Starter quiz
- Which equations would it be most efficient to solve using column subtraction?
- 476 − 376 =
- 565 − 284 = ✓
- 557 − 555 =
- 632 − 148 = ✓
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- Which equations could be more easily solved using a mental calculation?
- 222 + 199 = ✓
- 352 + 287 =
- 140 + 360 = ✓
- 388 + 165 =
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- Alex is trying to calculate the sum of 214 and 497 Which hundreds number will be closest to his answer?
- '700' ✓
- What is the most efficient way to calculate 285 − 99 = ?
- Start at 99 and count on to 285
- Use column subtraction
- Subtract 100 then add 1 ✓
- Subtract 100 then subtract 1
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- Look carefully at Alex’s column addition. Which of these statements about the sum is true?
- The ones digit of the sum is incorrect.
- The tens digit of the sum is incorrect. ✓
- The hundreds digit of the sum is incorrect.
- The sum is correct.
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- Look carefully at Alex’s column subtraction. Which of these statements about the difference is true?
- The ones digit of the difference is incorrect.
- The tens digit of the difference is incorrect.
- The hundreds digit of the difference is incorrect. ✓
- The difference is correct.
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Exit quiz
- Which equations could be more easily solved using a mental calculation?
- 3,000 - 2,988 = ___ ✓
- 2,568 - 1,567 = ___
- 4,565 + 100 = ___ ✓
- 8,658 - 2,454 = ___
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- Which equations would it be most efficient to solve using column subtraction?
- 5,623 - 324 = ___ ✓
- 4,265 - 2,431 = ___ ✓
- 1,758 - 10 = ___
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- What is the most efficient way to calculate 1,745 − 199 = ?
- Start at 199 and count on to 1,745
- Use column subtraction
- Subtract 1 from each number then find the difference
- Add 1 to each number then find the difference ✓
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- 4,004 - 10 = ______
- '3,994' ✓
- Complete the column addition. What number has been added to 3,065 to sum to 8,347? ______
- '5,282' ✓
- Complete the column subtraction. What is the missing whole? ______
- '6,746' ✓
Worksheet
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Presentation
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Lesson Details
Key learning points
- Equivalent calculations can be used with the same difference or same sum to make calculations ‘easier’.
- A number line can be used to represent more efficient methods.
- Inverse, the relationship between addition and subtraction, can be used to solve missing number problems.
Common misconception
When using adjustment (e.g. 456 − 199), pupils may forget to subtract or add 1 to both parts.
The emphasis of same difference can encourage children to ensure they have subtracted or added to both parts of the calculation. Clearly display the visuals in this lesson to support with this.
Keywords
Efficient - Working efficiently means finding a way to solve a problem quickly whilst also maintaining accuracy.
Equivalent - Two or more things have the same value.
Inverse - The opposite in effect. The reverse of.
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