# Gareth Evans's Shop

Secondary Mathematics Resources.

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Secondary Mathematics Resources.

#### Introducing Angles

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A year 7 unit of work on angles. (1) Types of Angles: Turns. Acute, obtuse and reflex angles. Naming angles. (2) Measuring Angles: Estimating angles. Using a protractor to measure angles. (3) Drawing Angles: Using a protractor to draw angles. Drawing special angles without a protractor. (4) Calculating Angles Angles around a point. Angles on a straight line. Vertically opposite angles. (5) Angles in Triangles Angles in a triangle. Types of triangles. The exterior angle of a triangle. Constructing triangles.

#### Year 7 Numeracy Homework Pack

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A weekly numeracy homework pack, covering two six-week periods. Each week contains 9 “bread &amp; butter” questions and a reasoning question. Questions and Answers are included. English and Welsh versions are included. Updated for 2021.

#### Year 8 Numeracy Homework Pack

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A weekly numeracy homework pack, covering two six-week periods. Each week contains 9 “bread &amp; butter” questions and a reasoning question. Questions and Answers are included. English and Welsh versions are included. Updated for 2021.

#### Year 9 Numeracy Homework Pack

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A weekly numeracy homework pack, covering two six-week periods. Each week contains 9 “bread &amp; butter” questions and a reasoning question. Questions and Answers are included. English and Welsh versions are included. Updated for 2021.

#### Accuracy of Measurements

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A year 10 unit of work covering the following topics. (1) Upper and Lower Bounds: Revision of how to round off. Upper and lower bounds. Problem solving (intermediate tier). Problem solving (higher tier). (2) Appropriate Degree of Accuracy: Calculating answers to an appropriate degree of accuracy. (3) Compound Measures: Distance, time and speed. Population, area and population density. Mass, volume and density. Other compound measures.

#### Data Handling and Statistics 4

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A year 10 unit of work covering the following topics: (1) Questionnaires: Designing questionnaires. Criticising questions. Hypotheses. (2) Sampling: Simple random sampling. Systematic sampling. Stratified sampling. (3) Frequency Polygons: Drawing frequency polygons. Interpreting frequency polygons. (4) Box and Whisker Diagrams: Drawing box and whisker diagrams. The connection between box and whisker diagrams and cumulative frequency diagrams. (5) Comparing Averages: Revising averages. Choosing the most appropriate average. Comparing averages.

#### Fractions, Percentages and Decimals

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A year 10 unit of work covering the following topics: (1) Calculating: Mastering the techniques. Problem solving. (2) Recurring Decimals: Changing fractions to decimals. Terminating and recurring decimals. Changing recurring decimals to fractions. (3) Converting: Converting between fractions, decimals and percentages. Starting with a percentage. Starting with a fraction. Starting with a terminating decimal. Starting with a recurring decimal. (4) Exam Technique: Summary. Assessing written communication. Mark schemes. Timing.

#### The End of Year 8

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A year 8 unit containing the following topics. (1) Directed Numbers: Ordering Directed Numbers. ‘Less than’ and ‘More than’. Calculating with Directed Numbers (Addition; Subtraction; Multiplication; Division). (2) Decimals: Adding and Subtracting Decimals. Multiplying and Dividing Decimals by a Whole Number Less Than 10. Ordering Decimals. Converting between Percentages and Decimals. Rounding Off to a Specified Number of Decimal Places. (3) Angles 2: Revision of Year 7 work. Angles with Parallel Lines. (4) Transformations: Rotation: Rotating a Shape Around a Specific Point.

#### Co-ordinates in the Four Quadrants

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A year 7 unit of work covering the following topics. (1) The First Quadrant: Plotting co-ordinates in the first quadrant. (2) The Four Quadrants: The four quadrants. Plotting co-ordinates in the four quadrants. (3) Mid-point of a Line: The first quadrant. Adding negative numbers. The four quadrants. (4) Using Co-ordinates: Missing co-ordinates. Translations using a column vector.

#### Measuring Solids

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A year 10 unit of work covering the following topics. (1) Solids: Volume and surface area of a cuboid. Volume of a prism. Volume and surface area of a cylinder. Volume of a pyramid. Surface area of a cone. Volume and surface area of a sphere. (2) Dimensions: Length, area and volume. Nonsensical formulae. (3) Composite Solids: Volume of composite solids. Frustum of a cone. Hemisphere. (4) Similar Shapes: Calculating the scale factor. Calculating missing lengths. Similar or not? Similar triangles. Scale factor for length, area and volume. Using similar triangles to calculate the volume of a frustum of a cone. (5) Pythagoras’ Theorem (3-D): Calculating lengths in three-dimensional shapes.

#### Factors and Multiples

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A year 8 unit of work covering the following topics. (1) Square Root and Cube Root: Revision of Square Numbers and Cube Numbers from Year 7 work. Square Root, Cube Root. (2) Factors and Prime Numbers: Listing common factors. Defining a prime number. Recognising a prime number. (3) Venn Diagrams: Two circle Venn diagrams. Three circle Venn diagrams. Set notation. (4) Index Form: Writing a number as a product of its prime factors. Writing numbers in index form. Square numbers in index form. (5) Highest Common Factor, Lowest Common Multiple: Finding the Highest Common Factor of two numbers. Finding the Lowest Common Multiple of two numbers.

