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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.

March 10, 2019

When calculating the volume of a pyramid we can substitute the values of the length, width and perpendicular height into the formula V = 1/3 lwh. In my experience this is often provided for the students with little explanation as to why a volume of a pyramid is exactly one third the volume of a […]

March 4, 2019

When teaching solving 3D problems using trigonometry we begin the lesson with a recap of Pythagoras’ Theorem and the three trigonometric ratios. We do this by matching the ratio and equations to the respective right-angled triangle. Students are encouraged to work in pairs and to show the diagrams as part of the working out on […]

January 29, 2019

When I teach rounding to a significant figure, I ask the class to discuss in pairs or small groups a definition for the word significant. It is a word that all the students have heard before but not all are able to define. After 2 or 3 minutes of conversation I ask the students to […]