GCSE Maths
- Description
- Curriculum
- Reviews
GCSE Maths – Your Complete Course
Master the essential knowledge, skills and problem-solving techniques needed for GCSE Maths success.
This comprehensive GCSE Maths course develops a strong understanding of the key mathematical principles across Number, Ratio and Proportion, Algebra, Geometry and Measures, Statistics, and Probability. Through engaging lessons, guided practice, and challenging real-life applications, students build the confidence and mathematical reasoning skills needed to tackle GCSE examination questions successfully.
Designed for students studying AQA, Edexcel, OCR, WJEC/Eduqas, or CCEA specifications, this course supports learners working at both Foundation and Higher Tier. It develops mathematical fluency, problem-solving, and reasoning skills while preparing students thoroughly for GCSE examinations and further study.
What You’ll Experience
Each unit is carefully structured to build confidence, reinforce understanding, and provide regular opportunities for assessment and revision through interactive learning activities.
- Interactive Lessons – Engaging, easy-to-follow lessons covering key mathematical concepts, methods, and problem-solving strategies, supported by worked examples, visual explanations, and practice activities.
- Graded End-of-Topic Tests – Every topic concludes with an assessment designed to check understanding, identify misconceptions, and measure progress across key GCSE skills.
- Foundation and Higher Tier Challenges – Carefully differentiated activities ensure that students can develop their understanding at the appropriate level while progressing towards increasingly challenging mathematical problems.
- Number Chase Games – Each unit concludes with an exciting Foundation and Higher Tier Number Chase game, designed to recap and consolidate key concepts, methods, and problem-solving skills in an engaging and competitive format.
- GCSE Practice Examinations – Students can test their knowledge using dedicated Foundation and Higher Tier GCSE Paper 1, Paper 2, and Paper 3 practice examinations, providing comprehensive preparation for the final GCSE assessments.
Course Units
The course is divided into five engaging and structured units:
1. Numbers
Develop confidence with the fundamental principles of number, including fractions, decimals, percentages, standard form, indices, surds, bounds, and calculations involving large and small numbers.
2. Ratio and Proportion
Explore ratios, percentages, direct and inverse proportion, exchange rates, compound measures, best-buy problems, and proportional reasoning in a range of mathematical and real-life contexts.
3. Algebra
Build essential algebraic skills, including simplifying and manipulating expressions, solving linear and quadratic equations and inequalities, sequences, graphs, functions, simultaneous equations, algebraic fractions, proof, and iteration.
4. Geometry and Measures
Develop spatial and geometric reasoning through topics including angles, polygons, area, perimeter, volume, transformations, Pythagoras’ theorem, trigonometry, bearings, constructions, circle theorems, vectors, and coordinate geometry.
5. Statistics and Probability
Learn how to collect, represent, interpret, and analyse data using tables, charts, graphs, averages, cumulative frequency, box plots, histograms, sampling, probability, and statistical reasoning.
Prepare for Your GCSE Exams
The course includes a complete suite of Foundation and Higher Tier GCSE practice examinations:
- Foundation Paper 1, Paper 2 and Paper 3
- Higher Paper 1, Paper 2 and Paper 3
These examinations provide extensive practice across the full GCSE curriculum, helping students become familiar with examination-style questions, develop effective problem-solving strategies, improve mathematical reasoning, and identify areas requiring further revision.
Why Choose This Course?
This course combines interactive learning, regular assessment, engaging revision games, and comprehensive GCSE examination practice to provide a structured pathway towards mathematical success.
By working through the lessons, completing graded end-of-topic tests, taking part in the Number Chase unit challenges, and practising with Foundation or Higher Tier examination papers, students can build the knowledge, confidence, fluency, and problem-solving skills needed to perform at their best in GCSE Maths.
Whether you are aiming to secure a strong pass or achieve the highest grades, GCSE Maths – Your Complete Course provides the structure, practice, and challenge needed to help you reach your full potential.
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1Lesson 1: Comparing and Ordering Decimals1 hour
Learning Objectives:
- Identify and represent decimals up to thousandths using base-10 concrete models.
- Sequence sets of decimal values correctly across ascending and descending sorted configurations.
- Compare pairs of decimal values securely using the inequality signs (<, >, =).
- Analyse mathematical student responses critically to locate and discuss structural place value errors.
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2Lesson 1: Comparing and Ordering Decimals End of Topic Test10 minutes
This end-of-topic test assesses students' understanding of comparing and ordering decimal numbers using place value. It covers comparing decimals with different numbers of decimal places, ordering decimals in ascending and descending order, comparing positive and negative decimals, and solving contextual and reasoning problems involving decimal values. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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3Lesson 2: Order of Operations ( BIDMAS )10 minutes
Learning Objectives:
- Verify priority parity across operations (+, -, *, /) and explain negative calculations.
- Determine bracket placements to transform erroneous equations into correct ones.
- Apply the Associative & Distributive Laws systematically using mathematical grouping structures.
- Interpret fractions as implicit divisions requiring high-priority execution models.
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4Lesson 2: Order of Operations End of Topic Test10 minutes
This end-of-topic test assesses students' understanding of the correct order of operations using the BIDMAS rules. It covers calculations involving brackets, indices, multiplication, division, addition, and subtraction, as well as expressions with multiple operations and powers. Students will also apply BIDMAS to solve contextual and reasoning problems, demonstrating accurate mathematical working and logical thinking. The assessment is designed to evaluate students' fluency, accuracy, and problem-solving skills, identify any misconceptions, and ensure they are well prepared for GCSE examination-style questions.
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5Lesson 3: Recurring Decimals1 hour
Learning Objectives:
- Convert simple single-digit recurring decimals to equivalent fractions.
- Process complex mixed/offset structures using dynamic multiplication indices.
- Cancel infinite decimal tails using multi-scale subtraction systems.
- Deduce variable generalisations and evaluate fractions using operations (
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6Lesson 3: Recurring Decimals End of Topic Test10 minutes
This end-of-topic test assesses students' understanding of recurring decimals and their relationship with fractions. It covers identifying recurring decimals, converting recurring decimals into fractions, converting fractions into recurring decimal form where appropriate, and solving contextual and reasoning problems involving recurring decimals. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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7Lesson 4: Comparing Fractions, Decimals & Percentages1 hour
Learning Objectives:
- Understand and apply inequality symbols (>,<, =) to express mathematical order.
- Compare mixed format pairs using common decimal or percentage benchmarks.
- Convert between equivalent fractions, decimals, and percentages smoothly.
- Sort multi-item lists into accurate ascending and descending sequences.
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8Lesson 4: Comparing Fractions, Decimals and Percentages End of Topic Test10 minutes
This end-of-topic test assesses students' understanding of comparing and ordering fractions, decimals, and percentages by converting between the different forms and applying place value and proportional reasoning. It covers converting fractions to decimals and percentages, converting decimals and percentages to fractions, comparing values presented in different forms, ordering mixed representations in ascending and descending order, and solving contextual and reasoning problems involving fractions, decimals, and percentages. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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9Lesson 5: Fractions, Decimals & Percentages Conversions1 hour
Learning Objectives:
- Convert decimals and percentages to simplified fractions using base-10 place value.
- Represent values greater than 1 (>100%) as mixed numbers, improper fractions, and decimals.
- Use equivalent fractions (scaling denominators to 10, 100, or 1000) for fast mental conversions.
- Identify recurring decimal patterns (ninths and elevenths) and solve contextual problems.
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10Lesson 5: Fractions, Decimals & Percentages Conversions End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of converting between fractions, decimals, and percentages using efficient mathematical methods. It covers converting fractions to decimals and percentages, converting decimals and percentages to fractions, expressing values in their simplest form, and selecting the most appropriate representation for a given context. Students will also solve contextual and reasoning problems involving conversions between fractions, decimals, and percentages. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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11Lesson 6: Percentages1 hour
Learning Objectives:
- Calculate percentages of quantities mentally and using decimal multipliers.
- Calculate original values before percentage increases or decreases (Reverse Percentages).
