Singapore Math Guru

Acing PSLE Foundation Mathematics, Common Mistakes & Misconceptions

Common mistakes, misconceptions and acing PSLE

This article is written to help parents whose weaker children who are taking the Foundation Mathematics paper or are just having difficulty in basic math skills. We also try to address common mistakes and misconceptions.

With regards to some of our weaker student, they tend to make certain mistakes that we see over and over again. And we are going to highlight them here in this article as a way to help parents get into the minds of these students, and to find a way to help parents help them. We will be highlighting some of these glaring mistakes  through the use of exemplary questions to help our weaker students and parents.
Mistake 1 : Students do not read carefully – Students do not read the final sentence which is usually the key to getting full marks for a question .
Question:
John has 3456 marbles.
Mary has 2345 more marbles than John.
How many marbles do they have?
Typically, for weaker students, they tend to oversimplify a question. A weaker student would do this:
3456 + 2345 = 5801
They have 5801 marbles.
Now, what is the question asking for? They are asking for the total. Some of our weaker students have a tendency to just oversimplify the problem. By not reading carefully, they think that the question is asking for the number of marbles that Mary has. Either that or they seem to think that Mary has 2345 marbles which is not factual.
In this case, method marks awarded is 0 and answer marks awarded is also 0.
The student has failed to understand the gist of the question.
The question is stating that Mary has 2345 more marbles than John. So if we add 2345 to 3456(which is what John has), we are getting what Mary has.
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3456 + 2345 = 5801
Mary has 5801 marbles.
5801 + 3456 = 9257
They have 9257 marbles altogether.
The other issue could be a weaker student may not be able to solve the question just by reading the question like that. They have to complement that with a comparison model. A comparison model is recommended regardless of the level of student ability. A lot of times, comparative statements like”more than”, “less than”, “twice as much”, “greater than” etc require a model to help the student fully appreciate and understand the question.In the case above, the student gets M1 and A1.
If we may add, being able to read carefully is a very important skill in solving Mathematics questions. It requires one to be detailed and to have a patient mind. A student may brush the above question as too easy and fail to read carefully. Sometimes, the problem is not that the student is weak in Maths but rather, it may signify a language problem in a sense that students have a difficulty interpreting the English language. It may be that way because English is not a spoken language at home. If you do some research as to why some children can’t read as well as the stronger readers, you will find that there is no clear answer. But what we recommend is this for students who are not strong readers :
1. Read the sentence twice in your head and visualize John. Give that sentence meaning and inject life into the character in your head.
John has 3456 marbles.
John has 3456 marbles.
2. Underline
John has 3456 marbles.
3. Repeat process with next sentence. Read the next sentence twice in your head. Visualize Mary.
Mary has 2345 more marbles than John.
Mary has 2345 more marbles than John.
4. Underline
Mary has 2345 more marbles than John.
5. React. Draw a model.
6.React. Perform workings & computations.
At this point, hopefully the student understands that Mary really has 2345 more marbles than John and it is not the case where Mary has 2345 marbles.
3456 + 2345 = 5801
Mary has 5801 marbles.
Now the student understands that Mary has 5801 marbles.
7. Read the next sentence twice in your head.
How many marbles do they have?
How many marbles do they have?
8. Underline.
How many marbles do they have?
“they” refers to the total.
9. React. Perform workings & computations.
5801 + 3456 = 9257
They have 9257 marbles altogether.
Wow, if you have made it this far, congratulations. But, we do this so that we can help your child, do the right things, think the right way and hopefully get full marks for the question. If reading is an issue for your child, we recommend reading a sentence twice. If you can tell, we do not move on until we have exhausted all clues, workings and computations from a sentence. In this way, it keeps a child super focused on one thing at a time. A lot of times, students suffer from information paralysis. A student reads the entire question but still does not know what to do because there is too much information in the question. They try to see the conclusion but can’t. They become paralyzed and panic sets in.
To prevent this, read and process one sentence at a time. For more refer to “The Importance Of Underlining.”
www.singaporemathguru.com has over 300 hours of video explanations. In our video explanations to our students, we explain all the do’s and the don’ts , taught by teachers all around Singapore. For example, we encourage breaking problem sums into chunks that can be acted on. This is a fundamental skill that the best students have. They know how to break questions into chunks and then, they act on that information. They may draw a model and a branch. The important thing is to react and not over analyse for starters. Once, you have all the necessary information in place, the brain and the mind will automatically put it all together to figure out what bit of information is required next and what needs to be done to get that bit of information. Our videos also highlight the different methods students can take to achieve the desired goal of getting correct. We often complement the model method with the units method to help all students understand. In our videos also, we try to answer the what, why, who, when, whose and how questions that a student often asks and we do it over and over again in all our videos.
Let’s look at another question.
John has 738 beads.
He has 57 more than Mary.
How many beads do both of them have?
The weaker students will do this :
738 + 57 = 795 ——– [M0]
795 + 738 = 1533 ——– [A0]
Once again, the weak student sees the word “more” and take it to mean that the 738 + 57 is Mary. Once again, the student in question has some reading and interpretation difficulty. It is important for parents to exercise patience and to really work through with the child on this. In this case 0 marks will be given. M0 and A0.
The correct thing to do is to follow the steps as given in the first question i.e. To read a sentence twice, underline keywords, react by drawing a model and performing workings before moving on to the next sentence and then repeating the process.
Draw a model as what you see below.
