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      Explore mental and written strategies to solve problems

      Lesson details

      Learning outcome

      I can explore written and mental strategies to solve problems.

      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?

      Teacher tip

      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.

      Licence

      This content is © Oak National Academy Limited (2026), 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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      Prior knowledge starter quiz

      6 Questions

      Q1.
      Match the equation to its sum.

      Correct Answer: 999 + 1 = ,1,000

      1,000

      Correct Answer:999 + 2 =,1,001

      1,001

      Correct Answer:998 + 5 = ,1,003

      1,003

      Correct Answer:998 + 7 =,1,005

      1,005

      Correct Answer:997 + 2 =,999

      999

      Q2.
      Match the equation to its sum.

      Correct Answer:30,000 + 20,000 =, 50,000

      50,000

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

      60,000

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

      70,000

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

      75,000

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

      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

      To help you plan your 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...