Explore mental and written strategies to solve problems | Maths

Starter quiz

Match the equation to its sum.
- 999 + 1 =
  
  ⇔
  
  1,000 ✓
- 999 + 2 =
  
  ⇔
  
  1,001 ✓
- 998 + 5 =
  
  ⇔
  
  1,003 ✓
- 998 + 7 =
  
  ⇔
  
  1,005 ✓
- 997 + 2 =
  
  ⇔
  
  999 ✓
Match the equation to its sum.
- 30,000 + 20,000 =
  
  ⇔
  
  50,000 ✓
- 40,000 + 20,000 =
  
  ⇔
  
  60,000 ✓
- 35,000 + 35,000 =
  
  ⇔
  
  70,000 ✓
- 45,000 + 30,000 =
  
  ⇔
  
  75,000 ✓
- 40,000 + 60,000 =
  
  ⇔
  
  100,000 ✓
Use a number line to calculate and find the missing part. 1,398 + ______ = 5,000
- '3,602 ' ✓
Use the formal written column subtraction algorithm to calculate 3,976,301 − 1,432,100 = ______
- '2,544,201 ' ✓
Use the formal written column subtraction algorithm to calculate 1,309,052 − 132,421 = ______
- '1,176,631' ✓
Lucas and Aisha play a game. Lucas wins 390,512 points and Aisha wins 200,000 fewer points. How many points does Aisha win? ______ points
- '190,512' ✓

Exit quiz

Use a number line to calculate 69,998 + ? = 100,000
- 20,002
- 30,001
- 30,002 ✓
- 30,003
- 40,002
Use a number line to calculate 190,000 − 137,999 = ______
- '52,001' ✓
By using the constant difference concept, calculate the difference: 2,000,000 − 409,371 = ______
- '1,590,629' ✓
By using the constant difference concept, calculate the missing number: 1,000,000 − ______ = 23,147
- '976,853' ✓
Use the most efficient method to solve this problem. A library has 50,000 books and some are out on loan. There are 17,998 books remaining in the library. How many are out on loan?
- '32,002' ✓
Use the most efficient method to solve this problem. A lottery winner won £1,500,000 and spent 387,399. How much money did they have left? £______
- '112,601' ✓

Worksheet

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Lesson Details

Key learning points

Looking at the numbers involved and using number-sense supports us to know which strategy is more efficient.
A number line is a useful mental strategy when it is obvious what to add or subtract.
When using a formal written method the concept of constant difference can be used to make the calculation easier.

Common misconception

Children may automatically use a formal written algorithm.

What do you notice about the numbers? What would you add/subtract to get to the nearest multiple of (a power of 10)? Can you represent this on a number line?

Keywords

Difference - The difference is the result of subtracting one number from another. It is how much one number differs from another - represented by how far apart they are on a number line.
Efficient - Being efficient means finding a way to solve a problem quickly whilst also maintaining accuracy.