9-1 GCSE lesson. Starter: Converting from terminating decimals into fractions. Definitions of terminating, recurring and non-repeating decimals. How to know if a fraction is a terminating or non-terminating decimal [non-calculator] using prime factors. How to convert from a recurring decimal to a fraction using algebra. All ideas have worked examples. Differentiated slide of questions. All answers included.

Starter looks at factorising numbers using square numbers as one of the factors. Rational and Irrational numbers are explained and defined. Surds are then defined and explained in the context of square roots. Simplifying a surd is demonstrated and full simplification is explained using root 48. Question slides on each skill included. All answers provided.

Plotting Quadratic Graphs using tables of values. Review of straight line graphs and substitution. Worked examples of different quadratic curves and what is meant by “appropriate axis”. Questions and all answers all included.

Lesson explores solving non-linear equations graphically. Examples look at adding horizontal lines [y=4 etc] and then sloping lines [y=x+2] to solve different problems.

Examines 4 types of graphs: Linear, Quadratic, Cubic and Reciprocal. Defines properties of each and similarities (intercept). Multiple Choice questions looking at matching names and then equations to graphs.

Multiple Choice starter identifying linear and quadratic functions. Reminder of solving linear simultaneous equations graphically. Follows similar process to solve quadratic and linear simultaneous equations. Also looks at styles of questions and manipulations of equations to find which graphs to plot.

Starter using Pythagoras to find diagonals of quadrilaterals. Use of Pythagoras to explain equation of a circle based on the origin. Extends to look at circles not centred on the origin. Plenary looks at an example of simultaneous equations with a circle. Worked examples and question slides. All answers included.

Starter asks pupils to describe number patterns from pictures. Then examining the properties of Linear Sequences from term-to-term rules, pictures, straight line graphs. Examples of how the general rule is used: finding terms, finding positions of terms, seeing if a number belongs in a sequence, finding common terms in two sequences. Worked examples and question slides on each topic. All answers included.

Starter look at two-way tables. Links made to similarities and differences between two-way tables and frequency trees. Worked examples including finding probabilities. Worksheet includes questions finding frequencies from proportions of the whole and extends to larger trees. All answers included. Worksheet answers provided on ppt.

Lesson introduces language of formulae, variables, subject etc. Uses simple formulae with rectangles and circles to explain calculating an alternative variable. Looks first at formulae where variables only occur once. Extenda to look at examples where variables occur more than once. All skills have worked examples and questions. All answers included.

A complete lesson on ‘Averages from Tables’, written for the new GCSE specification. Examines two different types of large data sets ungrouped and grouped. Explains when and why we sometimes have to find estimates of the averages. Worked examples of all skills included. Questions and all answers included.

Lesson explores finding area in non-right triangles using formula ½ abSinC. Worked examples and questions on 1. finding the area 2. finding a missing angle given the area 3. finding a missing side given the area. Looks at example of 3. with isosceles triangle. All answers included.

Starter looks at adding vectors. Demonstrates how to find the magnitude of a vector using Pythagoras. Explanation of proving vectors are parallel and then if three points are on a straight line (collinear). Worked examples and questions on all skills. All answers included on ppt.

Starter; MC asking pupils to recognise different transformations. Examines how each transformation affects specific points and their coordinates. Rules and methods are derived. Worked examples of all skills and question slides. All answers included on the ppt.

Starter asks pupils to recognise which transformation produced an image [MC]. Definition of invariance and then examination of how each transformation does (or doesn’t) produce invariant points. Question slides. All answers included on ppt.

2 lessons and a worksheet covering Venn Diagrams. Includes looking at describing sets, populating Venn diagrams from with elements from sets and from frequencies. explains how to find probabilities from Venn diagrams. Introduces conditional probability and extends to Venn diagrams with 3 sets. All answers included, worksheet answers on ppt.

Expanding two or three brackets using the Grid method. Starter covers algebraic multiplication grids and multiplying two-digit numbers reviewing the grid method. Worked examples and question slides for both two and three bracket examples of increasing difficulty. All answers included.

Rearrange an equation to produce an iterative formula. Understand that there can be more than one iterative formula for an equation. Use an iterative formula to solve an equation.

Apply an iterative formula to solving a problem. Understand when to stop iterating.

Understand and write proportions as fractions and as algebraic relationships. Compare ratios and fractions. Express one variable in terms of another when represented as a ratio.