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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

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 […]