Calculation
Column Addition and Subtraction
Year 3 · Year 4 · Year 5 · Year 6
- ✓Add numbers with up to 4 digits using the column method, including carrying.
- ✓Subtract numbers with up to 4 digits using the column method, including exchanging.
- ✓Solve multi-step word problems involving addition and subtraction of numbers up to 4 digits.
- ✓Understand and apply the concept of place value when performing column calculations.
- ✓Check the accuracy of calculations using inverse operations.
Key concepts
Column addition is a method for adding numbers by arranging them vertically, aligning digits according to their place value (ones, tens, hundreds, thousands). You start adding from the rightmost column (the ones column) and move left. If the sum of a column is 10 or more, you 'carry over' the tens digit to the next column on the left.
Column subtraction is a method for subtracting numbers by arranging them vertically, aligning digits by place value. You start subtracting from the rightmost column (the ones column) and move left. If a digit in the top number is smaller than the digit below it in the same column, you need to 'exchange' (sometimes called 'borrow') from the column to its left. This means taking one unit from the next column (e.g., one ten) and converting it into ten units of the current column (e.g., ten ones).
Place value tells us the value of each digit in a number based on its position. For example, in the number 3456, the '3' is in the thousands place (3000), the '4' is in the hundreds place (400), the '5' is in the tens place (50), and the '6' is in the ones place (6). Understanding place value is crucial for correctly aligning numbers in column calculations.
Multi-step word problems require more than one mathematical operation to solve. You need to read the problem carefully to identify all the information given, determine the sequence of operations (addition, subtraction, or both), and solve each step in order to find the final answer. It's important to show your working for each step.
Key facts to remember
- 1Always align digits carefully according to their place value (ones, tens, hundreds, thousands, etc.) before starting your calculation.
- 2Begin all column addition and subtraction calculations from the rightmost column (the ones column) and work your way to the left.
- 3In column addition, if the sum of a column is 10 or more, 'carry' the tens digit over to the next column on the left.
- 4In column subtraction, if a digit in the top number is smaller than the digit below it, you must 'exchange' (or 'borrow') from the column to its left.
- 5Use inverse operations (addition to check subtraction, and subtraction to check addition) to verify your answers.
- 6Read multi-step word problems thoroughly to understand all parts and the correct order of operations.
- 7Show all your working clearly, especially in multi-step problems, so you can track your progress and check for errors.
Worked examples
Example 1
Calculate 3458 + 1765.
Answer
5223
Example 2
Calculate 5032 - 2476.
Answer
2556
Be careful with multiple exchanges, especially when there are zeros in the top number.
Example 3
A shop starts the day with 1250 loaves of bread. By lunchtime, 875 loaves have been sold. In the afternoon, another 450 loaves are delivered. How many loaves of bread does the shop have at the end of the day?
Answer
The shop has 825 loaves of bread at the end of the day.
Break down word problems into smaller, manageable steps and perform each calculation carefully.
Common mistakes
- ✗Not lining up the digits correctly by their place value, leading to incorrect sums or differences.
- ✗Forgetting to add a 'carried' digit in addition or forgetting to adjust a digit after 'exchanging' in subtraction.
- ✗In subtraction, incorrectly subtracting the smaller digit from the larger digit in a column, regardless of which number it belongs to (e.g., calculating 6 - 2 instead of exchanging when the top digit is 2 and the bottom is 6).
- ✗Making errors when exchanging across multiple zeros in subtraction (e.g., in 500 - 123, incorrectly treating the zeros).
- ✗Misinterpreting the operations required in word problems, especially in multi-step questions, and performing them in the wrong order.
Exam tips
- ★Use squared paper to help keep your digits neatly aligned in columns, which reduces the chance of making place value errors.
- ★Always double-check your calculations, particularly when you have carried or exchanged digits multiple times, as these are common areas for mistakes.
- ★For word problems, underline key information and keywords that indicate whether to add or subtract, and break the problem down into smaller, manageable steps.
- ★After completing a calculation, quickly estimate the answer to see if your calculated result is reasonable and makes sense in the context of the problem.
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