Year 5NumberOperationsYear 5 Maths

Adding and subtracting big numbers

What this lesson covers

  • Addition and subtraction can be carried out mentally, using known facts, place value and partitioning, or column methods.
  • Standard written algorithms (e.g. column addition, column subtraction) rely on place value, regrouping, and renaming.
Key idea

Four ways, not one

  • There is more than one way to add two numbers.
  • The curriculum names four of them.
  • The skill is choosing, not memorising one method.
four tools, one job
methoduse it when
known factsyou already know the answer
place valuethe numbers are round
partitioningyou can split one of them up
columnsit is too awkward to hold in your head
Worked example

Known facts come free

  • 6 + 7 = 13. You do not work that out.
  • You remember it, and that is the fastest method there is.
  • Every other method leans on facts like this one.
Known facts come free
Worked example

Round numbers use place value

  • 4,000 + 3,000. Do not reach for a pencil.
  • 4 thousands plus 3 thousands is 7 thousands.
  • The same fact, 4 + 3, moved up a place.
Round numbers use place value
Worked example

Split one of them up

  • 2,350 + 1,400 looks awkward.
  • Split the 1,400 into 1,000 and 400.
  • 2,350 + 1,000 is 3,350. Then + 400 is 3,750.
one hard step becomes two easy ones
steprunning total
start2,350
add 1,0003,350
add 4003,750
Key idea

When to give up and write it down

  • Those three work when the numbers are kind.
  • 4,678 + 2,565 is not kind. Too much to hold.
  • That is what the column method is for.
all three done in your head
sumhowanswer
6 + 7known fact13
4,000 + 3,000place value: 4 + 3 thousands7,000
2,350 + 1,400partition: 2,350 + 1,000 + 4003,750
Key idea

Columns line up place value

  • Write one number above the other, ones under ones.
  • The columns are not tidiness. They are place value.
  • Then add one column at a time, starting from the right.
Columns line up place value
Worked example

A carry is a rename

  • 8 + 5 = 13. That will not fit in the ones column.
  • 13 ones is 1 ten and 3 ones. Write 3, carry the 1.
  • Nothing was invented. Ten ones were renamed as one ten.
4,678 + 2,565 = 7,243
columnaddwritecarry
ones8 + 5 = 1331
tens7 + 6 + 1 = 1441
hundreds6 + 5 + 1 = 1221
thousands4 + 2 + 1 = 770
Key idea

Check it roughly

  • Round both numbers before you trust the answer.
  • 4,678 is about 5,000. 2,565 is about 2,500.
  • About 7,500. Our answer was 7,243, so it is believable.
estimating is checking
exactrounded
4,6785,000
2,5652,500
7,243about 7,500
Key idea

Subtraction renames too

  • 5,003 − 1,476. Start at the ones: 3 − 6 will not go.
  • So borrow. But the tens are 0, and so are the hundreds.
  • Go to the thousands, and rename all the way down.
Subtraction renames too
Worked example

Rename across the zeros

  • 5,003 is 4 thousands, 9 hundreds, 9 tens and 13 ones.
  • The number did not change. Only its name did.
  • Now every column subtracts: 3,527.
5,003 − 1,476 = 3,527
columntake awayleft
ones13 − 67
tens9 − 72
hundreds9 − 45
thousands4 − 13
Key idea

Add it back to be sure

  • A subtraction can always be checked by adding.
  • 3,527 + 1,476 should give 5,003.
  • If it does not, the borrowing went wrong somewhere.
the answer checks itself
checkresult
3,527 + 1,4765,003
matches the start?yes
Your turn

Your turn

  • 1. In your head: 5,000 + 2,000, then 3,240 + 1,500.
  • 2. In columns: 3,847 + 1,976.
  • 3. In columns: 6,002 − 2,438.
  • 4. Check your answer to question 3 by adding.
Show answer

1. 7,000 and 4,740. 2. 5,823. 3. 3,564. 4. 3,564 + 2,438 = 6,002, so it is right.

Summary

What to take away

  • Four methods. Pick the one the numbers suit.
  • A carry or a borrow is a rename, not a trick.
  • Round to check an addition, add to check a subtraction.
the closing chart
methoduse it when
known factsyou already know the answer
place valuethe numbers are round
partitioningyou can split one of them up
columnsit is too awkward to hold in your head

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