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For access to such questions above, do take a look at the links here:
Let’s look at  another question.
Before we do so, we apologize for using John and Mary as characters all that often. Our brains just lack that creativity for now so please bear with us. We are trying to get this out as quick as possible.
John and Mary have 1200 marbles.
If John has 100 more marbles than Mary, how many marbles does John have?
The weaker students will do this:
1200/2 = 600
600 + 100 = 700
So here, they assume that John and Mary have an equal number of marbles. The weaker students here demonstrate a certain tendency to oversimplify the problem sum.
Since this is a more than/less than question, drawing models is highly recommended.
Once again, we prescribe the steps to help weaker students here because normally, the better students do not have such a problem and if they do, it is a one off event. The weaker students normally encounter such problems again and again.
So these are the steps:
1. Advise the student to read the first sentence twice.
John and Mary have 1200 marbles.
John and Mary have 1200 marbles.
Does John and Mary have the same number of marbles? No. There is no indication of that. So please do not assume.
2. Underline key information.
John and Mary have 1200 marbles.
3. At this point, we can’t react to the question yet. So read the next sentence twice.
If John has 100 more marbles than Mary, how many marbles does John have?
If John has 100 more marbles than Mary, how many marbles does John have?
4. Underline.
If John has 100 more marbles than Mary, how many marbles does John have?
The word “If” means it never happened. It is just an if. From this sentence we know that John has 100 more than Mary.
5. React by drawing a model when you see “more than” and then perform workings and computations.
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So from the model, we know that John has 100 more than Mary.
2 units = 1200 – 100
2 units = 1100
1 unit = 1100/2 = 550
550 + 100 = 650
John has 650 marbles.
Once again, congratulations if you have read this far. The reason why this is such a lengthy and dry article is because the we don’t want to skip the steps that should be taken to help students to solve a question. If they students read each sentence twice, underline and then react by drawing the model , the whole idea here is that by the time they are done doing so, the sentence would have made enough impression on the mind such that the student will be able to understand it and eventually is able to act on the information and solve it. If the mind can consistently think in those steps, solving a question would be easier.
Let’s take a look at another question.
John has some marbles. He gave 30% of his marbles away and had 210 marbles left.
How many marbles did John have at first?
The weaker students will do this:
30/100 x 210 = 63
Again an interpretation issue on the student’s part.
The student must be able to interpret that after giving 30% away, he has 70% left. Hence, 70% of the total must be equal to 210 marbles.
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70% of marbles = 210
1%  of marbles = 210/70 = 3
100% of marbles = 3 x 100 = 300
John had 300 marbles at first.
John has some beads.
20% of the beads are yellow in colour and 25% of the remaining beads are black in colour.
The rest are white beads.
If John has 1200 white beads, how many beads does he have in total?
In this question here, students are not able to differentiate ’20% of the beads’ and ’25% of the remaining beads’ actually belong to 2 different bases, 2 differing references.
This is what they do:
20% + 25% = 45%
55% of the beads = 1200
And when they work it our further, they find that they cannot get a whole number for 100% of the beads. This approach is wrong. So once again, you can tell from this that the student oversimplifies the problem and usually, they misinterpret the question. This is often a language issue on the part of the student.
The correct interpretation is this:
100% – 20% = 80%
80% of the beads are the ‘remaining beads’.
25/100 x 80% refers to 25% of the remaining beads.
So,
25/100 x 80% = 20%
20% of all the beads are black.
80% – 20% = 60%
60% of the beads = 1200
100% of the beads = 1200/60 x 100 = 2000
John has 2000 beads in total.
So the remedy to this is to read, underline and react. Read each sentence twice and make sure the meaning sinks in. Underline ’20% of the beads’ and ’25% of the remaining beads’ and understand its meaning. Then perform computations. Repeat process.
Let’s look at another question.
John has some rubber balls.
He gave 3/8 of the rubber balls away and had 80 rubber balls left.
How many rubber balls did John have at first?
For this question, the weak student will do this:
3/8 x 80 = 30
This is wrong.
They see the word “of” and take it that they must multiply. Again, an oversimplification of the problem.
Students should complement this with a model.
Draw 8 boxes and shade 3 boxes. 5 boxes refer to the 80 balls left. Hence:
5
80/5 = 16
16 x 8 = 128
John has 128 balls.
Let’s look at another question.
John has some balls.
He gave 1/5 of them away.
Next, he gave 1/2 of the remaining balls away.
What fraction of the balls did he give away?
The weak student will do this:
1/5 + 1/2 = 7/10
This is wrong.
Once again, an oversimplification of the problem.
1 – 1/5 = 4/5
4/5 of the balls remained.
1/2 x 4/5 = 2/5
1/5 + 2/5 = 3/5
He gave 3/5 of the balls away.
This has been a rather lengthy article and we hope that you have found it useful. It is not easy to address these common mistakes in the weaker students. Ultimately, it really boils down to reading carefully and interpreting correctly. We hope that this article has helped you and the truth of it is that in weaker students, the tutor or teacher can only do so much for a session per week. Parents must get their hands dirty and really learn to guide their children. And in our opinion, it can be done but it takes effort and discipline on the part of the parents and a mindset that is not entirely and overly reliant on the tutor or teacher. In a group tutorial setting, we assure you that it would be very hard to address the issues above especially when there are so many students in a group. If parents do find it difficult to guide their kids, we suggest  a subscription to 330 hour video solutions library, where the teacher guides the child step by step in a video, while emphasizing the dos and the don’ts. Parents who have signed up have found it particularly useful due to the extensive database of targeted video solutions when the child attempts the question. You can watch the video alongside with your child and reinforce from there.
Of course , there are more common mistakes to look out for and we are by no means exhausting all the common mistakes in this article here. Do look out for more of this and please share this with others if you have found this helpful.
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