New
New
Year 6

Explore mental and written strategies to solve problems

I can explore written and mental strategies to solve problems.

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?

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.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), 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

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