If you think that just knowing your numbers holds the key to acing the Primary School Leaving Examination’s (PSLE) Maths paper, think again. Junior will need to understand the words as well, points out maths consultant at ACE-Learning Systems, Dr Lai Chee Chong. Notes the author of Ministry of Education-approved maths textbooks, “Word problems require more thinking than straightforward calculations.”
Dr Lai adds that students should adopt Polya’s effective problem-solving strategy to crack word problems. Named after the Hungarian mathematician, George Polya, this method is split into four steps:
(a) Understand the problem Break down the question into chunks of information and try to make sense of them in parts.
(b) Make a plan To solve it, your child should stick to the approach he is most familiar with. However, remind him that he should be ready to change his method, if necessary.
(c) Solve the problem Be systematic ― know what steps to take and when stuck, relook and retrace your steps.
(d) Look back Don’t assume that the solution you have arrived at is the only correct one. ALWAYS check to see if it satisfies the question.
Apply these four steps when attempting practice papers. If your child makes it a habit, it will shave the time he spends solving problems. Besides adopting this critical strategy in solving word problems, Dr Lai stresses that junior’s revision should also cover four topics pupils commonly struggle with:
Break down the question into chunks of information and try to make sense of them in parts.
Problem Topic #1: Geometry
PROBLEM Not spotting the right geometric properties of shapes in a question.
TRY THESE Pull out the critical information the question provides and pencil it in the diagram, in case you need to make changes. Make inferences, then add this information to the diagrams: Label the right angles, parallel lines and equal lengths. Remember to be flexible ― to analyse the problem, turn the question paper (not your head) to examine the diagram and work out the answer.
Problem Topic #2: Area
PROBLEM Composite figures — a combination of different shapes in different sizes — tend to muddle students’ minds. Dr Lai cautions, “Beware of overlapping areas, too!”
TRY THESE Divide the composite into parts — triangles, circles, squares, rectangles — then use the additional information to find the area of each shape. As the composite is the sum of all the shapes put together, you arrive at the total area by adding up all its shapes/parts.
Problem Topic #3: Volume
PROBLEM Calculating the volume of composite solids — a combination of different solids in different sizes — can also be tricky.
TRY THESE Divide the composite into parts, then calculate the volume of each one. As the volume of the composite is cumulative, you get the volume of the composite by totalling the volume of each shape.
Click to learn about common pitfalls to avoid!
Problem Topic #4: Speed
PROBLEM Speed is calculated using time and distance, which tests your child’s understanding of all these three concepts.
TRY THESE Draw the distance-speed-time triangle (D/S x T), then fill up each segment of the triangle with the correct information. Take note that you may be given the speed in kilometres per hour, while the time is in minutes. So, you’ll need to convert it to the common unit of measurement, such as from minutes to hours.
PITFALLS TO AVOID
While time is of the essence in the exams, remind your child that he must not fall prey to these easy to avoid but common mistakes:
* Pitfall #1: Jumping to conclusions Don’t plunge into giving a solution without understanding the entire question properly.
DO THIS Read through the question thoroughly, so you don’t misread or misinterpret it. Underline, circle or highlight vital information and analyse these before offering a solution.
* Pitfall #2: Not having a plan or strategy to solve the problem Your child will waste precious time in the exams if he has no clue how he is going to work out the solution.
DO THIS Practice makes perfect. So, identify and apply problem-solving strategies — by learning and using the right formulas. If he needs to draw a model or diagram as part of his answer, make sure it represents the problem correctly.
Don’t plunge into giving a solution without understanding the entire question properly.
* Pitfall #3: Untidy and illegible handwriting Is that a zero or a six? A one or a seven? Scribbling down one’s working can actually cost junior dearly in the exams. He might even arrive at the wrong answer based on his own bad handwriting! Also, the person marking the script is not going to spend time trying to decipher a pupil’s handwriting.
DO THIS Urge junior to use practice papers as an opportunity to get his handwriting in order. Dr Lai says to be mindful of the ones (1) and sevens (7), sixes (6) and zeroes (0), plus the symbols for plus (+) and multiply (x). Don’t forget the placement of decimal points, too!
* Pitfall #4: Using the wrong unit of measure Conversion is a vital concept to master as part of the maths syllabus. So, giving your answers in the wrong unit of measurement is an all too easy way to lose marks.
DO THIS After attempting the question, read it one more time to ensure that you answer is in the correct unit of measure.
* Pitfall #5: Not double-checking Drawing models and diagrams lets junior get a clearer idea as to what the question is asking, but only if it is correctly labelled. He must also check if his answer suits the context of the question.
DO THIS Use a question mark on the diagram or model to show what the question is asking. Also, plug your answer back into the question to see if it make sense, Dr Lai advises.
Dr Lai Chee Chong is a maths consultant of ACE-Learning Systems and author of Ministry of Education-approved maths textbooks.
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