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Year 6

Explore mental and written strategies to solve problems

I can explore written and mental strategies to solve problems.

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New
New
Year 6

Explore mental and written strategies to solve problems

I can explore written and mental strategies to solve problems.

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Lesson details

Key learning points

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

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.

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?


To help you plan your year 6 maths lesson on: Explore mental and written strategies to solve problems, download all teaching resources for free and adapt to suit your pupils' needs...

Children may struggle to grasp the constant difference concept. Give lots of practice and represent the calculations on a number line to support children to grasp this concept.
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Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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6 Questions

Q1.
Match the equation to its sum.
Correct Answer: 999 + 1 = ,1,000
tick

1,000

Correct Answer:999 + 2 =,1,001
tick

1,001

Correct Answer:998 + 5 = ,1,003
tick

1,003

Correct Answer:998 + 7 =,1,005
tick

1,005

Correct Answer:997 + 2 =,999
tick

999

Q2.
Match the equation to its sum.
Correct Answer:30,000 + 20,000 =, 50,000
tick

50,000

Correct Answer:40,000 + 20,000 =,60,000
tick

60,000

Correct Answer:35,000 + 35,000 =, 70,000
tick

70,000

Correct Answer:45,000 + 30,000 =,75,000
tick

75,000

Correct Answer:40,000 + 60,000 =,100,000
tick

100,000

Q3.
Use a number line to calculate and find the missing part. 1,398 + = 5,000
Correct Answer: 3,602 , 3602
Q4.
Use the formal written column subtraction algorithm to calculate 3,976,301 − 1,432,100 =
Correct Answer: 2,544,201 , 2544201
Q5.
Use the formal written column subtraction algorithm to calculate 1,309,052 − 132,421 =
Correct Answer: 1,176,631, 1176631
Q6.
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
Correct Answer: 190,512

6 Questions

Q1.
Use a number line to calculate 69,998 + ? = 100,000
20,002
30,001
Correct answer: 30,002
30,003
40,002
Q2.
Use a number line to calculate 190,000 − 137,999 =
Correct Answer: 52,001, 52001
Q3.
By using the constant difference concept, calculate the difference: 2,000,000 − 409,371 =
Correct Answer: 1,590,629, 1590629
Q4.
By using the constant difference concept, calculate the missing number: 1,000,000 − = 23,147
Correct Answer: 976,853, 976853
Q5.
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?
Correct Answer: 32,002, 32002
Q6.
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? £
Correct Answer: 112,601, £112,601