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Students learn how to write and simplify algebraic expressions using the correct notation. Learning progresses from simplifying expressions by collecting like terms to factorising quadratics.

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

- use simple formulae
- generate and describe linear number sequences
- express missing number problems algebraically
- find pairs of numbers that satisfy an equation with two unknowns

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
- brackets

simplify and manipulate algebraic expressions by:

- collecting like terms
- multiplying a single term over a bracket
- taking out common factors
- expanding products of two or more binomials
- factorising quadratic expressions of the form 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.
- The multiplication symbol is omitted when using algebraic notation to avoid confusion between and ×. Quotients are written as using simplified fractions.
- 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.

- Students often forget ab = ba = a × b and b + a = + b when collecting like terms.
- 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.

January 13, 2020

To find the area of compound shapes students need to understand what the word compound means. Therefore, I ask students to discuss in pairs a definition for the word compound and to extend it to include the shapes below. As a result of their learning in science students agree that a compound can be defined […]

January 4, 2020

At the start of the Spring Term these are three main priorities for me as the Head of Mathematics.

January 1, 2020

I teach mutually exclusive outcomes directly after students have encountered Venn diagrams. This is the fifth Year 8 Probability lesson.