Most parents tell me that their child’s greatest weakness in Math is Problem Sums. Some say that their child fails to comprehend the question, while others don’t know the right method to solve the question.
Problem sums are introduced to students in Primary 2, and only get more difficult with each year.
Often times, students with misconceptions on problem sums allow these areas of doubt to stack up as they progress on, leading to confusion when tackling tougher questions in Primary 6.
It is without a doubt that the REAL challenge that students face in the exams are…PROBLEM SUMS.
I’ll share some simple tips for solving problem sums faster and with less confusion below.
Problems Sums are usually found in Paper 2, and are always accompanied by a lengthy “story” before the question.
They require students to have a strong ability to comprehend the full story, instinctively know what topics are needed to solve the problem, define the correct concept to solve the problem, and then explain every part of the process through workings, all while under the extreme pressure of exam conditions.
It’s no wonder that children can develop a fear of math and exams.
The good news is…it doesn’t need to be confusing or difficult!
As long as your child has a proven process to follow that delivers the perfect end result every time, almost like a recipe!
Problem Sums pose a huge problem to students due to the sheer number of types that can appear in the exams. This only gets harder when each topic taught in school can be applied to any type of Problem Sum.
Let’s get into some specifics by looking at an example below.
Jane spent 1/3 of her money on a hand phone and donated 3/4 of the remainder to charity. If she had $360 left, how much did she have at first?
The Problem Sum above has the topic of Fractions integrated into the question. Examiners can simply change the Problem Sum type by replacing the Fractions with Percentages.
As such, you can see why there are so many types of Problem Sums being tested.
In our research into past year PSLE and school papers, we have found that over a hundred different types of Problem Sums can appear in PSLE. So we’ve taken all the Problem Sum types and grouped them into only 15 basic Concepts. In other words, your child only needs to master these 15 Concepts to overcome Problem Sums.
Every problem sum has an underlying concept, and every concept has certain methodologies to tackle.
Concepts are like mental shortcuts, and these shortcuts are able to guide the child directly to the right methods to use without wasting too much time.
With the correct concept identified, they will know what to expect. They will know the first step to take and they will also recall the areas they need to pay more attention to.
To illustrate this, we will explain the 4 Step Assumption Method used to solve the Guess and Check Problem Sum Concept.
There are a total of 16 goats and ducks in a farm. If there are a total of 52 legs, how many ducks are there?
How would you solve this question?
Teachers at school teach students the Table Method, whereby a Guess and Check table is drawn, listing the possible combinations of Goats and Ducks one by one. This is very time consuming for students.
The table you see below is expected to be drawn by students in 3 minutes, since the mark allocation for this question is 3 marks.
Most students struggle to keep up under a time-limited and pressured environment.
1 Goat = 4 legs
1 Duck = 2 legs
|No. of Goats||Goat Legs||No. of Ducks||Duck Legs||Total Legs|
|15||15 x 4 = 60||1||1 x 2 = 2||60 + 2 = 62|
|14||14 x 4 = 56||2||2 x 2 = 4||56 + 4 = 60|
|13||13 x 4 = 52||3||3 x 2 = 6||52 + 6 = 58|
|12||12 x 4 = 48||4||4 x 2 = 8||48 + 8 = 56|
|11||11 x 4 = 44||5||5 x 2 = 10||44 + 10 = 54|
|10||10 x 4 = 40||6||6 x 2 = 12||40 + 12 = 52|
Answer: There are 6 ducks.
It is apparent that using the Table Method is very time consuming as the student is required to draw the table, and guess till he/she gets the answer. It will get even more tedious to draw should the numbers be increased to a larger degree.
The easier method that we teach is shown below.
Step 1. Assume all are Goats
16 x 4 = 64 legs
Step 2. Big difference – Difference between assumed total legs and actual total legs
64 – 52 = 12
Step 3. Small difference – Difference in legs between 1 goat and 1 duck
4 – 2 = 2
Step 4. Big Difference ÷ Small Difference
12 ÷ 2 = 6 Ducks
Answer: There are 6 ducks.
This Concept can be applied for any Guess and Check Question, exactly like a recipe.
This Assumption Method is easy to understand as it only consists of 4 steps. The idea behind the 4 steps are very simple, and we will be more than happy to explain the steps in detail to parents and students who are interested.
As students practice and get the hang of this method, they can do questions faster and save time, and utilise this extra time to check their answers. Furthermore, lesser steps also means lesser opportunities to make careless mistakes.
Problem sums like this may prove to be challenging to children at the beginning. But understanding the questions fully, knowing the underlying concept and the right method to solve greatly reduces the ambiguity.
If you would like to know more about Concepts like this, sign up today for your free 20-minute phone consultation.
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Math Consultant at Math Scholars Singapore
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