Mathematics
Vision
At Birchwood, we believe mathematics and numeracy underpin human thought and logic and are integral in understanding the human condition and the world around us. Our maths team are passionate about our subject and want to pass on our love of mathematics to create enthusiastic and confident maths students who take their skills into other subjects such as science, geography, music and art – as well as their home, community and eventually their working environment.
We strive to ensure that all students have access to high-quality, engaging mathematics instruction with ambitious expectations for all. Our aim is to provide a curriculum rich in knowledge, literacy and support that allow students to become strong critical thinkers who can apply mathematical reasoning to solve problems, both in the classroom and within wider contexts.
We want students to develop their mathematical application and resilience whilst having a sense of enjoyment and curiosity about our subject. We believe in the use of technology to engage our students and we use this as a tool to cultivate active engagement in lessons and with the subject, more broadly.
We strive to produce students who are confident to pursue mathematics beyond secondary school whilst increasing the life chances of all our students by equipping them with the numeracy skills to be confident, financially literate citizens of the modern world.
How do we build on what students learn at KS2?
We want to ensure that our students are thoroughly supported in their transition from KS2 to KS3 in maths, building on their knowledge from Primary school as well as introducing them to new, exciting areas of mathematics.
Students will use their understanding of KS2 mathematics to further explore
– Place Value, Powers and Roots
– Lines, Angles and Shape
– Data Handling
– Fractions, Decimals and Percentages
– Ratio
– Length, Area and Volume
– Transformations
– Construction and Loci
In addition, students are introduced to concepts such as probability and averages and their curriculum has as a strong emphasis on the development of the use of algebra which is developed and interleaved throughout their learning.
Students use SPARX maths and retrieval starters to help embed their knowledge and procedures. They continue to develop their understanding of key mathematical terminology, studying 60 key vocabulary words and prefixes in each year group and are introduced to the world of careers that mathematics can lead them into.
How do we cover the KS3 National Curriculum and beyond?
In years 7-9 the KS3 National Curriculum forms the basis for everything studied whilst laying the foundations for what students will study at GCSE.
In addition, students begin to study for the GCSE Statistics qualification that they will sit in the summer of Year 10. This qualification helps to develop students understanding of the application of maths in the world around them and is beneficial in developing the literacy skills needed in applying their knowledge to contextual questions in examinations in all subjects. Our Parvis Magna students also complete the Entry Level Mathematics qualification in Year 9 to strengthen their confidence in their mathematical abilities.
Beyond the curriculum we offer students
– One hour of independent maths retrieval per week through SPARX maths homework
– Optional TARGET and XP Boost homework
– UKMT maths club at lunch time
– UKMT Team Challenge competition
– UKMT challenge tests in school
– Mathematical Education on Merseyside homework competitions in school holidays
– Board Games Clubs at lunch time
What do we cover in KS4 and how do we aspire towards KS5?
At KS4 students build on the foundations set in KS3 to complete a rigorous GCSE EdExcel maths curriculum in order to complete the Foundation or Higher maths papers in Year 11.
In addition, all students outside of our Parvis Magna classes, undertake the GCSE Statistics examination in Year 10.
Students are given the option to complete the EdExcel Further Maths Level 3 Certificate alongside their studies and it is our hope that these students will go on to complete A/S or A Level maths at KS5.
We strive to ensure that all students are equipped to continue their studies beyond High School and have the life skills to be socially aware, numeracy literate members of society.
KS3 Curriculum Overview
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HT1 |
HT2 |
HT3 |
HT4 |
HT5 |
HT6 |
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Year 7 |
Topic 1: Learning question: Key Knowledge: Adding, subtracting, multiplying and dividing whole numbers. Adding and subtracting decimals. Place Value. Square roots, Primes, multiples and factors. HCF & LCM. Basic rules of indices. Topic 2: Learning question: Key Knowledge: |
Topic 1: Learning question: Key Knowledge: Adding, subtracting, multiplying and dividing negative numbers. Forming expressions. Collecting like terms. Substitution. Expanding brackets. Topic 2: Learning question: Key Knowledge:
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Topic 1: Learning question: Key Knowledge: Topic 2: Learning question: Key Knowledge: |
Topic 1: Learning question: Key Knowledge: Topic 2: Learning question: Key Knowledge: |
Topic 1: Learning question: Key Knowledge: Topic 2: Learning question: How can we ‘transform’ a 2d shape? Key Knowledge: |
Topic 1: Learning question: Key Knowledge: Topic 2: Learning question: How can we accurately construct lines, angles and shapes? Key Knowledge: |
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Building and revisiting |
Overview: All topics in Year 7 follow the Key Stage 3 National Curriculum Guidelines, reinforcing and building upon the skills and knowledge developed in Key Stage 2. Topics and Key Skills are revisited every lesson through Recall 5s. |
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Students reinforce their KS2 knowledge of factors, multiples and prime numbers. They use their basic angle facts to solve more complex problems in shape. |
Students are introduced to the concept of an expression and how these can be manipulated. Their KS2 knowledge of ‘averages’ is extended to mean, median, mode and together with the range they compare sets of data and display them in a suitable manner. |
