decide if it would take 2, 3, 4, or more than 5 minutes to solve. This extra information helps your child to plan his or her time wisely, and secure as many points in the shortest amount of time for paper 2, thus leaving more time to check for errors and eliminate careless mistakes. Of course, the ability to read, analyse, and identify comes with loads of timed practice. So, get started on timed assignments! Keeping to the time limits as stated in the table below would leave your child with 15 minutes to check his or her work.

 Questions Mark Allocation Time allocated 1-5 5 x 2 marks 15 minutes 6-17 3, 4, and 5 marks 60 minutes ### Identify the Right Concept

Most PSLE Math Paper 2 problem sums may look different on the surface, but really, they are just testing the same concept. In fact, at least half the questions would have been something your child had encountered. The only difference would be the names, the object, and the numbers. The way of solving it is exactly the same. The shortcut to identifying the right concept quickly is keywords.

Let us show you what we mean.

Example
There were 260 green and blue marbles in a bag. 1/2 of the green marbles and 3/4 of the blue marbles were then taken out by Amy. In the end, there were 80 green and blue marbles left in the bag. How many of the marbles in the bag were blue at first?

For this question, we cannot make the numerator and denominator the same because the question does not state that there is an equal number for the two quantities.
Therefore, we’ll use the Units (u) and Parts (p) and Simultaneous Equations to solve. At Jimmy Maths, we teach the students the BCA (Before – Change – After) table to clearly illustrate the problem sum.

 Green Blue 1-5 5 x 2 marks 15 minutes 6-17 3, 4, and 5 marks 60 minutes 1-5 5 x 2 marks 15 minutes 4p (all the blue marbles) –> 50 × 4 = 200 (Ans)

Let’s look at the next example that uses a completely different concept by changing some of the keywords.

Example
After using 2/3 of the green paper clips and 3/5 of the red paper clips, I had the same number of green and red paper clips left. If I had 56 paper clips left, how many paper clips did I have altogether at first?

Firstly, ask yourself, “Can you make the denominators the same?”

You can’t, because the fractions are of different wholes.

How about making the numerators the same?

Yes, you can! But you need to find the leftover fraction of each colours first.

Green –> 1 – 2/3 = 1/3

Red –> 1 – 3/5 = 2/5

The question states, “I had the same number of green and red paper clips left.”

Therefore, 1/3 green = 2/5 red

Since the same number of green and red paper clips were left, we make the numerators the same to show that the remainder is equal.

2/6 green = 2/5  red

(Keep in mind that the numerators represent the leftovers, while the denominators represent the clips at first)

Great! What’s next?

2u + 2u = 4u

4u = 56

1u = 14

Since the question ask for the total clips at first,

6u +5u = 11u

11u = 154 (Ans)

Do you see how some changes in the keywords can determine the method being used? Once your child identifies the method for solving the question, he or she can then determine the amount of time require to solve the given question. With that in mind, he or she will begin solving the easier questions first and hence half the battle has been won. ### Do not leave questions blank

Your mind may be empty, but your paper must not be blank. Your child may not be able to see the solution right away after reading the question but he or she will most likely be able to come up with at least one number statement based on the numbers given in the question. Write that down! Writing some workings would at least get your child some marks.

For questions in paper 2, students do get method marks when they are asked to show their workings clearly in the space provided. Even though your child may not arrive at the final answer, he or she has shown some understanding if he or she can get the initial steps right. Any point earned is better than scoring a zero for the question.

Let’s take a look at the following question.

Example
Lesley had some candies. She kept half of the number of candies plus 3 candies. She gave the remaining candies to Jane. Jane ate 1/3 of the candies plus 4 candies. Then Jane gave the remaining candies to Amos. Amos ate 1/4 of the candies and had 42 candies left. How many candies did Lesley have at first?

This question may seem daunting at first and many students give up after reading the question.

But if your child can draw the model for this question, it can become a piece of cake! As you can see, the model enables us to have a clear picture of the relationship of candies between the 3 people.

Since we are given the candies left and we need to find the candies at first, we can use the working backwards approach to arrive at the correct answer.

How do we work backwards? We begin solving the question by reading the last clue first. Amos was mentioned last in the question. Let’s pay attention to that first.

If Amos ate 1/4  of the candies and had 42 candies left, what fraction of his candies is 42 candies?

