Chapter 2: Operations, Order, Factors, and Multiples
Operations, Order, Factors and Multiples
Choose the right operation order, then use factors and multiples to work more efficiently.
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Workbook pages
Fun Maths Book 3 pages 11-20
Practise four operations, order of operations, factors, multiples and divisibility.
Think first
Good mathematicians decide what the question is asking before they calculate.
- 1Are there brackets?
- 2Which operation must happen before adding or subtracting?
- 3Are we looking for factors or multiples?
- 4Can divisibility help us avoid long working?
Visual teaching
See the method
An expression is highlighted in stages while factor cards snap into pairs and divisibility tests light up for 2, 3, 4, 5, 6, 8 and 9.
6 + 4 x (12 - 7)
Worked examples
Find 18 - 3 x 4.
Step 1: First, what operation must we do before subtraction?
Multiplication comes before subtraction, so calculate 3 x 4 first.
Why: The order of operations keeps everyone interpreting the expression the same way.
Step 2: Now what is left?
3 x 4 = 12, so the expression becomes 18 - 12.
Why: We replace the multiplication part with its value.
Be careful: Do not work left to right as 18 - 3 first.
Step 3: Finish the calculation.
18 - 12 = 6.
Why: Now only subtraction remains.
Common mistake: Doing 18 - 3 first, then multiplying by 4.
Find 6 + 4 x (12 - 7).
Step 1: What information tells us the first step?
The brackets show 12 - 7 must be done first.
Why: Brackets group part of the expression into one value.
Step 2: After brackets, what comes next?
12 - 7 = 5, so we have 6 + 4 x 5. Now multiply: 4 x 5 = 20.
Why: Multiplication comes before addition.
Step 3: Finish and check.
6 + 20 = 26.
Why: Adding last gives the final value.
Common mistake: Adding 6 + 4 before multiplying.
A teacher packs 24 rulers and 36 pencils into identical packs. What is the greatest number of packs?
Step 1: What are we trying to find?
We need the greatest number of equal packs with no items left over.
Why: Equal packs means we need a common factor.
Step 2: Which common factor is greatest?
Factors of 24 include 1, 2, 3, 4, 6, 8, 12, 24. Factors of 36 include 1, 2, 3, 4, 6, 9, 12, 18, 36.
Why: Common factors divide both numbers exactly.
Be careful: Multiples make numbers bigger. This question asks for splitting into packs, so use factors.
Step 3: Choose the highest common factor.
The greatest common factor is 12.
Why: 12 is the largest number that divides both 24 and 36 exactly.
Common mistake: Finding a common multiple when the question asks for equal groups.
Guided practice
Find 72 รท (8 + 4) + 3 x 5.
Independent practice
Your turn
Find 18 - 3 x 4.
Which number is divisible by 6?
Find the LCM of 6 and 8.
Mini checkpoint
Check your thinking
Find 42 - 5 x (3 + 4).
Which is a common multiple of 4 and 6?
Which number is divisible by 9?
Key idea
Before calculating, decide the structure: brackets, operation order, factors or multiples. Do not rush left to right. Read the expression, choose the next legal step, and use factors or multiples when the question is about grouping or repeating.
Parent signal
If the child works left to right without checking operation order, pause and mark the expression in stages.