Some terminology of strategies taught in tuition centres are:
1) Changed families (Applicable in 'Before-After' questions ONLY)
- Total unchanged
E.g.
At a book fair, there were 4/5 as many adults as children. After 120 children left and 120 adults entered the book fair, there were twice as many adults as children. How many adults were at the book fair at first?
- Difference unchanged
E.g.
Henry’s age is 2/9 of his grandmother’s. His grandmother will be 100 years old in 19 years’ time. In how many years’ time will Henry’s age be 1/4 that of his grandmother’s?
- External Unchanged or One Item Unchanged or One Quantity Unchanged
E.g.
Tom went shopping with some $5-notes and 126 $10-notes. The ratio of $10-notes to $5-notes was 9 : 7. After spending some $5-notes, the ratio of $10-notes to $5-notes became 7 : 2. What was the total value of the $5-notes spent by Tom?
1) Changed families (Applicable in 'Before-After' questions ONLY)
- Total unchanged
E.g.
At a book fair, there were 4/5 as many adults as children. After 120 children left and 120 adults entered the book fair, there were twice as many adults as children. How many adults were at the book fair at first?
- Difference unchanged
E.g.
Henry’s age is 2/9 of his grandmother’s. His grandmother will be 100 years old in 19 years’ time. In how many years’ time will Henry’s age be 1/4 that of his grandmother’s?
- External Unchanged or One Item Unchanged or One Quantity Unchanged
E.g.
Tom went shopping with some $5-notes and 126 $10-notes. The ratio of $10-notes to $5-notes was 9 : 7. After spending some $5-notes, the ratio of $10-notes to $5-notes became 7 : 2. What was the total value of the $5-notes spent by Tom?
- External Changed or Everything Changed or All Items Changed (Units & Parts)
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2) Gap & Difference/Excess & Shortage
E.g.
Ronald bought some lollipops for his friends. If he gives 3 lollipops for each friend, he will have 21 lollipops left. If he gives 5 lollipops for each friend, he will have 15 lollipops left.
(a) How many friends did Ronald give his lollipops to?
(b) How much lollipops did he buy?
3) Advanced Model Drawing
E.g. 1
Ella and Jenny had $252 altogether. Ella spent twice as much money as Jenny. The amount of money Jenny had left was $24 more than what she had spent. She had twice as much money left as Ella. How much money did Ella have at first?
E.g. 2
Mr Chen baked 160 more egg tarts than muffins. After selling 3/4 of the egg tarts and 1/2 of the muffins, he had a total of 118 egg tarts and muffins left.
(a) How many egg tarts were not sold?
(b) How many egg tarts and muffins did he sell altogether?
4) Equal Fractions ("Make the numerator to be the same")
E.g.
In a school hall, 5/6 of the boys and 2/3 of the girls wear spectacles. The number of boys and girls who wear spectacles is the same. Among the pupils who did not wear spectacles, there are 54 more girls than boys. How many pupils are there in the school hall?
5) Repeated Identity
E.g. 1
A ribbon is twice as long as a cane. The cane is thrice as long as the stick. The total length of the ribbon, the cane and the stick is 230 cm. Find the length of the ribbon.
E.g. 2
Jason, Eileen and Grace share some playing cards. Jason has 1/4 as many cards as the total of Eileen’s and Grace’s cards. The ratio of Eileen’s cards to the total cards is 3 : 10. Given that they have a total of 80 playing cards, how many more playing cards does Grace have than Jason?
6) Number/Quantity x Value
E.g.
Ronald bought some lollipops for his friends. If he gives 3 lollipops for each friend, he will have 21 lollipops left. If he gives 5 lollipops for each friend, he will have 15 lollipops left.
(a) How many friends did Ronald give his lollipops to?
(b) How much lollipops did he buy?
3) Advanced Model Drawing
E.g. 1
Ella and Jenny had $252 altogether. Ella spent twice as much money as Jenny. The amount of money Jenny had left was $24 more than what she had spent. She had twice as much money left as Ella. How much money did Ella have at first?
E.g. 2
Mr Chen baked 160 more egg tarts than muffins. After selling 3/4 of the egg tarts and 1/2 of the muffins, he had a total of 118 egg tarts and muffins left.
(a) How many egg tarts were not sold?
(b) How many egg tarts and muffins did he sell altogether?
4) Equal Fractions ("Make the numerator to be the same")
E.g.
In a school hall, 5/6 of the boys and 2/3 of the girls wear spectacles. The number of boys and girls who wear spectacles is the same. Among the pupils who did not wear spectacles, there are 54 more girls than boys. How many pupils are there in the school hall?
5) Repeated Identity
E.g. 1
A ribbon is twice as long as a cane. The cane is thrice as long as the stick. The total length of the ribbon, the cane and the stick is 230 cm. Find the length of the ribbon.
E.g. 2
Jason, Eileen and Grace share some playing cards. Jason has 1/4 as many cards as the total of Eileen’s and Grace’s cards. The ratio of Eileen’s cards to the total cards is 3 : 10. Given that they have a total of 80 playing cards, how many more playing cards does Grace have than Jason?
6) Number/Quantity x Value
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7) Branching
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