Recognise and use multiples, factors (divisors), common factor, highest common factor, lowest common multiple and primes.

Use squares, positive and negative square roots, cubes and cube roots, and index notation for small positive integer powers.

Recognise that equations of the form y = mx + c correspond to straight-line graphs.

Simplify or transform linear expressions by collecting like terms; multiply a single term over a bracket.

Plot the graphs of linear functions, where y is given explicitly in terms of x, on paper and using ICT.

Core:

Use the prime factor decomposition of a number.

Use ICT to estimate square roots and cube roots.

Use index notation for integer powers and simple instances of the index laws.

Given values for m and c, find the gradient of lines given by equations of the form y = mx + c.

Construct functions arising from real-life problems and plot their corresponding graphs; interpret graphs arising from real situations, including distance–time graphs.

Represent problems and synthesise information in algebraic, geometric or graphical form; move from one form to another to gain a different perspective on the problem.

Simplify or transform algebraic expressions by taking out single-term common factors.

Use formulae from mathematics and other subjects; substitute numbers into expressions and formulae; derive a formula and, in simple cases, change its subject.

Generate points and plot graphs of linear functions (y given implicitly in terms of x), e.g. ay + bx=0, y + bx + c= 0, on paper and using ICT.

Solve increasingly demanding problems; explore connections in mathematics across a range of contexts: algebra.

Extension:

Know and use the index laws (including in generalised form) for multiplication and division of positive integer powers; begin to extend understanding of index notation to negative and fractional powers, recognising that the index laws can be applied to these as well.

Investigate the gradients of parallel lines and lines perpendicular to these lines.

Plot graphs of simple quadratic and cubic functions, e.g. y=x2, y= 3x2 + 4, y = x3.

Square a linear expression, expand the product of two linear expressions of the form x±n and simplify the corresponding quadratic expression; establish identities such as a2 – b2 = (a + b)(a – b).

Solve linear inequalities in one variable, and represent the solution set on a number line; begin to solve inequalities in two variables.

Derive and use more complex formulae, and change the subject of a formula.

Key Vocabulary:

Multiple, LCM, prime factor, prime factor decomposition, LCD, algebraic proof, gradient, function, variable, proportion, proportionality.

## Objectives:

Support:Recognise that equations of the formy=mx+ccorrespond to straight-line graphs.Simplify or transform linear expressions by collecting like terms; multiply a single term over a bracket.Plot the graphs of linear functions, whereon paper and using ICT.yis given explicitly in terms ofx,Core:Given values formandc, find the gradient of lines given by equations of the formy=mx+c.Construct functions arising from real-life problems and plot their corresponding graphs; interpret graphs arising from real situations,including distance–time graphs.ygiven implicitly in terms ofx), e.g.ay+bx=0,y+bx+c= 0, on paper and using ICT.Extension:Know and use the index laws(including in generalised form)for multiplication and division of positive integer powers;begin to extend understanding of index notation to negative and fractional powers, recognising that the index laws can be applied to these as well.y=x2,y= 3x2 + 4,y=x3.Square a linear expression, expand the product of two linear expressions of the formx±and simplify the corresponding quadratic expression;nestablish identitiessuch asa2 –b2 = (a+b)(a–b).change the subject of a formula.## Key Vocabulary:

## Suggested Lesson Outcomes:

SUPPORT TARGET

CORE## Framework:

## Teaching & Learning Resources:

Index Laws Resources

LCM Resources

HCF Resources

PFD Resources

Graphs Resources

Gradient Resources

y=mx c Resources

Formulae Resources

Inequalities Resources

Quadratics Resources