- Express one quantity as a percentage of another and compute percentage changes.
- Solve multi-step financial, interest, and compound percentage problems.
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12Lesson 6: Percentages End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of calculating percentages, percentage change, and reverse percentages in a variety of mathematical and real-life contexts. It covers finding percentages of quantities, expressing one quantity as a percentage of another, calculating percentage increases and decreases, solving reverse percentage problems, and applying percentage calculations to contextual and reasoning questions involving finance, discounts, profit and loss, depreciation, and population change. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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13Lesson 7: Compound Percentage Change1 hour
Learning Objectives:
- Calculate compound interest using single-step decimal multiplier powers: P ( 1 + r/100 )t.
- Solve depreciation and wildlife population decay problems with negative multipliers.
- Compare simple interest versus compound growth across financial accounts over multiple years.
- Calculate original principal values, interest rates, and compounding intervals in reverse problems.
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14Lesson 7: Compound Percentage Changes End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of compound percentage changes, simple interest, and compound interest in mathematical and real-life financial contexts. It covers calculating repeated percentage increases and decreases, applying multipliers, determining simple and compound interest over multiple time periods, interpreting exponential growth, and solving contextual and reasoning problems involving savings, loans, investments, inflation, and depreciation. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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15Lesson 8: Standard Form1 hour
Learning Objectives:
- Multiply numbers in standard form using index laws ( 10m x 10n = 10m+n).
- Add and subtract values by aligning powers of ten or converting to ordinary numbers.
- Divide standard form numbers by rewriting as fractions and subtracting exponents.
- Adjust non-standard intermediate forms so the front number obeys 1 =< a < 10.
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16Lesson 8: Standard Form End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of performing calculations with numbers expressed in standard form. It covers converting numbers into and out of standard form, multiplying and dividing numbers in standard form, adding and subtracting numbers written in standard form where appropriate, applying the laws of indices during calculations, and solving contextual and reasoning problems involving very large and very small numbers in scientific and real-world contexts. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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17Lesson 9: Bounds & Error Intervals1 hour
Learning Objectives:
- Determine Lower Bounds (LB), Upper Bounds (UB), and write Error Intervals using a <= x < b.
- Perform bound calculations with +,- ,x ,/ and geometric formulas.
- Understand Truncation vs. Rounding and represent intervals on interactive number lines.
- Express answers to a suitable degree of accuracy by comparing bounds.
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18Lesson 9: Bounds & Error Intervals End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of upper and lower bounds, error intervals, and the effects of rounding on calculations. It covers determining error intervals for rounded values, calculating upper and lower bounds, performing calculations involving bounds, interpreting measurement accuracy, and solving contextual and reasoning problems involving estimation, measurement, and real-world applications. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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19Lesson 10: Prime Factorisation & LCM/HCF1 hour
Learning Objectives:
- Express numbers as products of prime factors in index form using factor trees.
- Calculate HCF ("what loses") and LCM ("what wins") using prime factor column alignment.
- Determine divisibility and count total factors using combinatorics.
- Solve real-world contextual problems involving repeating cycles and schedules.
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20Lesson 10: Prime Factorisation & LCM/HCF15 minutes
This end-of-topic test assesses students' understanding of prime factorisation and its use in finding the Highest Common Factor (HCF) and Lowest Common Multiple (LCM). It covers identifying prime numbers, expressing numbers as products of prime factors using factor trees and index notation, calculating the HCF and LCM of two or more numbers, and solving contextual and reasoning problems involving factors, multiples, divisibility, and repeated events. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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21Lesson 11: Laws of Indices & Exponential Rules1 hour
Learning Objectives:
- Apply multiplication, division, and power rules.
- Evaluate zero indices and negative indices.
- Simplify fractional powers and apply powers to algebraic product terms.
- Solve equations involving changing bases and reverse fractional powers.
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22Lesson 11: Laws of Indices & Exponential Rules End of Topic Test1 hour
This end-of-topic test assesses students' understanding of the laws of indices and their application to simplifying and evaluating algebraic and numerical expressions. It covers multiplying and dividing powers with the same base, raising a power to a power, zero, negative and fractional indices (where appropriate), simplifying expressions using the laws of indices, and solving contextual and reasoning problems involving exponential growth, decay, and scientific notation. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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23Lesson 12:Surds & Irrational Numbers1 hour
Learning Objectives:
- Distinguish between rational numbers and irrational surds.
- Simplify surds by extracting square factors.
- Perform arithmetic, expand brackets, and solve geometric surd problems.
- Rationalise denominators using monomial and conjugate binomial multipliers.
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24Lesson 12: Surds & Irrational Numbers End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of surds and irrational numbers, and their use in exact calculations. It covers identifying rational and irrational numbers, simplifying surds, adding, subtracting, multiplying, and dividing surds, rationalising denominators, and solving contextual and reasoning problems involving exact values and geometric applications. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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25Catch Game: Numbers Number ChaserText lesson
Number Chaser is an exciting, fast-paced CATCH GCSE Maths game designed to strengthen students’ confidence and fluency with key Number skills. Students race against the clock to solve GCSE-style numerical problems, select the correct answer and progress through increasingly challenging questions. The game can include topics such as fractions, decimals, percentages, negative numbers, powers and roots, standard form, rounding and estimation.
By combining timed challenges, instant feedback and repeated practice, Number Chaser encourages students to think quickly and accurately while making revision more enjoyable. The competitive, game-based format can boost motivation and encourage regular practice, helping students identify weaknesses, improve calculation speed, and build the confidence needed to tackle Number questions successfully in GCSE Mathematics.
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26Lesson 1: Ratio & Proportional Reasoning1 hour
Learning Objectives:
- Simplify 2-part and 3-part integer ratios to the simplest integer form.
- Solve sharing problems given the Total, a Single Quantity, or a Difference between parts.
- Combine two separate ratios into a single combined ratio.
- Solve advanced changing ratio problems algebraically using ax, bx equations and cross-multiplication.
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27Lesson 1: Ratio and Proportional Reasoning End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of ratio and proportional reasoning in mathematical and real-life contexts. It covers simplifying and interpreting ratios, dividing quantities in a given ratio, solving direct and inverse proportion problems, using scale factors and recipes, applying unit rates and best-buy comparisons, and solving contextual and reasoning problems involving proportional relationships. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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28Lesson 2: Direct and Inverse Proportion1 hour
Learning Objectives:
- Set up equations using the constant of proportionality k for direct proportion (y=kxn).
- Solve inverse proportion problems (y=k/xn) for linear, square, cubic, and root relations.
- Recognise graphical representations of direct linear, direct power, and reciprocal inverse proportion.
- Solve multi-variable exam scenarios combining proportional links between variables.
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29Lesson 2: Direct and Inverse Proportion End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of direct and inverse proportion and their application to mathematical and real-life situations. It covers identifying proportional relationships, using equations and graphs to represent direct and inverse proportion, solving problems involving proportional constants, interpreting proportional relationships in context, and applying proportional reasoning to contextual and multi-step problems. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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30Lesson 3: Best Buy & Value for Money1 hour
Learning Objectives:
- Calculate and compare unit prices (cost per item, cost per gram, or cost per litre).
- Use LCM and HCF scaling strategies to compare multi-pack quantities efficiently.
- Evaluate special promotional offers (percentage discounts vs. "Buy X Get 1 Free").
- Solve complex real-world comparisons involving unit conversions and additional travel costs.
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31Lesson 3: Best Buy & Value for Money End of Topic Test15 minutes
This end of topic test assesses students' understanding of best-buy and value-for-money calculations in a range of mathematical and real-life contexts. It covers comparing prices using unit costs, calculating cost per unit, evaluating special offers and discounts, making informed purchasing decisions, and solving contextual and reasoning problems involving shopping, budgeting, and financial comparisons. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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32Lesson 4: Exchange Rates1 hour
Learning Objectives:
- Convert between currencies using multiplicative ratio tables.
- Compare prices in different countries by standardising to a common base currency.
