Year 5 · Column Addition and Subtraction · Summary

Year 5 Column Addition and Subtraction: summary and key words

Part of the Year 5 column addition and subtraction chapter. Chapter overview · whole chapter on one page

Chapter summary

Skill	Method
Column addition	Line up ones under ones (on the right). Add from the right. If a column makes 10 or more, write the ones digit and carry. With three numbers the carry can be 2.
Column subtraction	Bigger number on top. Subtract from the right. If the top digit is smaller, exchange 1 from the next column (10 more in this column).
Zeros in the top number	You cannot exchange from a 0. Go left to the first column that is not 0. Each 0 you pass becomes 9. 1,000,000 − 468,325 works this way.
Mental strategies	Partition; bridge through 10, 100 or 1,000; compensate (add 9,999 = add 10,000, take away 1); number facts (75 + 25 = 100, so 7,500 + 2,500 = 10,000); count up; near doubles.
Estimating	Round each number (to the nearest 10, 100, 1,000, 10,000 or 100,000), then do the easy calculation. Use ≈. Round to a smaller place value for a closer estimate.
Level of accuracy	Choose how much to round to fit the question. If the estimate is close to a limit, use a closer estimate or the exact answer.
Checking	Use the inverse: check an addition by subtracting and a subtraction by adding. Compare the answer with your estimate. A wrong ones digit means a wrong answer.
Missing digits	Work from the ones column. Use the carry. Turn subtractions into additions with the inverse. The answer is always unique.
Bar models	Part-whole: parts added together make the whole. Comparison: the gap is the difference. Draw the bars before you choose the operation.
Multi-step problems	Read, draw a bar model, plan the steps, calculate, check that you answered the question. Do not stop after step 1.
Tables, charts, timetables, bank statements	Read the scale carefully. Count on to the next o’clock for time gaps. Money in adds and money out subtracts.

Can you…?

I can add numbers with up to 6 digits using the column method, including three numbers and carrying.
I can subtract numbers with up to 6 digits using the column method, with exchanging across zeros.
I can add and subtract in my head by partitioning, bridging, compensating, using number facts and near doubles.
I can round to estimate an answer and choose how accurate I need to be.
I can check an answer with the inverse operation.
I can find missing digits and missing numbers.
I can use part-whole and comparison bar models.
I can solve multi-step problems and explain which operations and methods I chose.
I can solve problems from tables, bar charts, timetables and bank statements.

Key terms

Column method: A written way to add or subtract. Numbers go one under the other with the same place values lined up.
Carry: When a column adds to 10 or more, you write the ones digit and move the rest to the next column.
Exchange: In subtraction, swapping 1 of the next column for 10 of this column (for example 1 thousand for 10 hundreds). Also called borrowing.
Sum / total: The answer to an addition.
Difference: How far apart two numbers are. It is the answer to a subtraction.
Inverse: The opposite operation. Addition and subtraction undo each other.
Estimate: A close answer found by rounding the numbers first.
Accuracy: How close an answer is to the exact answer.
Partition: To split a number into parts, such as 36,400 = 30,000 + 6,000 + 400.
Bridging: Jumping to the next round number (10, 100 or 1,000) and then doing the rest.
Compensate: To use an easier number and then fix the answer, such as adding 10,000 and taking away 1 to add 9,999.
Number bond: A pair of numbers that make a given total, such as 36 + 64 = 100.
Near double: A sum of two numbers that are almost the same.
Bar model: A drawing of bars that shows the numbers in a problem. Part-whole models show parts and a whole. Comparison models show two amounts side by side.
Balance: The amount of money in a bank account.
Multi-step problem: A problem that needs more than one calculation to solve.