#### Data Handling and Statistics 1

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A year 7 unit of work covering the following topics. (1) The Mean: Calculating the mean; Calculating the mean from a table; Comparing two distributions. (2) The Range: Calculating the range; Comparing two distributions. (3) Bar Charts: Types of data; Bar charts; Frequency diagrams; Interpreting charts. (4) Mean of Grouped Data: Estimating the mean from a table. (5) Pie Charts: Drawing pie charts; Interpreting pie charts

#### Working with Money

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A year 9 unit of work containing the following topics. (1) Rounding Off: Significant Figures: Rounding a number off to a specified number of significant figures. Labelling the significant figures of a number. (2) Estimation: Estimating the answer to calculations. (3) Compound Interest: Revising simple interest. The compound interest method of borrowing and investing money. (4) Foreign Money: Exchange rates. Exchanging money. (5) Household Bills: Electricity; gas; water; sewerage and mobile phone bills.

#### The End of Year 11

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A year 11 unit of work covering the following topics: (1) Surds: Rational and irrational numbers. Surds. Simplifying surds. Expanding with surds. (2) AER, APR. Annual Equivalent Rate (AER). Alternative method of calculating AER. Annual Percentage Rate (APR). (3) Histograms: Frequency density. Drawing a histogram. Interpreting a histogram. Estimating the median from a histogram. Estimating the quartiles from a histogram. Comparing histograms.

#### Data Handling and Statistics 2

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A year 8 unit of work containing the following topics. (1) The Mode: Calculating the mode. Calculating the mode from a table. The modal class. Comparing two distributions. (2) Pictograms: Drawing pictograms. Interpreting pictograms. (3) Vertical Line Diagrams Revising types of data. Drawing vertical line diagrams. Interpreting vertical line diagrams. (4) Line Graphs: Drawing line graphs. Interpreting line graphs. Revising displaying data. (5) Probability in Words: Vocabulary of probability. Probability scale. Probability as a number.

#### Straight Line Graphs

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A year 9 unit of work on the following topics: (1) Gradient of a Line: Measuring and finding the gradient of straight lines. (2) Straight Line Graphs: Vertical lines of the form 𝑥 = 𝑎. Horizontal lines of the form 𝑦 = 𝑏. General lines of the form 𝑦 = 𝑚𝑥 + 𝑐. Solving simultaneous equations graphically. (3) The Gradient of Parallel and Perpendicular Lines: The gradient of parallel lines. The gradient of perpendicular lines. (4) Transformations: Reflection: Reflecting shapes in lines of the form 𝑥 = 𝑎 and 𝑦 = 𝑏. Reflecting shapes in lines of the form 𝑦 = 𝑚𝑥 + 𝑐.

#### Data Handling and Statistics 3

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A year 9 unit of work containing the following topics. (1) The Median: Calculating the median. Calculating the median from a table. Comparing two distributions. (2) The Median Class: Finding the median class or the estimate for the median. (3) The Interquartile Range: Calculating the interquartile range of a set of data. (4) Cumulative Frequency Diagrams: Cumulative frequency tables. Drawing a cumulative frequency diagram. Estimating the median and the interquartile range. (5) Scatter Diagrams: Drawing a scatter diagram. Types of correlation. Line of best fit. (6) Probability as a Fraction Writing the probability of an event as a fraction. The probability that an event will not happen. Sample space diagrams. Expected frequency.

#### Developing Algebra 2

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A year 10 unit of work covering the following topics. (1) Simple Factorising: Reversing Expansion. Simple Factorising.More than one Variable. (2) Factorising Quadratic Expressions: Preparation. Factorising Quadratic Expressions of the form 𝑥² + 𝑎𝑥 + 𝑏. Solving Quadratic Equations through Factorising. Factorising Quadratic Expressions of the form 𝒂𝒙² + 𝒃𝒙 + 𝒄. The Difference of Two Squares. (3) Simultaneous Equations: Multiplying Equations. Subtracting Equations. Multiplying Equations to obtain Equal Coefficients. Solving Linear Equations. Solving Simultaneous Equations. (4) Changing the Subject: Re-arranging formulae. (5) Expression, Equation, Formula, Identity: Recognising expressions, equations, formulae and identities. Proving identities.

#### Introducing Algebra

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A year 8 unit of work covering the following topics: (1) Sequences: Number patterns. Function machines. (2) Forming Expressions Rules of algebra. Writing algebraic expressions. (3) Substitution: Substituting into algebraic expressions. Substituting into formulae. (4) Collecting Like Terms: Collecting like terms using one variable. Collecting like terms using more than one variable. (5) Solving Equations Solving one step equations. Solving more complex equations. Solving problems with equations.

#### Measuring Shapes 4

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A year 11 unit of work covering the following topics. (1) Congruent Shapes: Recognising congruent shapes. Congruent triangles proofs. (2) Angles in Polygons: The interior angles of a polygon. The exterior angles of a polygon. Tessellations. (3) Circle Theorems: Intermediate tier circle theorems. Higher tier circle theorems. (4) Transformations: Translation. Rotation. Reflection. Enlargement. Combinations.