- Evaluate foreign exchange deals with flat and percentage commission fees or banknote limits.
- Analyse market exchange rate fluctuations and multi-item holiday budgets.
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33Lesson 4: Exchange Rates End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of exchange rates and currency conversions in a range of mathematical and real-life contexts. It covers converting between different currencies using exchange rates, interpreting and applying exchange rate information, calculating the cost of purchases and travel expenses in foreign currencies, and solving contextual and reasoning problems involving currency exchange, budgeting, and international transactions. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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34Lesson 5: Compound Measures & Rate of Flow1 hour
Learning Objectives:
- Calculate Speed, Density, and Pressure using compound formula triangles.
- Convert time units (hours to decimal hours, minutes, seconds) and unit scales ( m/s to km/h).
- Analyse multi-leg journeys and combined density mixtures using structured tables.
- Solve rates of flow in 3D prism containers, composite cuboids, and conical silos.
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35Lesson 5: Compound Measures & Rate of Flow End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of compound measures and rate of flow in a range of mathematical and real-life contexts. It covers calculating and interpreting speed, density, pressure, and flow rates; selecting and applying the correct compound measure formula; converting between appropriate units; and solving contextual and reasoning problems involving travel, engineering, science, and fluid flow. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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36Catch Game : Ratio and Proportion Number ChaserText lesson
Number Chaser is an exciting, fast-paced CATCH GCSE Maths game designed to strengthen students’ confidence and fluency with key Ratio and Proportion skills. Students race against the clock to solve GCSE-style problems, select the correct answer and progress through increasingly challenging questions. The game can include topics such as simplifying ratios, sharing quantities in a given ratio, direct and inverse proportion, scale drawings, unit conversions and proportional reasoning.
By combining timed challenges, instant feedback and repeated practice, Number Chaser encourages students to think quickly, accurately and logically while making revision more enjoyable. The competitive, game-based format can boost motivation and encourage regular practice, helping students identify weaknesses, improve problem-solving skills, and build the confidence needed to tackle Ratio and Proportion questions successfully in GCSE Mathematics.
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37Lesson 1: Algebraic Expressions1 hour
Learning Objectives:
- Model terms, constants, and zero pairs using visual algebra tiles.
- Multiply and divide single algebraic terms using coefficient commutativity and index laws.
- Formulate algebraic expressions from real-world contexts, ages, prices, and perimeters.
- Simplify complex expressions by collecting like terms and cancelling zero pairs.
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38Lesson 1: Algebraic Expressions End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of algebraic expressions and their application in mathematical problem-solving. It covers writing and interpreting algebraic expressions, simplifying expressions by collecting like terms, expanding single and double brackets, factorising simple expressions, substituting numerical values into expressions, and solving contextual and reasoning problems involving algebraic relationships. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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39Lesson 2: Substitution with Powers and Roots1 hour
Learning Objectives:
- Substitute positive and negative integers into multi-term algebraic expressions.
- Understand the differences in order of operations between cx2 and (cx)2.
- Evaluate fractional bases, decimal exponents, square roots, and higher-order roots.
- Apply substitution to real-world physics, kinematics, geometry, and environmental growth models.
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40Lesson 2: Substitution with Powers and Roots End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of substituting numerical values into algebraic expressions involving powers and roots. It covers substituting positive and negative numbers into expressions, evaluating expressions containing squares, cubes, square roots, cube roots, and higher powers, applying the correct order of operations, and solving contextual and reasoning problems involving algebraic formulae. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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41Lesson 3: Expanding Single, Double and Multiple Brackets1 hour
Learning Objectives:
- Expand single brackets using area models and distribute coefficients.
- Multiply double brackets and collect like terms using grid representations.
- Multiply three brackets and cubic expressions in descending powers.
- Apply bracket expansion to cuboid volumes, geometric areas, and Pythagoras problems.
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42Lesson 3: Expanding Single, Double and Multiple Brackets15 minutes
This end-of-topic test assesses students' understanding of expanding algebraic expressions involving single, double, and multiple brackets. It covers expanding single brackets, expanding two or more brackets, multiplying binomials, simplifying expressions by collecting like terms after expansion, and solving contextual and reasoning problems involving algebraic expressions and formulae. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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43Lesson 4: Factorising Expressions1 hour
Learning Objectives:
- Factorise single terms using area models and the highest common numerical/variable factors.
- Factorise expressions with common bracketed factors.
- Factorise higher-power expressions.
- Apply bracketed factorisation to geometric composite areas and algebraic proofs.
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44Lesson 4: Factorising Expressions End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of factorising algebraic expressions using a range of algebraic techniques. It covers factorising by taking out common factors, factorising into bracketed factors, using area models to factorise expressions, factorising expressions involving higher powers, and solving contextual and reasoning problems involving algebraic manipulation and mathematical modelling. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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45Lesson 5: Factorising Quadratics1 hour
Learning Objectives:
- Factorise single terms and extract the highest common numerical & variable factors.
- Factorise quadratic expressions of the form x2 + bx + c using sum & product factor pairs.
- Apply the Difference of Two Squares a2-b2 = (a-b)(a+b) to algebraic & numerical terms.
- Factorise harder quadratics ax2 + bx + c by splitting the middle term and pairwise grouping.
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46Lesson 5: Factorisation Quadratics End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of factorising quadratic expressions using a range of algebraic techniques. It covers factorising simple quadratics of the form (x^2 + bx + c), factorising more complex quadratics where the coefficient of (x^2) is greater than 1, using pairwise (splitting the middle term) factorisation, recognising and factorising common factors, and solving contextual and reasoning problems involving quadratic expressions and equations. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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47Lesson 6: Algebra & Linear Equations1 hour
Learning Objectives:
- Recognise common algebraic traps (expanding squares, negative distribution, unlike terms).
- Solve linear equations with brackets, negative coefficients, and unknown terms on both sides.
- Formulate and solve algebraic equations from age scenarios, angles, perimeters, and shaded areas.
- Eliminate algebraic denominators by multiplying terms by the Lowest Common Multiple (LCM).
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48Lesson 6: Algebra & Linear Equations End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of algebraic techniques and solving linear equations in a variety of mathematical contexts. It covers forming and simplifying algebraic expressions, solving one-step and multi-step linear equations, solving equations involving brackets and fractions, rearranging simple formulae, and solving contextual and reasoning problems involving algebraic relationships and real-life situations. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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49Lesson 7: Solving Quadratic Equations by Factorisation1 hour
Learning Objectives:
- Apply the Zero Product Principle.
- Rearrange non-zero quadratics to standard form.
- Expand brackets and clear fractional denominators prior to solving.
- Formulate and solve quadratic models for area, perimeter, and right triangles.
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50Lesson 7: Solving Quadratic Equations by Factorisation End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of how to solve quadratic equations using the method of factorisation. It covers factorising simple and more complex quadratic expressions, applying the zero-product rule to find solutions, solving quadratic equations with common factors, checking solutions by substitution, and solving contextual and reasoning problems involving quadratic relationships and real-life applications. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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51Lesson 8: Linear Inequalities1 hour
Learning Objectives:
- Translate verbal statements ("at most", "at least", "between") into algebraic inequalities.
- Represent single-ended and double-ended inequalities on number lines with filled/unfilled circles.
- Solve linear inequalities using balance methods and handle negative coefficient sign flips.
- Solve double-ended inequalities and combine overlapping ranges using vertical scanning.
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52Lesson 8: Linear Inequalities End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of solving and interpreting linear inequalities in a variety of mathematical contexts. It covers solving one-step and multi-step linear inequalities, solving inequalities involving brackets and fractions, representing solutions on a number line, writing solutions using inequality notation, and solving contextual and reasoning problems involving constraints and feasible values. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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53Lesson 9: Quadratic Inequalities1 hour
Learning Objectives:
- Understand why quadratic inequalities have infinite solution sets in continuous ranges or disjoint arms.
- Execute the 3-step strategy: Rearrange to 0, Factorise for critical values, and sketch the parabola.
