MULTIPLICATION & DIVISION · TEXTBOOK LESSON
Multiplication describes equal groups, scaling and repeated addition. Fluency with multiplication facts supports division, fractions, algebra, area and ratio.
Learning objectives
By the end of this lesson, you should be able to:
- Represent multiplication with equal groups and arrays.
- Recall and derive multiplication facts.
- Use factors and place value to multiply efficiently.
- Recognise factors, multiples and prime numbers.
1. Key vocabulary and definition
Definition
In a × b = c, a and b are factors and c is the product. Multiplication is commutative, so a × b = b × a.
factorproductmultiplearrayprimecommutative
2. Essential facts and rules
These are the facts you should know before attempting the worked example.
Key mathematical facts
- Multiplying by 10 shifts each digit one place to the left in place-value terms.
- A prime number has exactly two positive factors: 1 and itself.
- The distributive law allows a(b+c)=ab+ac.
3. Standard method
A reliable method helps prevent errors and makes your reasoning easy to follow.
1
Identify the factors and decide whether a known fact can be used.
2
Partition a factor when useful, for example 7 × 24 = 7 × 20 + 7 × 4.
3
Calculate each partial product.
4
Combine the partial products.
5
Check using estimation or division.
4. Worked example
Worked example
Calculate 7 × 24.
1
Partition 24 as 20 + 4.
2
7 × 20 = 140.
3
7 × 4 = 28.
4
140 + 28 = 168, so 7 × 24 = 168.
5. Common mistakes
Watch out for these
- Starting calculations before deciding what the question is asking.
- Skipping important steps or changing notation midway through a solution.
- Accepting an answer without checking whether its size, sign or unit is sensible.
6. Video lesson
This topic is ready for a matching video lesson. The written textbook lesson is fully available now; additional videos can be added to the same lesson template.
7. Practice exercise
Complete these without looking at the answers first.
- Calculate 8 × 7.
- Calculate 6 × 34 using partitioning.
- List all factors of 18.
- Write the first five positive multiples of 9.
- Is 29 prime? Explain briefly.
Show answers
- 56
- 204
- 1, 2, 3, 6, 9, 18
- 9, 18, 27, 36, 45
- Yes; its only positive factors are 1 and 29
8. Chapter summary
- Understand the underlying idea before memorising a procedure.
- Use precise mathematical notation and show a logical method.
- Always check the final result.