New
New
Year 6

Explain how constant difference can make written calculations more efficient

I can explain how using the same difference rule can make written calculations easier.

New
New
Year 6

Explain how constant difference can make written calculations more efficient

I can explain how using the same difference rule can make written calculations easier.

Lesson details

Key learning points

  1. It is easier to use a written strategy for subtraction when no exchanging is required.
  2. If the minuend and subtrahend are both increased by the same amount, the difference stays the same.
  3. If the minuend and subtrahend are both decreased by the same amount, the difference stays the same.

Keywords

  • Minuend - The minuend is the number being subtracted from.

  • Subtrahend - A subtrahend is a number subtracted from another.

  • Difference - The difference is the result after subtracting one number from another.

  • Constant - A constant is a quantity that has a fixed value that does not change or vary, such as a number.

Common misconception

Pupils may struggle to understand the purpose of transforming calculations using constant difference, especially if they are less confident in calculating using mental strategies.

Show pupils sequences of calculations with a constant difference and get them to spot which of them is easiest to complete. Start as simply as you need to here. Constant difference is a helpful tool not a new method designed to lower confidence.

Even after adjustment, some of the mental maths required is tricky so change the calculations if needed or select simpler ones to establish the 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 pairs of number complements to 100
Correct Answer:16,84

84

Correct Answer:55,45

45

Correct Answer:31,69

69

Correct Answer:42,58

58

Q2.
Use a mental strategy to sum these multiples of 10 560 + 120 =
Correct Answer: 680
Q3.
Add together these multiples of 1,000 using a mental strategy. {{ ]} = 15,000 + 27,000
Correct Answer: 42,000
Q4.
Complete this subtraction using a mental strategy. 67,000 − 12,000 =
Correct Answer: 55,000
Q5.
How much change would I get from £20 if I spent £11.75 on a new football? £ change.
Correct Answer: 8.25, £8.25, 8.25p
Q6.
I have a ball of old plasticine that weighs 750 g and a new jumbo pack that weight 1.2 kg. What mass of plasticine do I have altogether?
Correct Answer: 1.95 kg, 1,950 g, 1.95, 1,950

6 Questions

Q1.
Which of the following expressions is not equivalent to the others?
57 − 51
56 − 50
Correct answer: 55 − 45
54 − 48
53 − 47
Q2.
Which of the following expressions is not equivalent to the others?
248 − 203
249 − 204
250 − 205
Correct answer: 250 − 206
252 − 207
Q3.
Match the expression with the adjustment to the minuend and subtrahend that will make them more efficient for calculation.
Correct Answer:81 − 24,− 1

− 1

Correct Answer:69 − 43,+ 1

+ 1

Correct Answer:52 − 37,− 2

− 2

Correct Answer:65 − 47,+ 3

+ 3

Q4.
Use adjustment of the minuend and subtrahend followed by your understanding of place value. 20.58 − 5.96 =
Correct Answer: 14.62
Q5.
Use adjustment of the minuend and subtrahend followed by partitioning to calculate the following subtraction. 70,559 − 54,504 =
Correct Answer: 16,055
Q6.
Use adjustment followed by a written procedure to calculate the following. 40,000 − 2,654 =
Correct Answer: 37,346