- Distinguish between y > 0 (above x-axis) and y < 0 (below x-axis) region conditions.
- Solve monic, non-monic, squared binomials, cubic/quartic polynomials, and applied geometric bounds.
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54Lesson 9: Quadratic Inequalities End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of solving and interpreting quadratic inequalities using algebraic and graphical techniques. It covers solving quadratic inequalities by factorisation, identifying critical values, determining solution intervals, interpreting quadratic graphs to find solution sets, representing solutions using inequality notation and number lines, and solving contextual and reasoning problems involving quadratic relationships and constraints. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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55Lesson 10: Changing the Subject1 hour
Learning Objectives:
- Apply inverse operations ("undoing") in reverse order to isolate a single variable.
- Release variables trapped inside negative terms using addition or the "subtraction swap" rule.
- Clear denominators by multiplying across or cross-multiplying fractional expressions.
- Rearrange expressions where the target variable appears multiple times by gathering and factorising.
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56Lesson 10: Changing the Subject End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of rearranging algebraic formulae to make different variables the subject. It covers changing the subject of formulae involving addition, subtraction, multiplication, division, brackets, powers, roots, and fractions, as well as selecting appropriate algebraic techniques to isolate the required variable. Students will also solve contextual and reasoning problems involving scientific, geometric, and real-life formulae. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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57Lesson 11: Arithmetic and Geometric Sequence1 hour
Learning Objectives:
- Distinguish between Arithmetic, Geometric, and Fibonacci-type progressions.
- Apply constant difference and constant ratio properties.
- Use general nth term formulas.
- Formulate and evaluate recurrence relations in real-world contexts.
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58Lesson 11: Arithmetic and Geometric Sequence End of Topic Test1 hour
This end-of-topic test assesses students' understanding of arithmetic, geometric, and term-to-term sequences. It covers identifying patterns in sequences, generating terms using term-to-term and position-to-term rules, finding the nth term of arithmetic sequences, recognising and continuing geometric sequences, and solving contextual and reasoning problems involving numerical patterns and algebraic relationships. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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59Lesson 12: Quadratic Sequences1 hour
Learning Objectives:
- Recognise quadratic sequences by their constant second difference (2a).
- Halve the second difference to find the coefficient a in an2 + bn + c.
- Subtract the an2 term to isolate and solve the linear progression remainder bn + c.
- Set up and solve simultaneous equations for a,b,c using u1, u2, u3.
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60Lesson 12: Quadratic Sequence End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of quadratic sequences and their algebraic representation. It covers identifying quadratic sequences using first and second differences, finding and using the nth term of a quadratic sequence, generating terms from a quadratic rule, recognising patterns in numerical sequences, and solving contextual and reasoning problems involving quadratic relationships. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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61Lesson 13: Iteration and Recurrence Relations1 hour
Learning Objectives:
- Interpret recurrence notation xn+1 = f (xn) starting from a seed xo.
- Rearrange non-linear equations f(x) = 0 into fixed-point forms x = g(x).
- Prove roots lie within an interval [a,b] using the sign-change method ( f(a) · f(b) < 0 )
- Understand geometric convergence on Staircase and Cobweb diagrams ( y = x vs y = g(x) )
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62Lesson 13: Iterations and Recurrence Relations End of Topic Test15 minutes
Learning Objectives:
This end-of-topic test assesses students' understanding of iterative methods and recurrence relations for generating and approximating numerical solutions. It covers using iterative processes to find approximate solutions to equations, applying recurrence relations to generate successive terms, interpreting recursive formulae, recognising convergence and divergence, and solving contextual and reasoning problems involving iterative models and sequences. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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63Lesson 14: Straight Line Graphs1 hour
Learning Objectives:
- Understand lines as coordinate rules.
- Find x-intercepts and y-intercepts.
- Calculate gradient , midpoints, and section ratio divisions.
- Form line equations.
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64Lesson 14: Straight Line Graphs End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of the properties and equations of straight line graphs. It covers calculating the gradient from coordinates, graphs, and equations, determining the midpoint of a line segment, finding the equation of a straight line in the forms (y = mx + c) and (y - y1 = m(x - x1)), interpreting the gradient and y-intercept, and solving contextual and reasoning problems involving linear relationships and graphical models. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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65Lesson 15: Parallel and Perpendicular Lines1 hour
Learning Objectives:
- Identify parallel lines by matching gradients.
- Calculate perpendicular gradients using negative reciprocals.
- Find line segment lengths using Pythagoras.
- Calculate areas of triangles enclosed by intersecting lines and coordinate axes.
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66Lesson 15: Parallel and Perpendicular Lines End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of the properties of parallel and perpendicular lines and their application in coordinate geometry. It covers determining whether lines are parallel or perpendicular using gradients, finding the equations of parallel and perpendicular lines, calculating the length of a line segment using coordinates, calculating the area enclosed by straight lines and the coordinate axes or simple polygons, and solving contextual and reasoning problems involving coordinate geometry and linear relationships. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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67Lesson 16: Linear and Quadratic Simultaneous Equations1 hour
Learning Objectives:
- Solve linear systems graphically by finding line intersection points ( x,y)
- Solve linear systems by Elimination (adding/subtracting scaled equations).
- Solve linear systems by Substitution (rearranging for single variable).
- Solve Higher Tier Linear & Quadratic systems.
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68Lesson 16: Linear and Quadratic Simultaneous Equations End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of solving simultaneous equations involving one linear and one quadratic equation using algebraic and graphical methods. It covers solving linear and quadratic simultaneous equations by substitution, interpreting graphical solutions, determining the points of intersection between a line and a quadratic curve, selecting appropriate solution methods, and solving contextual and reasoning problems involving quadratic models and real-life applications. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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69Lesson 17: Completing the Square1 hour
Learning Objectives:
- Understand perfect squares geometrically using algebra tile area models.
- Complete the square for monic quadratics.
- Complete the square for non-monic & negative quadratics.
- Identify minimum and maximum turning points of curves .
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70Lesson 17: Completing the Square End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of completing the square and its application to quadratic expressions and equations. It covers rewriting quadratic expressions in completed square form, solving quadratic equations by completing the square, identifying the turning point and axis of symmetry of quadratic graphs, sketching and interpreting quadratic functions from completed square form, and solving contextual and reasoning problems involving quadratic models and optimisation. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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71Lesson 18: Solving Quadratics with Quadratic Formula15 minutes
Learning Objectives:
- Identify coefficients from general forms.
- Apply quadratic formula to obtain exact surd form solutions.
- Rearrange non-standard quadratic equations (expanding brackets, clearing denominators).
- Understand the discriminant and derive the formula algebraically.
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72Lesson 18: Solving Quadratics by using the Quadratic Formula End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of solving quadratic equations using the quadratic formula and interpreting the solutions in mathematical and real-life contexts. It covers identifying appropriate quadratic equations for the quadratic formula, substituting coefficients accurately into the formula, simplifying exact and decimal solutions where appropriate, interpreting the discriminant to determine the nature and number of roots, and solving contextual and reasoning problems involving quadratic models and applications. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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73Lesson 19: Quadratic and Cubic Graphs1 hour
Learning Objectives:
- To deduce the roots and turning points of quadratic and cubic graphs.
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74Lesson 19: Quadratic and Cubic Graphs15 minutes
This end-of-topic test assesses students' understanding of sketching and interpreting quadratic and cubic graphs using their key features. It covers identifying and plotting intercepts, turning points, roots, lines of symmetry (for quadratics), and the general shape and behaviour of quadratic and cubic functions. Students will also interpret graphical transformations, estimate solutions to equations from graphs, and solve contextual and reasoning problems involving quadratic and cubic models. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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75Lesson 20: Algebraic Fractions.1 hour
Learning Objectives:
- To add, subtract, multiply and divide algebraic fractions.
- To simplify algebraic fractions.
