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Students learn how to expand and factorise algebraic linear and quadratic expressions. Learning progresses to expanding cubic and factorising quadratics in the form ax^{2} +bx + c.

This unit takes place in Term 2 of Year 9 and is followed by solving equations.

Use and interpret algebraic notation, including:

- ab in place of a × b
- 3y in place of 3 × y
- a
^{2}in place of a × a, a^{3}in place of a × a × a and a^{2}b in place of a × a × b - a/b in place of a ÷ b
- Coefficients written as fractions rather than decimals

simplify and manipulate algebraic expressions by:

- Multiplying a single term over a bracket
- Taking out common factors
- Expanding products of two or more binomials
- Factorising quadratic expressions of the form (a)x
^{2}+ bx + c, including the difference of two squares - Simplifying expressions involving sums, products and powers including the laws of indices

- Students need to appreciate that writing with algebra applies the rules of arithmetic to unknown numbers which are represented as letters.
- It is important to define the difference between an expression, equation and formula.
- Linear (x), quadratic (x
^{2}) and cube terms (x^{3})cannot be collected together. - Understanding quadratics in the general form x
^{2}+ bx + c helps to factorise and expand expressions. - Developing mental methods to factorise quadratics is key to gaining confidence with quadratics equations later on.

- When multiplying out brackets students incorrectly forget to multiply the second term especially with negative products. E.g., 2(x + 5) = 2x + 10 and -2(x + 5) = -2x – 10
- When factorising expressions a common misconception is to not fully factorise. E.g., 18x + 24y can be written as 9x + 12y
- When expanding the product of two or more brackets students often incorrectly collect the like terms associated to the linear unknown.

July 6, 2019

Earlier this week, my school took part in a trial OFSTED inspection as part of getting ready for the new inspection framework in September 2019. This involved three Lead Inspectors visiting our school over the course of two days. The first day involved a ‘deep dive’ by each of the Lead Inspectors into Mathematics, English […]

June 30, 2019

The method of how to solve quadratics by factorising is now part of the foundational knowledge students aiming for higher exam grades are expected to have. Here is an example of such a question. Solve x2 + 7x – 18 = 0 In my experience of teaching and marking exam papers students often struggle with […]

June 24, 2019

When learning how to write 3-part ratios students need to understand how ratios can be made equivalent. The start of the lesson reminds students by asking which of six ratios is the odd one out. This is presented to the class as they come into the lesson. Writing Equivalent Ratios A few students immediately go […]