Part A — Multi-Step Word Problems
Real problems rarely tell you which operation to use. Read carefully, decide what each step needs, and keep your working tidy so you can check it.
1
A book costs $24. The shop takes 25% off in a sale. How much do you save, and how much do you pay?
2
There are 240 students at a school. ¾ of them walk or cycle to school. How many is that? How many do not?
3
A recipe for 4 people needs 600 g of flour. How much flour is needed for 10 people? Show your reasoning.
4
Three friends share the cost of a $45 gift equally and also buy a card for $6 shared equally. How much does each friend pay in total?
5
Multi-step. A cinema sells 320 tickets. 40% are child tickets at $8 and the rest are adult tickets at $14. How much money is taken altogether?
6
Prove it. Leah says “finding 50% then 10% of a number is the same as finding 60%.” Is she right? Test it on $80 and explain.
Part B — Order of Operations & Mental Strategies
When an expression has several operations, we follow an agreed order: brackets first, then × and ÷ (left to right), then + and − (left to right). Smart mental strategies — doubling, halving, and compensation — can make hard calculations quick.
1
Evaluate, using the correct order of operations.
(a) 5 + 3 × 4 =
(b) (5 + 3) × 4 =
(c) 20 − 6 ÷ 2 + 1 =
2
Insert brackets to make each sentence true.
(a) 6 + 2 × 5 = 40
(b) 12 − 4 − 3 = 11
3
Use a smart mental strategy (doubling, halving or compensation) and explain it.
(a) 25 × 16 =
(b) 198 + 47 =
4
Estimate first, then calculate. For 312 × 19, write a sensible estimate, then the exact answer. How close were you?
5
Find the error. A student wrote 8 + 4 × 2 = 24. Explain the mistake and give the correct answer.
6
Open challenge. Using exactly four 4s and any operations and brackets, write an expression equal to 24. Can you find a second way?