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76Lesson 20: Algebraic Fractions End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of algebraic fractions and their manipulation using algebraic techniques. It covers simplifying algebraic fractions, finding equivalent algebraic fractions, adding, subtracting, multiplying, and dividing algebraic fractions, solving equations involving algebraic fractions, and solving contextual and reasoning problems involving algebraic relationships. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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77Lesson 21: Algebraic Proofs1 hour
Learning Objectives:
- Construct algebraic proofs by using variables and algebraic manipulation to show that a mathematical statement is always true.
- Use algebraic reasoning to prove properties involving even and odd numbers, consecutive integers, multiples, and divisibility.
- Justify each step of an algebraic proof using correct mathematical notation and logical reasoning, and distinguish between proof and verification using examples.
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78Lesson 21: Algebraic Proofs End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of constructing and interpreting algebraic proofs using logical mathematical reasoning. It covers proving identities, demonstrating that expressions are always even, odd, or divisible by a given number, proving general results using algebraic manipulation, identifying valid mathematical arguments, and solving contextual and reasoning problems that require students to justify and communicate algebraic proofs clearly. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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79Lesson 22: Functions1 hour
Learning Objectives:
- Map inputs to outputs using , perform algebraic substitutions, and evaluate sequential composite functions .
- Master the 3-step algebraic method to reverse function mappings and identify self-inverse functions.
- Determine input domains , calculate output ranges , analyze piecewise graphs, and construct linear functions.
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80Lesson 22: Functions End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of functions and their use in representing mathematical relationships. It covers function notation, evaluating functions, finding composite and inverse functions where appropriate, interpreting mappings and function machines, and solving contextual and reasoning problems involving functional relationships and algebraic models. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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81Lesson 23: Equations of Circles1 hour
Learning Objectives:
- To understand and apply the equation of a circle.
- To deduce the centre coordinates and radius of circles.
- To calculate the equation of a tangent to a circle.
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82Lesson 23: Equation of Circles End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of the equation of a circle and its application in coordinate geometry. It covers interpreting and using the equation of a circle, determining the radius from a given equation, identifying whether points lie on a circle, and finding equations of circles with a given centre and radius. Students will also solve contextual and reasoning problems involving coordinates, distances, and geometric relationships. The assessment evaluates students' fluency, accuracy, and mathematical reasoning, identifies misconceptions, and ensures they are well prepared for GCSE examination-style questions.
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83Catch Game: Algebra Number ChaserText lesson
Number Chaser is an exciting, fast-paced CATCH GCSE Maths game designed to strengthen students’ confidence and fluency with key Algebra skills. Students race against the clock to solve GCSE-style algebraic problems, select the correct answer and progress through increasingly challenging questions. The game can include topics such as simplifying and expanding expressions, factorising, solving linear and quadratic equations, inequalities, sequences, simultaneous equations, algebraic fractions and functions.
By combining timed challenges, instant feedback and repeated practice, Number Chaser encourages students to think quickly and accurately while making revision more enjoyable. The competitive, game-based format can boost motivation and encourage regular practice, helping students identify weaknesses, improve algebraic fluency and problem-solving skills, and build the confidence needed to tackle Algebra questions successfully in GCSE Mathematics.
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84Lesson 1: Units and Conversions1 hour
Learning Objectives:
- Master standard unit multipliers for length, mass, and capacity.
- Memorise and apply core GCSE conversion factors.
- Convert between complex rates and solve real-world multi-step exam questions.
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85Lesson 1: Units and Conversions End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of converting between metric and imperial units and applying unit conversions in mathematical and real-life contexts. It covers converting units of length, mass, capacity, area, volume, and time, using compound units where appropriate, converting between metric and imperial measurements, and solving contextual and reasoning problems involving measurement, scale, and practical applications. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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86Lesson 2: Angles on Parallel Lines1 hour
Learning Objectives:
- Recognise and distinguish between Corresponding (equal), Alternate (equal), and Co-interior (sum to 180 ) angles formed by transversals.
- Write full, standard GCSE reasoning statements (e.g. "alternate angles on parallel lines are equal") to satisfy exam mark schemes.
- Form algebraic equations, test whether lines are parallel, and calculate missing angles in composite polygon figures.
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87Lesson 2: Angles on Parallel Lines End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of angle relationships involving parallel lines and transversals. It covers identifying and applying corresponding angles, alternate angles, co-interior (allied) angles, and vertically opposite angles, using coordinate geometry to determine angles and justify geometric relationships, solving problems involving unknown angles using algebra, and solving contextual and reasoning problems that require logical geometric reasoning and proof. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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88Lesson 3: Angles in Triangles and Quadrilaterals1 hour
Learning Objectives:
- Understand why interior angles in any 4-sided shape add up to 360° by splitting into 2 triangles ( 2 x 180° ).
- Apply symmetry rules to kites, parallelograms, trapeziums, and squares to find missing opposite and equal angles.
- Combine straight lines (180°), angles around a point (360°), and isosceles triangles in complex GCSE geometry figures
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89Lesson 3: Angles in Triangles and Quadrilaterals End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of angle relationships in triangles and quadrilaterals and their application to geometric problem-solving. It covers calculating unknown angles in triangles and quadrilaterals, applying the angle sum properties of triangles and quadrilaterals, using alternate, corresponding, co-interior, and vertically opposite angles to solve multi-step problems, applying coordinate geometry to determine and justify angle relationships where appropriate, and solving contextual and reasoning problems involving geometric proofs and deductive reasoning. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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90Lesson 4: Polygons1 hour
Learning Objectives:
- Find the total angle inside any shape using the triangle rule.
- Use the full-turn rule and straight-line rule to find side numbers.
- Solve complex angle problems combining polygon corner properties and isosceles triangles.
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91Lesson 4: Polygons End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of the properties and angle relationships of polygons. It covers calculating interior and exterior angles of regular and irregular polygons, determining the sum of interior and exterior angles, solving problems involving unknown angles in polygons, applying angle facts including alternate, corresponding, and co-interior angles where polygons involve parallel lines, using coordinate geometry to determine geometric relationships where appropriate, and solving contextual and reasoning problems involving polygon properties and geometric proof. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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92Lesson 5: Area and Perimeter of 2D ShapesText lesson
Learning Objectives:
- Calculate area and perimeter, perform reverse square calculations, and solve multi-shape problems.
- Master additive and subtractive area splitting methods, and apply perimeter-preserving corner rules for L-shapes and U-shapes.
- Apply formulas for Triangles, Parallelograms, and Trapeziums, and dissect complex shaded regions.
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93Lesson 5: Area and Perimeter of 2D Shapes End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of how to calculate the area and perimeter of a range of two-dimensional shapes. It covers finding the perimeter and area of rectangles, triangles, parallelograms, trapezia, kites, circles, and composite shapes; applying appropriate formulae; solving problems involving missing lengths and dimensions; and using coordinate geometry, where appropriate, to determine distances and dimensions. Students will also solve contextual and reasoning problems involving geometric measurements, optimisation, and real-life applications. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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94Lesson 6: Volume and Surface Area of 3D Shapes1 hour
Learning Objectives:
- Identify faces, vertices, and edges for 3D polyhedra and curved solids, and match 3D solids to their 2D unfolded nets.
- Calculate cross-sectional volumes and total surface areas for triangular prisms, L-prisms, and cylinders.
- Master 3D Pythagoras for pyramids/cones, frustums, hemispherical bowls, and algebraic volume/surface area conservation problems.
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95Lesson 6: Volume and Surface Area End of Topic Test20 minutes
This end-of-topic test assesses students' understanding of how to calculate the volume and surface area of a range of three-dimensional shapes. It covers finding the volume and surface area of prisms, cylinders, pyramids, cones, spheres, and composite solids; applying appropriate formulae; solving problems involving missing dimensions; and using unit conversions where required. Students will also solve contextual and reasoning problems involving capacity, packaging, optimisation, and real-life applications of three-dimensional geometry. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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96Lesson 7: Bearings and Map Scale Navigation1 hour
Learning Objectives:
- Understand the 3 core rules: measured clockwise from North, always formatted with 3 digits (e.g. 045 ), and calculate back bearings by adding or subtracting 180°.
