The RUCSAC Strategy

RUCSAC is a handy way to remember the steps for solving word problems. Follow each letter in order:

R

Read the problem

U

Understand what is asked

C

Choose an operation

S

Solve the problem

A

Answer in a sentence

C

Check your work

Clue Words for Operations

Certain words in a problem tell you which operation to use. Look for these clues:

Addition (+)

total, altogether, sum, combined, more than, increase

Subtraction (−)

difference, less than, fewer, how many more, left over, decrease

Multiplication (×)

times, each, every, groups of, double, triple, product

Division (÷)

share, divide, split equally, each person gets, half, quarter

Multi-Step Problems

Some problems need two or more steps to solve. You must work out one part before you can find the final answer.

Example: The School Canteen

"The canteen sold 48 pies on Monday and 35 pies on Tuesday. Each pie costs $4. How much money did the canteen make in total?"

Step 1: Find the total pies: 48 + 35 = 83 pies

Step 2: Multiply by the price: 83 × $4 = $332

Answer: The canteen made $332 in total.

Using Bar Models

A bar model is a diagram that helps you see what is happening in a word problem. Draw bars to represent the numbers.

"Mia saved $125 and her brother saved $87. How much more did Mia save?"

Mia

$125

Brother

$87

?

Answer: $125 − $87 = $38 more.

Key Vocabulary

Operation

A mathematical process: addition, subtraction, multiplication or division.

Multi-Step

A problem that needs two or more calculations to find the answer.

Bar Model

A diagram using bars to represent numbers and show relationships.

Estimate

A rough answer to check if your exact answer is reasonable.

Worked Examples

1

A farmer has 6 paddocks with 24 sheep in each. He sells 39 sheep. How many remain?

Step 1: Total sheep: 6 × 24 = 144

Step 2: After selling: 144 − 39 = 105

Answer: 105 sheep remain.

2

Tickets cost $12 each. A family buys 5 tickets and pays with a $100 note. How much change do they get?

Step 1: Cost of 5 tickets: 5 × $12 = $60

Step 2: Change: $100 − $60 = $40

Answer: They receive $40 change.

3

96 students are split equally into 8 groups. Each group then splits into pairs. How many pairs are there altogether?

Step 1: Students per group: 96 ÷ 8 = 12

Step 2: Pairs per group: 12 ÷ 2 = 6

Step 3: Total pairs: 6 × 8 = 48

Answer: 48 pairs altogether.

Knowledge Check

Select the correct answer for each question.

Question 1

A bakery makes 150 loaves of bread each day. They sell 128 on Monday and 135 on Tuesday. How many loaves were left over across both days?

17 27 47 37

Question 2

A school bought 8 boxes of pencils with 12 pencils in each box. The pencils were shared equally among 6 classes. How many pencils did each class get?

16 18 14 12

Question 3

Liam earns $9 per hour mowing lawns. He works for 3 hours on Saturday and 4 hours on Sunday. How much does he earn for the weekend?

$54 $63 $72 $45

Question 4

A bus can carry 52 passengers. If 3 buses are full and a fourth bus carries 31 passengers, how many passengers are there altogether?

176 208 187 183

Question 5

A shop sells apples for $3 per kilogram and bananas for $5 per kilogram. Mum buys 4 kg of apples and 2 kg of bananas. How much does she spend?

$18 $24 $20 $22

Word Problems