# Chris Barclay's Shop

Features of my lesson plans for KS3 and KS4 maths include sub-dividing topics into steps so that students develop one skill at a time, colour coded diagrams and explanations, worked solutions and putting the maths into real-life contexts. I am also focusing on different types of problem-solving questions and on questions where different topics are combined, say shape and algebra, probability and algebra, proportion and area. I welcome feedback and am open to suggestions for new lesson topics.

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Features of my lesson plans for KS3 and KS4 maths include sub-dividing topics into steps so that students develop one skill at a time, colour coded diagrams and explanations, worked solutions and putting the maths into real-life contexts. I am also focusing on different types of problem-solving questions and on questions where different topics are combined, say shape and algebra, probability and algebra, proportion and area. I welcome feedback and am open to suggestions for new lesson topics.

#### Transformation of Trigonometric Graphs

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The resource is for KS4 students. It consists of a lesson presentation, a worksheet which includes a matching exercise and a handout with the three trig graphs. The presentation includes a starter and worked solutions to the worksheet. The lesson starts with a revision of the trig graphs and transformations. Four examples of transformations of trig graphs are given before students complete a matching exercise. Students are then asked to do an exercise in finding maximum and minimum values, an exercise finding where axes are intersected and then to sketch some transformed graphs.

#### Rate of Flow

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This lesson is for KS4 students and teaches them to tackle problems involving rate of flow of a liquid, the volume of a liquid and time. The topic follows the model used to teach density and speed. The resource consists of a lesson presentation and worksheet. The lesson presentation consists of a starter, examples and worked solutions to all the questions on the worksheet. There are three exercises in the lesson with examples before each. The first exercise requires students to find the rate of flow, the second volume or time and the third exercise has more difficult contextual questions.

#### Depth-time Graphs in Different Vessels

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The lesson is aimed at low ability KS4 students, who struggle to construct or match a graph showing the depth of water against time as water flows at a steady rate into vessels of different shapes. The resource consists of a lesson presentation and a worksheet. The lesson presentation goes through the topic thoroughly. The worksheet gives a summary of the teaching, so that pupils don’t have to copy it down, and three questions. The lesson presentation also has a starter and worked solutions to the questions.

#### Plotting Graphs of Ax + By = C

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The lesson is aimed at KS4 students, who can plot a linear graph if expressed in the form y = mx + c, but who are slightly baffled by the graph being expressed in the form Ax + By = C.

#### Different Graphs in Real-life Contexts

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The lesson is aimed at KS4 students who are wondering what relevance different types of graph have. The learning objective is for students to see that these graphs do have real-life meaning and that this helps them differentiate between the different types of graph.

#### KS4 Geometric Proof

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This lesson looks at geometric proof for advanced KS4 students. The resource consists of a lesson presentation and a worksheet. The lesson presentation includes a starter and worked solutions to all questions on the worksheet. The starter asks students to prove that the sum of angles in a triangle is 180 degrees and prove the size of the interior and exterior angles in a pentagon. The first part of the lesson involves an example and questions involving proving properties of a common shape. The second part of the lesson involves an example and questions involving properties of composite shapes.

#### KS3 Geometric Proof

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This resource looks at geometric proof for KS3 students. The resource consists of a lesson presentation, a worksheet and a handout showing the conditions for congruent triangles. The lesson presentation includes a starter, examples and worked solutions to the questions on the differentiated worksheet. Questions include the angles in regular polygons, the angles between diagonals, using parallel lines and a line of symmetry.

#### Area to Money Contextual Problems

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This resource is for all KS4 students and teaches them how to tackle a common GCSE problem solving question. This lesson teaches students to tackle problems involving measuring an area, calculating the number of items such as tins or bags required and the cost of purchasing these items. The resource consists of a lesson presentation, a worksheet and a handout. The lesson presentation includes examples and fully worked solutions for the questions on the worksheet. The lesson is structured so that students start with easier two-stage problems involving finding area and then cost, before tackling the harder three-stage questions. The handout (HO) is a copy of the examples covered in the lesson and can be printed out for students to save them having to copy off the board.