- Convert between map measurements and real-world ground distances using ratio scales (e.g. 1: 40000 or 1cm: 25km) and plot target coordinates.
- Solve complex multi-step navigation problems using co-interior angles ( 180 - ɵ), alternate interior angles, isosceles triangle properties, and algebraic equations.
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97Lesson 7: Bearings and Map Scale Navigation End of Topic Test20 minutes
This end-of-topic test assesses students' understanding of bearings, map scales, and navigation in mathematical and real-life contexts. It covers measuring and calculating three-figure bearings, interpreting and using map scales, calculating actual and scaled distances, applying trigonometry and coordinate geometry where appropriate to solve navigation problems, and solving contextual and reasoning problems involving routes, directions, maps, and geographical planning. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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98Lesson 8: Transformations1 hour
Learning Objectives:
- Shift shapes using column vectors , where top is horizontal movement and bottom is vertical movement.
- Reflect shapes across horizontal lines , vertical lines , and diagonal axes.
- Rotate shapes by 90°, 180°, 270° clockwise or anticlockwise about a specified centre point.
- Scale shapes by positive/negative/fractional scale factors , and determine single equivalent transformations.
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99Lesson 8: Transformation End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of geometric transformations and their application on the coordinate plane. It covers translations using vectors, reflections in lines, rotations about a given centre, enlargements with positive, negative, and fractional scale factors, identifying and describing transformations, and solving contextual and reasoning problems involving geometric properties, symmetry, and coordinate geometry. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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100Lesson 9: Area and Perimeter of Circles1 hour
Learning Objectives:
- Calculate circle perimeter, solve distance/wheel rotation problems, and convert between exact and decimal forms.
- Find enclosed area. Understand geometric bounding rules and work backwards to find radius or diameter.
- Work out areas and perimeters of semicircles and quarter circles. Always remember to add straight-edge radii/diameters to perimeters!
- Apply additive methods (rectangles + semicircles) and subtractive methods (squares/plates minus circles/annulus rings).
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101Lesson 9: Area and Perimeter of Circles End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of calculating the circumference, area, and perimeter of circles and parts of circles. It covers using the formulae for circumference and area, calculating the radius and diameter from given information, solving problems involving semicircles, sectors, and composite shapes, and applying circle measurements to contextual and reasoning problems involving length, area, and geometric relationships. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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102Lesson 10: Arcs and Sectors1 hour
Learning Objectives:
- Calculate arc length and sector area.
- Rearrange sector formulas to determine unknown radius or central angle given arc length or enclosed area.
- Work with annulus sectors (shaded regions between concentric radii) and composite sector-polygon shapes.
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103Lesson 10: Arcs and Sectors End of Topic Test20 minutes
This end-of-topic test assesses students' understanding of calculating the lengths of arcs and the areas of sectors of circles. It covers using the formulae for arc length and sector area, calculating missing angles, radii, and arc lengths, working with fractions of a full circle, and solving problems involving semicircles, sectors, and composite shapes. Students will also apply circle geometry to contextual and reasoning problems involving distance, area, and real-life applications. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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104Lesson 11: Pythagoras Theorem in 2D1 hour
Learning Objectives:
- In any right-angled triangle, the area of the square on the hypotenuse equals the sum of the areas on the legs.
- Calculate hypotenuse length by adding square areas, or leg length by subtracting.
- Verify right angles using the converse rule, and split isosceles or equilateral triangles down symmetry lines to find height and area.
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105Lesson 11: Pythagoras Theorem in 2D End of Topic Test20 minutes
This end of topic test assesses students' understanding of Pythagoras' theorem and its application to right-angled triangles in two-dimensional geometry. It covers finding missing sides and hypotenuses, identifying right-angled triangles, rearranging and applying (a2+b2=c2), solving problems involving diagrams and composite shapes, and applying Pythagoras' theorem to contextual and reasoning problems involving distances, heights, and geometric measurements. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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106Lesson 12: Trigonometry of Right-Angled Triangles1 hour
Learning Objectives:
- Identify Hypotenuse, Opposite, and Adjacent regardless of triangle rotation or which acute angle is selected.
- Calculate unknown side lengths using numerical side ratios, and solve unknown angles.
- Derive exact non-calculator side values for 30°,45°,and 60°. Solve multi-step problems involving bearings, incline heights, and compound shapes.
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107Lesson 12: Trigonometry of Right-Angled Triangles End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of trigonometric ratios and their application to right-angled triangles. It covers using sine, cosine, and tangent to calculate missing sides and angles, identifying the appropriate trigonometric ratio, rearranging trigonometric equations, using inverse trigonometric functions, and solving contextual and reasoning problems involving heights, distances, angles of elevation and depression, and real-life applications. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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108Lesson 13: 3D Trigonometry1 hour
Learning Objectives:
- Isolate right-angled triangles in 3D space. Apply cuboid space diagonals and calculate pyramid vertical heights.
- Use the orthogonal "Drop Method" to project a 3D line onto a base plane, forming a 2D right triangle to calculate the projection angle.
- Identify lines of greatest slope on sloped faces and roofs. Solve complex multi-stage problems on prisms, truncated pyramids, and masts.
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109Lesson 13: 3D Trigonometry End of Topic Test20 minutes
This end-of-topic test assesses students' understanding of applying trigonometry and Pythagoras' theorem to three-dimensional problems. It covers identifying and solving right-angled triangles within 3D shapes, calculating missing lengths and angles using sine, cosine, and tangent, applying Pythagoras' theorem in multiple dimensions, and solving contextual and reasoning problems involving heights, distances, angles of elevation and depression, and 3D geometric models. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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110Lesson 14: Congruent Triangles1 hour
Learning Objectives:
- Congruent shapes are identical in both shape AND size (rotations & flips allowed). Similar shapes have equal angles but different scale sizes.
- Master SSS (3 sides), SAS (2 sides + included angle), ASA (2 angles + side), and RHS (Right angle, hypotenuse, side).
- Structure formal proofs: Provide 3 bullet points justifying equal corresponding sides/angles, then 1 bullet point stating the condition.
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111Lesson 14: Congruent Triangles End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of congruent triangles and the conditions required to establish congruence. It covers identifying congruent triangles; applying the congruence criteria SSS, SAS, ASA, and RHS; corresponding sides and angles; using congruence to determine unknown lengths and angles; and solving contextual and reasoning problems involving geometric relationships and proof. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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112Lesson 15: Plans and Elevations1 hour
Learning Objectives:
- To identify the plan, front elevation and side elevation of 3D objects.
- To draw the plan, front elevation and side elevation of 3D objects.
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113Lesson 15: Plans and Elevation End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of plans and elevations and their use in representing three-dimensional objects. It covers interpreting and drawing plans, front and side elevations, using scale and measurements accurately, visualising 3D shapes from two-dimensional representations, and solving contextual and reasoning problems involving dimensions, construction, and geometric models. The assessment is designed to evaluate students' spatial reasoning, accuracy, and mathematical understanding, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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114Lesson 16: Circle Theorems1 hour
Learning Objectives:
- Identify and state the key circle theorems, including angles in the same segment, angles at the centre, and the angle in a semicircle.
- Apply circle theorems to calculate unknown angles and solve multi-step geometric problems, giving clear reasons for each step.
- Use circle theorems to solve unfamiliar and real-life problems, including problems involving tangents, chords and cyclic quadrilateral
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115Lesson 16: Circle Theorems End of Topic Test20 minutes
This end-of-topic test assesses students' understanding of the key theorems and angle properties associated with circles. It covers angles in the same segment, angles subtended by a diameter, the angle between a tangent and a radius, the alternate segment theorem, the perpendicularity of tangents and radii, cyclic quadrilaterals, and applying circle theorems to calculate unknown angles and lengths. Students will also solve contextual and reasoning problems requiring clear geometric justification and proof. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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116Lesson 17: Vectors1 hour
Learning Objectives:
- Understand and represent vectors using column vector notation and describe the magnitude and direction of a vector.
