Home → Curriculum Hub → Maths Lessons → Schemes of Work → Three-Year GCSE Foundation → Decimal Numbers
This Foundation GCSE scheme of work unit covers decimal numbers in Year 9. It is the written arithmetic of decimals. Students add and subtract by lining up the decimal point, then use a grid or long multiplication for products and long division for quotients, including decimal answers.
Students have to estimate first and align digits by place, not by the last digit. Those two checks stop the common error that multiplication always makes a number larger.
A student who has secured this unit:
Students should be secure with the following before beginning this unit.
In addition and subtraction the decimal points sit in a column. Each digit then occupies its true place.
A rough calculation, such as 4.8 × 3.1 ≈ 15, is the check. If the written answer is 148.8, the point has moved.
4.6 × 3 can be done as 46 × 3, then divided by 10. The number of decimal places in the product is not a rule to apply blindly.
A long division is often easier after the calculation is written as an equivalent fraction and simplified.
| Misconception | Teaching focus |
|---|---|
| Believing multiplication always increases a number and division always decreases it. | Calculate 6 × 0.5 and 6 ÷ 0.5 on the same board and leave both answers visible. |
| Skipping the estimate, so a point in the wrong place is not noticed. | Require a one-line estimate before the written method is allowed to start. |
| Lining up the last digits instead of the decimal points. | Draw a vertical line through the points of both numbers before any adding begins. |
| Counting decimal places in a product without checking the estimate. | Compare 1.2 × 1.2 = 1.44 with 12 × 12 = 144 and talk about the two zeros that were the tenths. |
| Stopping a long division when the remainder first appears, and leaving it as a remainder in a decimal question. | Bring down a zero after the point and continue until the asked accuracy is reached. |
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Students learn how to add and subtract with decimal numbers using the place value table.
As learning progresses they solve problems involving number pyramids and money.
Students learn how to perform long multiplication using the grid method.
To progress, students apply this multiplication method to include decimal products.
Students learn how to perform long division using equivalent and simplified fractions.
As learning progresses, they apply place value to divide with decimal numbers.
Additional practice adding with decimal numbers.
The problem-solving activity challenges students to find the perimeter of a composite shape.
Students are challenged to apply the rules of arithmetic to a series of real-life, functional problems.
Five problems link to money and the order of operations.
Students revise how to calculate the product of two or more decimal numbers using written methods.
As learning progresses they use written methods to solve real-life financial problems.
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Students revise how to divide with decimal numbers using either long division or equivalent fractions.
Includes exam-style questions where students use written methods to solve real-world division problems.
Revision Hub
Browse the Mr Mathematics Revision Hub for more maths revision lessons organised by topic and GCSE grade.
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