Addition and Subtraction Columns
Addition and Subtraction Columns
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Addition and Subtraction Columns
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Learning goal
I can add and subtract numbers using the column method.
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Words you link with column addition or subtraction
Use this to surface prior knowledge such as columns, ones, tens, carry, exchange, line up, add and subtract.
Place value in columns
Put ones under ones
Put tens under tens
Put hundreds under hundreds
Digits must line up in straight columns
Correct place value helps us calculate accurately
Stress that the method works because each column contains the same place value. A common error is writing numbers without lining up the digits.
Lining up numbers
Write the larger and smaller numbers clearly
Start from the right-hand side
Check that each digit is in the correct column
Leave space for the answer line
Model how to set out a simple example such as 45 + 23 and 67 - 24. Emphasise neat layout before any calculation begins.
Column addition
Work from right to left.
Add the ones column first
Then add the tens column
Then add any hundreds column
Write each answer digit in the correct place
Keep the first examples free of carrying so students focus on the order and layout of the method.
When the total is 10 or more
Sometimes a column total is greater than 9.
Write the ones digit in the answer
Carry the tens digit to the next column
Add that carried digit into the next total
Keep moving from right to left
Use the term 'carry' consistently. You may also mention that some schemes say 'regroup', but keep one label on the slides.
Checking an addition
Re-read each column
Check any carried digit
Make sure the answer digits are aligned
Estimate first to see if the answer looks sensible
A quick estimate can be done by rounding to the nearest ten. This helps students spot answers that are much too big or too small.
Why must digits line up in columns?
To keep place value
To make numbers bigger
To start on the left
To change the answer
Checks the key idea from slides 2–6: accuracy comes from matching ones, tens and hundreds in the same column.
Complete the method
In column addition, start from the right side. Add the ones column first. If the total is 10 or more, carry to the next column. Then check that the answer digits are aligned.
Echoes the taught routine: right to left, ones first, carry if needed, then check alignment.
Column subtraction
Work from right to left.
Subtract the ones column first
Then subtract the tens column
Then subtract any hundreds column
Write each answer digit in the correct place
Begin with examples where each top digit is larger than the digit below it, so the subtraction structure is clear before exchange is introduced.
When you need to exchange
Sometimes the top digit is smaller than the bottom digit.
Exchange 1 ten for 10 ones
Or exchange 1 hundred for 10 tens
Subtract after the exchange
Keep the new digits clear in the columns
Use place value language: 1 ten = 10 ones. Avoid presenting exchange as a trick; link it to regrouping the value.
Checking a subtraction
Re-read each column
Check each exchange carefully
Make sure digits stay in the right columns
Use addition to check the answer
Show that difference + smaller number = larger number. This gives a reliable way to check subtraction answers.
Common mistakes
Digits not lined up correctly
Forgetting to carry in addition
Forgetting to exchange in subtraction
Starting from the left instead of the right
Writing answer digits in the wrong column
These errors are often layout errors as much as number errors. Encourage neat, slow set-up before calculating.
What do you do if the top digit is smaller?
Carry a ten
Start again
Exchange first
Add the digits
Tests the subtraction step from slides 7–10. A common confusion is mixing up carry in addition with exchange in subtraction.
Complete the subtraction check
In column subtraction, work from right to left. Subtract the ones column first. If needed, exchange before you subtract. You can use addition to check the answer.
Reinforces the subtraction procedure and the checking method: difference + smaller number = larger number.
Which mistake do students make most in columns?
Expected ideas: digits not lined up, forgetting to carry, forgetting to exchange, starting from the left, answer in the wrong column.
What is one thing you learned today?
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What helped you understand columns best?
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What part still feels tricky?
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Glossary
column - a vertical line of digits with the same place value
place value - the value of a digit because of its position in a number
ones - digits in the first column from the right
tens - digits in the second column from the right
hundreds - digits in the third column from the right
carry - moving a value to the next column in addition
exchange - changing a larger place value into smaller place values of the same total
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