- Perform vector calculations involving addition, subtraction, scalar multiplication, and combinations of vectors.
- Use vectors to solve geometric problems, including proving that lines are parallel, points are collinear, and determining ratios and positions of points.
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117Lesson 17: Vectors End of Topic Test20 minutes
This end-of-topic test assesses students' understanding of vectors and their application to geometric problems. It covers representing and interpreting vectors, performing vector addition and subtraction, multiplying vectors by scalars, using vectors to describe translations and geometric relationships, finding midpoints and ratios, and solving contextual and reasoning problems involving parallel lines, collinearity, and geometric proof. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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118Lesson 18: Non-Right Angled Triangles1 hour
Learning Objectives:
- Calculate the missing side lengths and interior angles in non-right-angled triangles using the Sine and Cosine Rules.
- Identify when to use the Sine Rule vs the Cosine Rule based on given angle-side opposite pairs, included wedged angles, or 3-side setups.
- Calculate the area of non-right-angled triangles.
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119Lesson 18: Non-Right Angled Triangles End of Topic Test20 minutes
This end-of-topic test assesses students' understanding of solving problems involving non-right-angled triangles using advanced trigonometric techniques. It covers applying the sine rule and cosine rule to calculate unknown sides and angles, using the area formula, identifying the appropriate method for different triangle configurations, and solving contextual and reasoning problems involving distances, bearings, heights, and real-life applications. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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120Lesson 19: Trigonometric Graphs and Equations1 hour
Learning Objectives:
- Recognise and Use Trigonometric Curves
- Apply Trigonometric Curve Symmetry Laws
- Solve Equations and Prove Identities.
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121Lesson 19: Trigonometric Graphs and Equations End of Topic Test20 minutes
This end-of-topic test assesses students' understanding of trigonometric graphs and equations and their application to mathematical problems. It covers sketching and interpreting sine, cosine, and tangent graphs, identifying amplitude, period, intercepts, and key features, solving trigonometric equations using graphs and algebraic methods, interpreting solutions within specified intervals, and applying trigonometric graphs to contextual and reasoning problems. The assessment is designed to evaluate students' fluency, accuracy, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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122Lesson 20: Construction & Loci1 hour
Learning Objectives:
- To master construction of angles and shapes using a compass and protractor.
- Solve compound loci and shading.
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123Lesson 20: Construction & Loci End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of geometric constructions and loci and their application to practical and mathematical problems. It covers constructing perpendicular bisectors, angle bisectors, perpendiculars from points to lines, constructing triangles using given measurements, identifying and drawing loci based on distance and geometric conditions, and interpreting regions defined by multiple loci. Students will also solve contextual and reasoning problems involving construction, navigation, positioning, and geometric constraints. The assessment is designed to evaluate students' accuracy, spatial reasoning, and mathematical understanding, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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124Catch Game: Geometry and Measures Number ChaserText lesson
Number Chaser is an exciting, fast-paced CATCH GCSE Maths game designed to strengthen students’ confidence and fluency with key Geometry and Measures skills. Students race against the clock to solve GCSE-style problems, select the correct answer and progress through increasingly challenging questions. The game can include topics such as angles, polygons, transformations, constructions and loci, Pythagoras’ theorem, trigonometry, perimeter, area, volume, circles and geometric reasoning.
By combining timed challenges, instant feedback and repeated practice, Number Chaser encourages students to think quickly, accurately and logically while making revision more enjoyable. The competitive, game-based format can boost motivation and encourage regular practice, helping students identify weaknesses, improve problem-solving and spatial reasoning skills, and build the confidence needed to tackle Geometry and Measures questions successfully in GCSE Mathematics.
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125Lesson 1: Mean, Median, Mode & Range1 hour
Learning Objectives:
- To calculate mean, median, mode and range of raw dataset.
- To find mean of grouped data.
- To solve reverse-mean equations and determine optimal averages in context with extreme outliers.
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126Lesson 1: Mean, Median, Mode and Range End of Topic Test20 minutes
This end-of-topic test assesses students' understanding of measures of central tendency and spread when analysing and interpreting data. It covers calculating the mean, median, mode, and range from raw and ordered data, identifying the most appropriate average for a given data set, finding missing values using the mean, interpreting statistical information, and solving contextual and reasoning problems involving averages and spread. The assessment is designed to evaluate students' fluency, accuracy, data-handling skills, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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127Lesson 2: Two-Way Tables & Frequency Trees1 hour
Learning Objectives:
- Construct and complete two-way tables.
- Build and solve frequency trees.
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128Lesson 2: Two-Way Table & Frequency Trees End of Topic Test20 minutes
This end-of-topic test assesses students' understanding of organising, interpreting, and analysing data using two-way tables and frequency trees. It covers completing two-way tables and frequency trees from given information, calculating frequencies and totals, interpreting relationships between different categories, using fractions and percentages to analyse data, and solving contextual and reasoning problems involving probability and statistical information. The assessment is designed to evaluate students' fluency, accuracy, data-handling skills, and mathematical reasoning, while identifying any misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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129Lesson 3: Pictogram, Bar Charts & Time Series Graphs1 hour
Learning Objectives:
- To construct and interpret pictograms.
- To master dual and composite bar charts.
- To analyse time series and trends.
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130Lesson 3: Pictogram, Bar Chart, & Time Series Graphs End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of how to represent, interpret, and analyse data using pictograms, bar charts, and time series graphs. It covers constructing and interpreting pictograms and bar charts, selecting appropriate scales, extracting and comparing information from charts, plotting and interpreting time series data, identifying trends and patterns, and solving contextual and reasoning problems involving statistical information. The assessment evaluates students' accuracy, data-handling skills, mathematical reasoning, and ability to interpret graphical representations, while identifying misconceptions and ensuring they are well prepared for GCSE examination-style questions.
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131Lesson 4: Pie Chart1 hour
Learning Objectives:
- Calculate multipliers and angles.
- Construct a pie chart.
- Interpret angles and proportions.
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132Lesson 4: Pie Chart End of Topic Test20 minutes
This end-of-topic test assesses students' understanding of how to represent and interpret data using pie charts. It covers calculating sector angles and frequencies, constructing pie charts accurately, interpreting information in pie charts, finding missing values and categories, and converting between frequencies, fractions, percentages, and angles. Students will also solve contextual and reasoning problems involving statistical data and proportional relationships. The assessment evaluates students' accuracy, data-handling skills, and mathematical reasoning, identifies misconceptions, and ensures they are well prepared for GCSE examination-style questions.
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133Lesson 5: Scatter Graphs & Correlation1 hour
Learning Objectives:
- To identify correlation types.
- To construct lines of best fit.
- To interpolate and extrapolate graphs.
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134Lesson 5: Scatter Graphs and Correlation End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of how to represent, interpret, and analyse bivariate data using scatter graphs. It covers plotting and interpreting scatter graphs; identifying positive, negative, and no correlation; drawing and using lines of best fit; making estimates and predictions from data; recognising interpolation and extrapolation; and evaluating the reliability of conclusions. Students will also solve contextual and reasoning problems involving relationships between variables and real-life data. The assessment evaluates students' accuracy, data-handling skills, statistical understanding, and mathematical reasoning, identifies misconceptions, and ensures they are well prepared for GCSE examination-style questions.
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135Lesson 6: Cumulative Frequency, Quartiles & Box Plots1 hour
Learning Objectives:
- To draw cumulative frequency curves.
- To calculate the lower quartile, upper quartile and interquartile range.
- To draw box plots.
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136Lesson 6: Cumulative Frequency, Quartiles and Box Plots End of Topic Test15 minutes
This end-of-topic test assesses students' understanding of how to represent, interpret, and analyse data using cumulative frequency graphs and box plots. It covers constructing and interpreting cumulative frequency diagrams, estimating the median and quartiles, calculating and interpreting the interquartile range, constructing and comparing box plots, and analysing data distribution and spread. Students will also solve contextual and reasoning problems involving statistical comparisons and data interpretation. The assessment evaluates students' accuracy, data-handling skills, statistical understanding, and mathematical reasoning, identifies misconceptions, and ensures they are well prepared for GCSE examination-style questions.
