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YEAR 2 · ADDITION AND SUBTRACTION · 12 MIN

Checking addition and subtraction

Check a calculation by estimating, using a different method or undoing it.

In this lesson

Before you start
  • Use tens and ones and related facts.
01 / LEARN

Understand the idea.

Ask if the size makes sense

First ask whether the answer has a sensible size. For 41+28, a nearby calculation is 40+30=70. Because you are adding a positive amount, the exact total must also be greater than forty-one.

Undo or try another way

Then check exactly by undoing the calculation. For an addition, subtract one part from the total. For a subtraction, add the removed part to the amount left. A different method can reveal a mistake that repeating the same steps misses.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Undo an addition

Check 27 + 15 = 42.

Worked solution

  1. 1

    Undo the addition by removing fifteen.

    42−10=32

    Split fifteen into ten and five to subtract it from the proposed total.

  2. 2

    Remove the remaining five.

    32−5=27

    Both parts of fifteen have been removed, leaving the other added number.

  3. 3

    Compare with the starting part.

    42−15=27

    The inverse calculation returns twenty-seven, so 27+15=42 is correct.

Answer

The calculation is correct.

EXAMPLE 02

Spot a wrong subtraction

A student writes 54 − 21 = 75. Is this correct?

Worked solution

  1. 1

    Check the size of the proposed answer.

    75>54

    Removing twenty-one must leave less than fifty-four, so seventy-five cannot be correct.

  2. 2

    Subtract the tens and then the one.

    54−20=34,34−1=33

    Twenty and one together account for the full amount removed.

  3. 3

    Check by adding the removed part back.

    33+21=54

    The remaining thirty-three and removed twenty-one rebuild the starting whole.

Answer

No. The correct answer is 33.

03 / YOUR TURN

Try it yourself.

Check your understanding

Check 48 − 16 = 32 using addition.

Show answer & reasoning

32 + 16 = 48

Add the remaining part and the removed part: 32+10=42 and 42+6=48. Thus 32+16=48, which checks 48−16=32.

Keep practising

6 worksheet questions

Open worksheet Worked solutions
Read the questions online
  1. Check 24+13=37 using subtraction.
  2. Check 45−12=33 using addition.
  3. Is 32+26=58 correct? Show a different calculation.
  4. A student writes 67−20=65. Fix the answer.
  5. Would 86 be a sensible answer for 29+18? Explain.
  6. Find and check 53−28.
Read the worked solutions
  1. Check 24+13=37 using subtraction.

    Undo the addition by removing one part.

    37−13=24 (or 37−24=13).
  2. Check 45−12=33 using addition.

    Add the removed amount back.

    33+12=45.
  3. Is 32+26=58 correct? Show a different calculation.

    Combine tens and ones separately.

    Yes. 30+20+2+6=58.
  4. A student writes 67−20=65. Fix the answer.

    Subtract 2 tens from 6 tens; the 7 ones stay unchanged.

    47
  5. Would 86 be a sensible answer for 29+18? Explain.

    The exact total is 47, far less than 86.

    No. The answer should be close to 30+20=50.
  6. Find and check 53−28.

    53−20=33; 33−8=25.

    25; check 25+28=53.
Checking saved progress…
Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Facts within 20; one-/two-digit calculations; partitioning; related facts; missing numbers; checking.

Official curriculum source ↗

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