# Chris Barclay's Shop

Average Rating4.73
(based on 81 reviews)

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.

#### Comparing Two Offers

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This resource is for low ability KS4 students. The resource consists of a lesson presentation and a worksheet. the lesson presentation includes worked solutions to all the questions on the worksheet. Students first learn how to find unit costs in order to compare different offers. They then learn how to compare prices given for different numbers of kg and other units. Finally they learn how to compare special offers such as BOGOF.

#### Equations with Indices

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This resource consists of a short lesson plus two full lessons. Between the three lessons, all the types of harder questions involving indices are covered. For each lesson, there is a presentation and worksheet. The presentations include starters, examples and worked solutions to the questions on the worksheets. ‘Writing number as power of another’ covers two types of questions: (a) writing one number as a power of another and (b) finding the base which when raised to a given index equals a given value. ‘Solving Equations by Equating Indices’ looks at questions where the unknown is part of the indices. The lesson is structured to cover (a) equations where all the bases arrre the same, (b) the bases are all integer powers of one of them and © where the bases are not integer powers of any of them. ‘Simultaneous Equations with Powers’ looks at questions where (a) the two unknowns are in the indices of the two simultaneous equations and (b) the two unknown are the bases.

#### 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.

#### Finding Turning Points

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The resource is for advanced KS4 students. It consists of a lesson presentation and a worksheet. The lesson presentation includes a starter, the teaching part and worked solutions to all the questions on the worksheet. The starter is revision of completing the square. Students are then taught how to use the completed square to find the coordinates of the turning point for a quadratic whose coefficient of x squared is 1. There are 8 examples for the students to do themselves. There is an extension of 6 questions involving quadratics where the coefficient of the x squared is either more than 1 or negative.

#### Surds and Shapes

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The resource is for KS4 students preparing for the Higher paper. The resource assumes that students know how to add and subtract surds, how to multiply and divide surds and how to simplify surds. A worksheet is included and the lesson presentation includes a starter, examples and worked solutions. The new specification GCSE Higher papers feature many questions where two or more topics are combined. This lesson prepares students for questions that combine knowledge of surds with the properties of shapes and using formulae. In the first half of the lesson, students learn how to find and simplify expressions involving surds for the perimeter and area of shapes. In the second half of the lesson, students learn how to find a missing length in surd form from the area or perimeter of the shape and other dimensions. In both cases the questions are structured to start with easier examples and to end with harder examples.

#### 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.

#### 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.

#### Density of a Mixture of Liquids

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This resource is designed for KS4 students attempting the Higher paper. It consists of a cover slide, a worksheet of 10 questions and a whole lesson including starter, examples and worked solutions to all the questions. The resource aims to equip students to tackle problems involving the mixture of two liquids and requiring students to find the density of the mixture or, if given that quantity, other properties of the mixture or of the constituent parts. The principles that mass and volume are conserved are given and an example is solved. The worksheet is structured: 2 questions where the properties of the parts are given and students have to find the density of the mixture; 2 questions where students have to find a property of a part; 2 questions with unit mismatches; 2 questions involving solids composed of two materials; 2 questions where students are asked to use percentages and ratios.

#### 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.

#### Proportion of Shapes

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This resource is for KS4 students. It consists of a lesson presentation, including starter, examples and worked solutions, and a worksheet including extension questions. The lesson intends to help students answer GCSE questions where they are asked to give the proportion of a larger shape that is shaded. They are shown that the proportion is a fraction equal to the shaded area divided by the larger area. Examples are given and then students answer questions on a structured worksheet. Initially the questions involve normal shapes whose areas are given by formulae but they become harder requiring students to be more enterprising in order to find the areas.

#### Using Sine and Cosine Rules

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The resource is for advanced KS4 students. The ability to use the sine rule, the cosine rule and the formula for the area of triangles is assumed. The lesson focuses on using two or three of these techniques to find missing lengths, angles and areas in problems involving adjoining triangles. The lesson presentation includes a starter and worked solutions to the problems on the worksheet.

#### Properties of Shapes using Algebra

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The resource is for KS4 students. It consists of a lesson presentation and a worksheet. The example and questions involve using the sum of angles for a shape to form an equation, then to solve the angle, to substitute the solution into the expressions for angles and to then draw a conclusion from the angles of the shape.

#### Probabilities and Two-way tables

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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 and worked solutions to all the questions on the worksheet. The starter is revision of completing two-way tables. Students then learn to find probabilities from two-way tables. They then learn how to construct two-way tables from text and then to find probabilities.

#### 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.

#### Compound Quantities and Units

6 Resources
This bundle consists of 6 resources, all involving compound quantities such as speed, density and rate of flow. All the resources have been designed in response to changes under the new GCSE specification and new types of questions seen in the Higher papers. These changes include questions about two-stage journeys, the mixture of two liquids of different density and unit mismatches including the units for compound quantities.

#### Trigonometry in 3D including sine and cosine rules

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This resource is for KS4 pupils taking the Higher paper. The objective of the resource is to help pupils tackle 3D problems where they need to apply Pythagoras’ Theorem, trigonometry in right-angled triangles and the cosine rule. The presentation has a starter, two examples and worked solutions to the 6 questions on the worksheet. The shapes covered are cuboids, pyramids, cylinders and wedges. (There is another resource available which does not require the application of cosine rule in similar problems).

#### 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.

#### Proving whether Triangle is Right-angled

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This resource is a short piece of work (less than a full lesson) for KS4 students. Knowledge of Pythagoras’ Theorem to find missing lengths of right-angled triangles is assumed. The resource uses the Theorem to show whether a triangle whose three lengths are given is right-angled or not.

#### 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.