Selective maths: turning a word problem into an equation

Quick Answer

Write down what each quantity is, turn the sentence into an equation one phrase at a time, solve it, then put the answer back into the original words to check. This page has ten original problems worked that way. It is general practice from Braintree Coaching Australia, not a copy of the Department's questions.

Who is this set for?

Year 5 and Year 6 children who can solve a one-step word problem and are ready to write the sentence as an equation before solving it. Every problem has one unknown and needs no calculator.

The NSW Department of Education describes Selective Mathematical Reasoning as 35 questions in 40 minutes with no calculator, and publishes its own sample questions with explanations there. Use those for the real format. For more worked samples see our Selective practice hub and the format guide.

How do I turn words into an equation?

1. Quantities. Say what the letter stands for, in words: "n is Leo's stickers". Then say what every other quantity is in terms of n.
2. Equation. Translate one phrase at a time. Read each phrase back before moving on.
3. Check. Put the answer into the story, in the story's own words, and see that every sentence is true.

Two phrases cause most of the trouble. "5 more than Leo" means Leo's number plus 5, so the person with more has the bigger number. "Three times as many girls as boys" means girls = 3 × boys, so the boys are the smaller group.

The questions

Try each on paper first. Choose A, B, C or D.

Question 1. Three consecutive whole numbers add to 78. What is the largest of the three?

• A. 25
• B. 26
• C. 27
• D. 28

Question 2. Two consecutive even numbers add to 46. What is the smaller number?

• A. 22
• B. 23
• C. 24
• D. 44

Question 3. Mia has 5 more stickers than Leo. Together they have 41 stickers. How many stickers does Mia have?

• A. 18
• B. 23
• C. 36
• D. 46

Question 4. A choir has three times as many girls as boys. There are 36 children in the choir. How many boys are in the choir?

• A. 27
• B. 12
• C. 18
• D. 9

Question 5. Tom is 6 years younger than his brother. Their ages add to 30. How old is Tom?

• A. 15
• B. 12
• C. 18
• D. 24

Question 6. Maya is 8 years old and her father is 38. In how many years will her father be three times as old as Maya?

• A. 14
• B. 15
• C. 7
• D. 45

Question 7. A notebook costs $2 more than a pen. Three pens and one notebook cost $26 altogether. How much does the notebook cost?

• A. $5
• B. $6
• C. $6.50
• D. $8

Question 8. A rectangular garden has a perimeter of 46 m. One side is 15 m long. How long is the other side?

• A. 8 m
• B. 16 m
• C. 23 m
• D. 31 m

Question 9. Jo, Kim and Lee share 60 stickers. Jo gets twice as many as Kim, and Lee gets 6. How many stickers does Kim get?

• A. 27
• B. 36
• C. 18
• D. 54

Question 10. I think of a number, multiply it by 4, then subtract 7. The answer is 29. What number did I think of?

• A. 5.5
• B. 9
• C. 7.25
• D. 36

Answers with quantities, equation and check

Answer key: Q1 C, Q2 A, Q3 B, Q4 D, Q5 B, Q6 C, Q7 D, Q8 A, Q9 C, Q10 B.

Question 1: C, 27.

• Quantities: the smallest number is n, then n + 1, then n + 2. The question asks for the largest, which is n + 2.
• Equation: n + (n + 1) + (n + 2) = 78, so 3n + 3 = 78, 3n = 75, n = 25. The largest is 27.
• Check: 25 + 26 + 27 = 78, and the three numbers follow one after another, so the largest is 27.

Question 2: A, 22.

• Quantities: the smaller even number is n, the next even number is n + 2.
• Equation: n + (n + 2) = 46, so 2n + 2 = 46, 2n = 44, n = 22.
• Check: 22 and 24 are both even, they follow each other in the even numbers, and 22 + 24 = 46.

Question 3: B, 23.

• Quantities: let m be Mia's stickers. Leo has 5 fewer than Mia, so Leo has m − 5.
• Equation: m + (m − 5) = 41, so 2m − 5 = 41, 2m = 46, m = 23.
• Check: Mia has 23 and Leo has 18. Together that is 41, and Mia has 5 more than Leo.

Question 4: D, 9.

• Quantities: let b be the number of boys. Girls are three times the boys, so girls are 3b.
• Equation: b + 3b = 36, so 4b = 36, b = 9.
• Check: 9 boys and 27 girls make 36 children, and 27 is three times 9, so there are three times as many girls as boys.

Question 5: B, 12.

• Quantities: let t be Tom's age. His brother is 6 years older, so the brother is t + 6.
• Equation: t + (t + 6) = 30, so 2t + 6 = 30, 2t = 24, t = 12.
• Check: Tom is 12 and his brother is 18. Their ages add to 30, and Tom is 6 years younger.

Question 6: C, 7.

• Quantities: let x be the number of years from now. Maya will be 8 + x and her father will be 38 + x.
• Equation: 38 + x = 3 × (8 + x), so 38 + x = 24 + 3x, 14 = 2x, x = 7.
• Check: In 7 years Maya is 15 and her father is 45. Her father is three times as old as Maya, 45 = 3 × 15.

Question 7: D, $8.

• Quantities: let p be the cost of a pen in dollars. The notebook costs $2 more, so it is p + 2.
• Equation: 3p + (p + 2) = 26, so 4p + 2 = 26, 4p = 24, p = 6. The notebook is p + 2 = 8.
• Check: Three pens at $6 are $18, and the $8 notebook makes $26. The notebook costs $2 more than a pen.

Question 8: A, 8 m.

• Quantities: let w be the other side in metres. A rectangle has two sides of 15 m and two of w.
• Equation: 2 × (15 + w) = 46, so 15 + w = 23, w = 8.
• Check: The garden is 15 m by 8 m, so going round it is 15 + 8 + 15 + 8 = 46 m.

Question 9: C, 18.

• Quantities: let k be Kim's stickers. Jo has twice as many as Kim, so Jo has 2k. Lee has 6.
• Equation: k + 2k + 6 = 60, so 3k = 54, k = 18.
• Check: Kim has 18, Jo has 36 and Lee has 6. That is 60 stickers, and Jo has twice as many as Kim.

Question 10: B, 9.

• Quantities: let n be the number I thought of. Multiply by 4 gives 4n. Subtract 7 gives 4n − 7.
• Equation: 4n − 7 = 29, so 4n = 36, n = 9.
• Check: Start with 9, multiply by 4 to get 36, subtract 7 to get 29, which is the answer in the story.

Where do children go wrong?

The wrong options come from a small set of slips:

• Writing the sentence the wrong way round. "5 more than Leo" written as Leo's number take away 5. "Three times as many girls as boys" written as boys = 3 × girls. Both give a tidy whole number, so the wrong answer looks fine until it is put back into the story.
• Answering for the letter, not the question. The child solves for n and stops, when the question asked for the largest number, the notebook or Kim's stickers.
• Skipping the check. An answer such as 23 for "the smaller of two consecutive even numbers" fails in one glance at the story.

If your child gets one wrong, ask them to read the Check line aloud and find the sentence that is not true.

Can my child write a problem for a given equation?

Give your child this equation: 3n + 4 = 25. Ask them to write a short story it could solve, then solve it, then check the answer in their own story. More than one story is right. For example: "Three bags hold the same number of apples and 4 loose apples sit beside them. There are 25 apples in all" works, and so does "I think of a number, multiply by 3, and add 4 to get 25". Both give n = 7.

For a test-day timed set, try our free mock tests or the next steps on the Selective preparation course page.