Ratio (age 10+)
Perform mental calculations including with mixed operations and large numbers, using strategies such as partitioning, compensation, and derived facts
What a learner can do afterwards
- Mentally compute 45 × 8 by partitioning into 40 × 8 + 5 × 8
- Use known facts to derive 6.5 × 4 mentally
- Solve a multi-operation mental calculation such as 250 × 3 + 500 and explain the strategy used
The lesson
You already know how to multiply big numbers on paper. Mental maths asks you to do the same job in your head, by breaking one hard problem into smaller, friendlier ones.
To work out 45 × 8 in your head: split 45 into 40 + 5. Work out 40 × 8 = 320 and 5 × 8 = 40. Add them together: 320 + 40 = 360.
Derived facts save you work. If you already know 6 × 4 = 24, you don't need to start over for 6.5 × 4. Just add half of 4, which is 2, so 6.5 × 4 = 26.
When a problem has more than one step, like 250 × 3 + 500, do the multiplication first, then the addition. Say each step out loud so you don't lose track: 750, then 750 + 500 = 1250.
Split a hard problem into easy pieces, use facts you already know, and take one step at a time.
Watch it
Where it sits
This opens up
Nothing builds on it yet.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.