Use place value
4 × 6 = 24 helps us see that 4 × 60 = 240.
The basic fact stays the same but one factor is ten times larger.
Year 3
Mentally calculate using place value, known and derived facts
Use known facts, doubling and place value to work out related multiplication and division mentally.
Lesson overview
Number - multiplication and division
Derived facts come from facts we already know. If 4 × 6 = 24, then 4 × 60 = 240. If 8 × 3 = 24, then 24 ÷ 8 = 3. We can use doubling and place value to reason quickly.
Use doubling
4 × 7 = 28, so 8 × 7 = 56.
Doubling one factor doubles the product.
Use inverse thinking
If 3 × 8 = 24, then 24 ÷ 3 = 8.
Multiplication facts help division facts.
Worked example
Use 4 × 9 = 36 to work out 8 × 9.
- Start with the known fact 4 × 9 = 36.
- 8 is double 4.
- So the answer must be double 36.
- Double 36 is 72, so 8 × 9 = 72.
Try it
Find the known fact first, then use doubling, halving or place value to derive the new one.
Question 1
If 4 × 5 = 20, what is 4 × 50?
Question 2
If 4 × 7 = 28, what is 8 × 7?
Question 3
Which fact matches 32 ÷ 8?
Question 4
Use 3 × 8 = 24. What is 24 ÷ 3?
Question 5
If 4 × 6 = 24, what is 40 × 6?
Common mistakes
Watch for these when working through the lesson.
- Forgetting to change the answer when a factor doubles.
- Using a division fact that does not match the same numbers.
- Ignoring the zero when using place value facts like 40 × 6.
Related topics
These ideas fit closely with this lesson.
- Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables.
- Multiply two-digit and one-digit numbers using practical resources and formal written layout.