#### Timetables

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This lesson is for KS4 students working towards the Foundation paper. The resource consists of a lesson presentation and a worksheet. The lesson presentation show students how to interpret and use timetables. It also includes a starter and worked solutions to the questions on the worksheet.

#### Problems of Area and Algebra (Linear)

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This resource is for KS4 students. The resource consists of a lesson presentation and a worksheet. The lesson presentation includes a starter, examples and worked solutions to the questions on the worksheet. The lesson teaches pupils how to find a linear expression for a composite area, how to form an equation and how to solve the linear equation to find the unknown.

#### Utility Bills

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This resource is for KS4 students working towards the Higher paper. It consists of a lesson presentation and worksheet. The lesson presentation includes a starter and worked solutions to the questions on the worksheet. The lesson is differentiated. It starts with using meter readings to find the amount of energy used and the cost of that energy. It then includes a standing charge and finally VAT on the total bill.

#### Probability Problems involving Algebra

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This lesson is for middle to high ability KS4 students. It teaches them how to use algebra to solve probability problems where there is an unknown. This could involve solving a linear equation or deriving a quadratic equation from a tree diagram and solving it. The resource consists of a lesson presentation and a worksheet. The lesson presentation includes a starter, an example and worked solutions to the questions on the worksheet.

#### Mutually exclusive events

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The resource is for KS4 students. It consists of a lesson presentation and a worksheet. The lesson presentation includes a starter, examples and worked solutions to the questions on the worksheet. The lesson introduces the concept of mutually exclusive events. Students are shown how to determine whether two events are mutually exclusive or not. The questions involve rolling dice, spinning spinners and choosing marbles. There is a question where the sum of probabilities for two events proves that they are not exclusive.

#### KS3 Algebraic Proof

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These two lessons are for capable KS3 students. Start with ‘1. Algebraic Proof Introduction’ and the accompanying handouts and then continue with ‘2. Algebraic Proof Multiples’ and its worksheet. Students are introduced to the idea of letting any number be n and to finding expressions for consecutive numbers, odd and even numbers. Students then find expressions for sums and products and finally learn how to prove that such an expression is a multiple of a specified number.

#### Profit and Loss

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This resource is for KS4 students preparing for the Foundation paper. The resource consists of a lesson presentation and a worksheet. The lesson presentation includes worked solutions to the questions on the worksheet. Students learn how to subtract costs from revenue and to interpret the answer as profit or loss. The questions on the worksheet are structured from straightforward to more complex.

#### Upper and Lower Bounds with Division

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This lesson is the third in the series and follows on from ‘Upper and Lower Bounds for Area and Volume’. This time the upper and lower bounds are calculated for a quantity involving the DIVISION of one quantity by another, for both of which upper and lower bounds are known. Again the concept is explained using real-life contexts.

#### Problems of Area and Algebra (Quadratic)

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This resource is for KS4 students. The resource consists of a lesson presentation and a worksheet. The lesson presentation includes a starter, examples and worked solutions to the questions on the worksheet. The lesson teaches pupils how to find a quadratic expression for a composite area, how to form an equation and how to solve the quadratic equation to find the unknown.

#### Upper & Lower Bounds with Multiplication

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This lesson follows on from ‘Upper and Lower Bounds in Context’ and again uses real life contexts to explain the concept. It teaches students how to find the upper and lower bounds for area and volume involving the multiplication of two or three lengths, each of which have their own upper and lower bounds.

#### Surface Area of Composite Shapes

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This resource is for advanced KS4 students. The resource consists of a lesson presentation and a worksheet. The lesson presentation includes a starter and worked solutions to all the questions on the worksheet. The lesson starts with a revision of the surface area for spheres, cylinders and cones. Students are then extended to learn how to find the surface area of shapes such as hemispheres, frustums and composite 3D shapes.

#### Functional Problems involving Area

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This resource is for KS4 students. The resource consists of a lesson presentation and a worksheet. The lesson presentation includes worked solutions to the questions on the worksheet. Students learn to tackle functional problems involving dividing one area by another. The contexts include finding the number and cost of tiles and the amount and cost of paint.