Using Mental Strategies to Solve Word Problems

1. Listen for the operation

A word problem is a story with a calculation hidden inside. Your first job is not to calculate — it is to decide what to calculate. Certain words and phrases are clues to the operation. Learn them as a vocabulary, the way you learn spellings.

Notice the clever reverse questions at the bottom of each row. "What must be added to 63 to make 100?" uses the word added, but you answer it by subtracting (or by counting on). "What must be divided by 4 to give 9?" uses the word divided, but you answer it by multiplying. Each operation has an opposite (an inverse), and these questions test whether you can use it.

2. A plan for every word problem

1. 1Read the whole problem. Picture the situation.
2. 2Find the question: what exactly must you find, and in what unit?
3. 3Choose the operation(s) using the key words and your picture.
4. 4Make the numbers friendly: change units, round and adjust, halve and double.
5. 5Calculate mentally, then check: is the answer sensible? Does it have the right unit?

Use this plan on the curriculum question: Find the cost of three 5 kg bags of rice at GH₵2 per kg. Picture three bags, each holding 5 kg. The question is a cost in cedis. First find the total mass: 3 × 5 = 15 kg. Then the cost: 15 × 2 = GH₵30. Sensible? Each bag costs 5 × 2 = GH₵10, and three bags cost GH₵30 ✓.

For subtraction, counting on is often faster than taking away. To answer "What must be added to 63 to make 100?", jump from 63 to the next ten, 70 (that is 7), then from 70 to 100 (that is 30). Add the jumps: 7 + 30 = 37. The number line below shows the jumps.

▶ Counting on from 63 to 100 in two friendly jumps: +7 and +30 make 37.

3. Money, time and measures

Many word problems mix units. Mental work is much easier if you know the unit facts by heart and change to a single unit before calculating. Remember: 100 pesewas = GH₵1; 60 minutes = 1 hour; 100 cm = 1 m; 1,000 ml = 1 litre; 1 dozen = 12.

Money. One dozen eggs at 80 pesewas each costs 12 × 80 = 960 pesewas. Divide by 100 to change to cedis: GH₵9.60. Another way: 80 pesewas = GH₵0.80, and 12 × 0.8 = 9.6.

Time. To find the minutes from 10:15 a.m. to noon, count on in friendly jumps: from 10:15 to 11:00 is 45 minutes, and from 11:00 to 12:00 is 60 minutes. Altogether 45 + 60 = 105 minutes (1 hour 45 minutes).

▶ Count on from 10:15 to 11:00 first (45 minutes), then a full hour to noon.

Fractions of a measure. What fraction of a litre is 250 ml? A litre is 1,000 ml, so 250 ml is $\frac{250}{1000}=\frac{1}{4}$ of a litre. In the same way, 60 pesewas as a decimal of GH₵2.40 is 60 ÷ 240 = $\frac{1}{4}$ = 0.25.

4. Shapes, angles and remainders

Mental maths quizzes also use facts from geometry. The area of a square is side × side, so a square board with area 81 cm² has a side of 9 cm (because 9 × 9 = 81) and a perimeter of 4 × 9 = 36 cm. The angles of a triangle add up to 180°, so if two angles add up to 98°, the third angle is 180° − 98° = 82°.

Division problems often leave a remainder, and you must decide what it means in the story. "How many 21 cm pieces can I cut off a string one metre long?" Change 1 m to 100 cm. Then 21 × 4 = 84 and 21 × 5 = 105, which is too long. So you get 4 pieces, with 100 − 84 = 16 cm left over. You cannot round up to 5 pieces, because the fifth piece would be too short.

Worked examples

Try each one yourself first, then open the solution and compare every step.