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Properties of numbers is a key topic for Foundation GCSE maths students as it lays the groundwork for fractions, standard form, ratios and percentages. Throughout this topic, students learn the importance of place value and the order of operations.

Properties of number takes place in Term 1 of Year 9 and is followed by fractions and mixed numbers.

- read, write and interpret mathematical statements involving addition (+), subtraction (–) and equals (=) signs
- represent and use number bonds and related subtraction facts within 20
- add and subtract one-digit and two-digit numbers to 20, including zero
- solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = – 9.

- Understand and use place value
- Order positive integers
- Apply the four operations, including formal written methods, to integers
- Recognise and use relationships between operations
- Use the concepts and vocabulary of prime numbers, factors (divisors) and multiples

- Students need to be very secure in their knowledge of applying the place value table to identify the value of any digit.
- Understanding the additive and multiplicative number properties are vital building blocks for the remainder of this course. For example, 2 x 3 = 3 x 2 and 2 + 3 = 3 + 2.
- When calculating factors of integers it is beneficial to use factor pairs rather than individual values.
- Use the place value table to demonstrate column addition and subtraction.

- Students often define a prime number as ‘divides by 1 and itself. This leads to the incorrect assumption of 1 to be a prime number.
- When subtracting, students may find knowing when to ‘borrow’ confusing and instead incorrectly subtracting the smaller digit from the larger one. E.g., 43 – 25 = 22
- Aligning the correct value digits for column addition and subtraction can prove troublesome. Encourage the use of the place value table.

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