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Students learn how to form and simplify algebraic expressions involving multiplication, addition, division and subtraction. They use this knowledge to begin solving equations using the balance method.

This unit takes place in Year 7 Term 2 and is followed by Expressions, Equations and Formulae

- 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
- Enumerate possibilities of combinations of two variables.

- An expression can be simplified by collecting like terms. Like terms are those which contain the same letter symbol and equal powers.
- Just as 2 + 2 + 2 can be written as 3 × 2, a + a + a can be written as 3 × a. However, with algebraic notation × and ÷ symbols are not included. 3 × a is written as 3a and 3 ÷ a is written as a fraction 3/a.
- An algebraic expression is a collection of mathematical terms with no stated value.
- Multiplicative relationships such as xy = yx can be used to simplify some expressions.
- The order of operations is used when substituting known values into expressions.

Develop fluency

- Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships
- Substitute values in expressions, rearrange and simplify expressions, and solve equations

Reason mathematically

- Identify variables and express relations between variables algebraically and graphically

Solve problems

- Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems
- Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

Algebra

- use and interpret algebraic notation, including:
- ab in place of a × b
- 3y in place of y + y + y and 3 × y
- a
^{2}in place of a × a, a^{3}in place of a × a × a; 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 to maintain equivalence by:
- collecting like terms
- taking out common factors

June 8, 2018

To introduce teaching reciprocals of numbers and terms I begin the lesson explaining that everything has an opposite. The opposite of shutting a door is to open it. The opposite of saying hello is to say goodbye. Numbers have opposites too we call them reciprocals. Teaching Reciprocals of Numbers and Terms To start the lesson […]

May 11, 2018

When I teach how to find the surface area of cylinders I like to add a constant level of challenge and enjoyment to the lesson. Rather than repetitively calculating the surface area of a cylinder I introduce more complex cylindrical shapes. How to find the Surface Area of Cylinders To find the surface area of […]

April 15, 2018

Inspiring students to enjoy maths and feel the success that comes with attempting a difficult challenge is why I teach. The feeling of success is addictive. The more students experience it the more they want it and the further out of their comfort zone they are willing to go to get more of it. Teaching […]