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137Lesson 7 : Histogram1 hour
Learning Objectives:
- To draw histograms.
- To calculate frequency density.
- To estimate frequency using the area under a histogram.
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138Lesson 7: Histogram End of Topic Test20 minutes
This end-of-topic test assesses students' understanding of how to represent, interpret, and analyse continuous data using histograms. It covers calculating and using frequency density, constructing histograms with equal and unequal class widths, interpreting bar areas as frequencies, estimating frequencies from histograms, and solving contextual and reasoning problems involving grouped data and statistical distributions. The assessment evaluates students' accuracy, data-handling skills, statistical understanding, and mathematical reasoning, identifies misconceptions, and ensures they are well prepared for GCSE examination-style questions.
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139Lesson 8: Sampling & Population Estimation1 hour
Learning Objectives:
- To distinguish between a census and a sample and spot sample bias.
- To estimate animal population using the capture-recapture method.
- To explain stratified sampling and survey critique.
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140Lesson 8: Sampling & Population Estimation20 minutes
This end-of-topic test assesses students' understanding of sampling methods and population estimation in statistical investigations. It covers identifying populations and samples, selecting appropriate sampling methods (including random and systematic sampling), recognising potential sources of bias, using sample data to estimate population values, and evaluating the reliability and validity of conclusions. Students will also solve contextual and reasoning problems involving surveys, data collection, and population estimates. The assessment evaluates students' statistical understanding, data-handling skills, accuracy, and mathematical reasoning, identifies misconceptions, and ensures they are well prepared for GCSE examination-style questions.
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141Lesson 9: Sets & Venn Diagram1 hour
Learning Objectives:
- To identify different sets.
- To evaluate and interpret the union and intersection of sets.
- To calculate probability using Venn diagrams.
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142Lesson 9: Sets & Venn Diagram End of Topic Test20 minutes
This end-of-topic test assesses students' understanding of sets and how to represent them using Venn diagrams. It covers identifying and describing sets, using set notation, interpreting and completing Venn diagrams, finding unions, intersections, and complements, and solving problems involving two and three sets. Students will also apply their understanding to contextual and reasoning problems involving classification, data, and logical relationships. The assessment evaluates students' fluency, accuracy, and mathematical reasoning, identifies misconceptions, and ensures they are well prepared for GCSE examination-style questions.
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143Lesson 10: Probability1 hour
Learning Objectives:
- To calculate probability and express it as a fraction, decimal or percentage.
- To use tree diagrams to calculate probability.
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144Lesson 10 : Probability End of Topic Test20 minutes
This end-of-topic test assesses students' understanding of probability and its application to a range of mathematical and real-life situations. It covers calculating probabilities using fractions, decimals, and percentages; understanding the probability scale; identifying mutually exclusive and complementary events; calculating theoretical and experimental probabilities; and interpreting probability from tables, diagrams, and data. Students will also solve contextual and reasoning problems involving chance, risk, and likelihood. The assessment evaluates students' fluency, accuracy, statistical understanding, and mathematical reasoning, identifies misconceptions, and ensures they are well prepared for GCSE examination-style questions.
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145Catch Game : Statistics and Probability Number ChaserText lesson
Number Chaser is an exciting, fast-paced CATCH GCSE Maths game designed to strengthen students’ confidence and fluency with key Statistics and Probability skills. Students race against the clock to solve GCSE-style problems, select the correct answer and progress through increasingly challenging questions. The game can include topics such as averages and range, frequency tables, charts and graphs, scatter graphs, histograms, cumulative frequency, box plots, probability, tree diagrams and Venn diagrams.
By combining timed challenges, instant feedback and repeated practice, Number Chaser encourages students to think quickly, accurately and logically while making revision more enjoyable. The competitive, game-based format can boost motivation and encourage regular practice, helping students identify weaknesses, improve data interpretation and probability skills, and build the confidence needed to tackle Statistics and Probability questions successfully in GCSE Mathematics.
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146Higher GCSE Practice Paper 1 Examination1 hour
This examination assesses students' understanding and application of mathematical knowledge and skills across a broad range of Higher GCSE Maths topics. It covers number, algebra, ratio and proportion, geometry and measures, statistics, and probability, including multi-step problem-solving and mathematical reasoning questions. Students will apply their knowledge to familiar and unfamiliar contexts, communicate their methods clearly, and select appropriate strategies to solve challenging problems. The assessment evaluates students' fluency, accuracy, problem-solving, and mathematical reasoning, identifies areas for improvement, and ensures they are well prepared for Higher Tier GCSE examination-style questions.
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147Foundation GCSE Practice Paper 1 Examination1 hour
This examination assesses students' understanding and application of mathematical knowledge and skills across a broad range of GCSE Foundation Maths topics. It covers number, algebra, ratio and proportion, geometry and measures, statistics, and probability, including routine calculations, problem-solving, and mathematical reasoning questions. Students will apply their knowledge to familiar contexts, communicate their methods clearly, and select appropriate strategies to solve a range of mathematical problems. The assessment evaluates students' fluency, accuracy, problem-solving, and mathematical reasoning, identifies areas for improvement, and ensures they are well prepared for Foundation Tier GCSE examination-style questions.
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148Higher GCSE Practice Paper 2 Examination1 hour
This examination assesses students' understanding and application of mathematical knowledge and skills across a broad range of GCSE Higher Maths topics. It covers number, algebra, ratio and proportion, geometry and measures, statistics, and probability, including challenging multi-step problem-solving and mathematical reasoning questions. Students will apply their knowledge to familiar and unfamiliar contexts, communicate their methods clearly, and select appropriate strategies to solve complex mathematical problems. The assessment evaluates students' fluency, accuracy, problem-solving, and mathematical reasoning, identifies areas for improvement, and ensures they are well prepared for Higher Tier GCSE examination-style questions.
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149Foundation GCSE Practice Paper 2 Examination1 hour
This examination assesses students' understanding and application of mathematical knowledge and skills across a broad range of GCSE Foundation Maths topics. It covers number, algebra, ratio and proportion, geometry and measures, statistics, and probability, including routine calculations, multi-step problem-solving, and mathematical reasoning questions. Students will apply their knowledge to familiar and less familiar contexts, communicate their methods clearly, and select appropriate strategies to solve a range of mathematical problems. The assessment evaluates students' fluency, accuracy, problem-solving, and mathematical reasoning, identifies areas for improvement, and ensures they are well prepared for Foundation Tier GCSE examination-style questions.
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150Higher GCSE Practice Paper 3 Examination1 hour
This examination assesses students' understanding and application of mathematical knowledge and skills across a broad range of GCSE Higher Maths topics. It covers number, algebra, ratio and proportion, geometry and measures, statistics, and probability, including challenging multi-step problem-solving and mathematical reasoning questions. Students will apply their knowledge to familiar and unfamiliar contexts, communicate their methods clearly, and select appropriate strategies to solve complex mathematical problems. The assessment evaluates students' fluency, accuracy, problem-solving, and mathematical reasoning, identifies areas for improvement, and ensures they are well prepared for Higher Tier GCSE examination-style questions.
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151Foundation GCSE Practice Paper 3 Examination1 hour
This examination assesses students' understanding and application of mathematical knowledge and skills across a broad range of GCSE Foundation Maths topics. It covers number, algebra, ratio and proportion, geometry and measures, statistics, and probability, including routine calculations, multi-step problem-solving, and mathematical reasoning questions. Students will apply their knowledge to familiar and less familiar contexts, communicate their methods clearly, and select appropriate strategies to solve a range of mathematical problems. The assessment evaluates students' fluency, accuracy, problem-solving, and mathematical reasoning, identifies areas for improvement, and ensures they are well prepared for Foundation Tier GCSE examination-style questions.