1 – 1/4 = 3/4

3/4 of Amos -> 42

Number of candies Amos had at first ->42 ÷ 3 × 4 = 56

Let’s apply the same logic to the sentence before that.
If Amos received the remaining candies from Jane after she ate 1/3 and an additional 4 candies, how many candies did Jane begin with? Let’s zoom into the model below for a clearer depiction. It is obvious that once you add 56 to the 4 additional candies Jane had eaten, you would find out what 2/3 of Jane’s candies was.
2/3 of Jane -> 56 + 4 = 60

Number of candies Jane had at first -> 60 ÷ 2 × 3 = 90

Let’s repeat the same logic one more time to find Lesley.
1/2 of Lesley -> 90 + 3 = 93
Number of candies Lesley had at first -> 93 × 2 = 186 (Ans)

Students often trip over questions like these that require them to add and multiply many different numbers. So long as each step is written out clearly, and it is apparent that students know how to derive the answer, method marks would still be given even if there had been a miscalculation or a mislabelling that cause the student to arrive at the wrong answer.

The same tip applies for questions involving Area and Perimeter!

If your child is stuck in a Circle question, find the area or circumference of the circle in the question.

Writing that one single step could earn your child a mark. It beats leaving the question blank! ### Write all workings – do not skip steps

Do list out all the workings required for the question, no matter how simple or straightforward it may be.

Numbers cannot randomly fall from the sky. Any number that is not given in the question needs to be accounted for in your number statements.

Remember that each problem sum tells us a story. Your role is to convert the word statements in the story into the right mathematical statement.

If the question states, ‘…A has 1/3 more than B…’, write down the ratio of A : B = 4 : 3.

If the question states, ‘…A is 20% more than B…’, write down the ratio of A : B = 120 : 100.

If the question states, ‘…A is increased by 10%…’, multiply A by 110/100 to find the new value of A.

You will be surprised at how many marks your child can salvage for PSLE Math Paper 2 by simply writing down all workings!  Unlike the languages, Math allows you to check your work for 100% accuracy.

Although not as complex as reverse engineering, working backwards with the written answer you plugged in would allow you to know at once if your answer is correct. If you arrived at the same numbers provided in the question, your answer is correct. If you managed to come up with a different set of numbers that is different from those given in the question, your answer is wrong.

Example
There are some chickens and cows on a farm. The total number of heads is 28 and the total number of legs is 86. How many chickens and cows are there?

We are showing you an example of a common question that tests students on the Assumption or Guess-and-Check method. The question reads as follows:

Suppose your child used the Guess-and-Check method and arrived at the answer 15 chickens and 13 cows. This would seem correct at a glance since 15 + 13 add up to a total of 28 heads. Let us plug our answers into the question. We already fulfilled one of statements in the question (total number of heads is 28), now, let us see if we would fulfil the next requirement that states that the total number of legs is 86. 15 chickens would mean that there is a total of 15 × 2 legs = 30 legs.

13 cows would mean that there is a total of 13 × 4 legs = 52 legs

30 legs + 52 legs = 82 legs

Uh oh, something is terribly wrong here.

The question clearly stated 86 legs, how did we fall short of that? Perhaps your child could have labelled the statements incorrectly.

In fact, the numbers 15 and 13 are correct, it just did not mean 15 chickens and 13 cows.

Let’s use the Assumption method which is a much faster way.

Assumption Method

1. Let’s assume that all the animals on the farm are cows.

Total number of legs -> 28 × 4 = 112 2. There are, however, only 86 legs in total. This means there is an excess in the number of legs.

What is this excess?

Excess -> 112 – 86 = 26

3. The difference in the number of legs between a cow and chicken is 2. This means that for every cow I remove and replace with a chicken, the total number of legs would decrease by 2.

What is the difference between the item with the higher value/quantity and the item with the lower value/quantity?

Difference -> 4 – 2 = 2

4. Since there is an excess of 26 legs, how many chickens must replace cows so that the total number of legs would decrease by 26?

Opposite -> 26 ÷ 2 = 13 (No. of chickens)

No. of cows -> 28 – 13 = 15

Total number of cow legs -> 15 × 4 = 60

Total number of chicken legs -> 13 × 2 = 26

Adding 60 and 26 indeed gives us a total of 86. Once the numbers you arrived at fit the numbers given in the question, you can say with 100% certainty that you have indeed found the correct answer to the question. Hurray!

If your child works on mastering heuristics, managing time wisely, labelling statements accurately, and checking his or her work carefully, a perfect score is within reach, even for PSLE Math Paper 2.

Remember, practice makes perfect. Study hard and work smart!   ### Follow Jimmy Maths on Telegram here!

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