Students build upon their KS2 knowledge of fractions and decimals and gain an increased understanding of percentages. They begin to learn about how FDP are interchangeable. The concept of proportion is introduced through ratio. |
Students are introduced to the concept of an equation and how they can be ‘solved’. Their KS2 knowledge of area and volume is reinforced through work with 2d shape and cuboids. They begin to solve angle, area and perimeter problems with algebra. |
Students are introduced to different types of sequences and find the nth term of a linear sequence. They are introduced to simple linear sequences and how they can be represented graphically. They further their KS2 knowledge of transformations, applying them to a coordinate grid. |
Students are introduced to the probability scale in both word form and as fractions, decimals and percentages. They use diagrams to represent probability and are introduced to the concept of OR and Mutually Exclusive events. They further their KS2 protractor skills, using a set of compasses and a ruler to construct accurate drawings. |
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Assessment |
RAP x 2: 15 Skills Retrieval Test in final week Initial Baseline Test Week 2 |
RAP x 2: 15 Skills Retrieval Test in final week |
RAP x 2: 15 Skills Retrieval Test in final week Mid Year KASTs |
RAP x 2: 15 Skills Retrieval Test in final week |
RAP x 2: 15 Skills Retrieval Test in final week |
RAP x 1: 15 Skills Retrieval Test in final week End of Year KASTs |
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HT1 |
HT2 |
HT3 |
HT4 |
HT5 |
HT6 |
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Year 8
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Topic 1: Place Value, Powers & Roots Learning question: Key Knowledge: Topic 2: Lines, Angles & Shape
Learning question: Key Knowledge: |
Topic 1: Algebraic Manipulation Learning question: Key Knowledge: Topic 2: Data Handling
Key Knowledge: |
Topic 1: Fractions & Decimals Learning question: Key Knowledge: Topic 2: Ratio & Percentages
Learning question: Key Knowledge: |
Topic 1: Equations Learning question: What are the similarities between solving and rearranging? Key Knowledge: Topic 2: Length, Area & Volume Learning question: Key Knowledge: |
Topic 1: Sequences, Functions and Graphs Learning question: What are the characteristics of linear graphs? Key Knowledge: Topic 2: Transformations Learning question: What information do we need to transform shapes on a coordinate grid? Key Knowledge: Reflection, Rotation, Translation and Enlargement (positive scale factor) on a coordinate grid. |
Topic 1: Probability Learning question: What are independent and mutually exclusive events? Key Knowledge: Simple Venn diagrams. Relative frequency. Basic probability trees. Topic 2: Learning question: What is the relationship between the sides of right angled triangles? Key Knowledge: |
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Building and revisiting |
Overview: The topics studied in Year 8 are identical to those in year 7 and build upon the KS2 skills reinforced and the new knowledge introduced in Year 7. Topics and Key Skills are revisited every lesson through Recall 5s and through retrieval SPARX homework.. |
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Students use their knowledge of the rules of indices and place value developed in Year 7 to work with standard form. They develop their knowledge of angles facts from KS2 to include those on parallel lines and within regular polygons. |
Students review the manipulation of expressions from Year 7 and are introduced to the concept of factorisation. They continue to analyse data from frequency tables and are develop their knowledge to construct more complicated Pie Charts. They are introduced to Scatter graphs and correlation. |
Students advance their fractions skills by working with mixed numbers. They are introduced to the concept of a reciprocal and further their understanding of the Order of Operations. They continue to develop their understanding of ratio and percentage from year 7 solving more complex ratio questions. They use proportion to solve ‘Best Value’ questions and begin to use a decimal multiplier to manipulate values. |
Students continue to solve more complex equations involving one variable and learn how to change the subject of an equation or formula. They develop their knowledge of the area of 2d shape by finding compound area. They learn about the parts of a circle and begin to calculate area and circumference of whole and semi-circles. |
Students compare different types of sequences and develop their understanding of nth term. They plot linear graphs using a table of values and also using the characteristics of linear graphs. They continue to investigate the concepts of rotation, reflection and translations and extend their knowledge of enlargement to include a point of enlargement. |
Students develop their understanding of mutually exclusive and independent events through the use of probability trees. They find probabilities from Venn diagrams and explore relative frequency and the concept of experimental probability. Students are introduced to the concept of The Pythagorean Theorem in right angled triangles. |
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Assessment |
RAP x 2: 15 Skills Retrieval Test in final week |
RAP x 2: 15 Skills Retrieval Test in final week |
RAP x 2: 15 Skills Retrieval Test in final week Mid Year KASTs |
RAP x 2: 15 Skills Retrieval Test in final week |
RAP x 2: 15 Skills Retrieval Test in final week |
RAP x 1: 15 Skills Retrieval Test in final week End of Year KASTs |
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HT1 |
HT2 |
HT3 |
HT4 |
HT5 |
HT6 |
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Year 9 Foundation
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Topic 1: Learning question: Key Knowledge: 4 rules with negative numbers and decimals. Rounding to decimal places and significant figures. Estimation. Laws of indices. Topic 2: Learning question: Key Knowledge: Converting between ordinary numbers and standard form. Multiplying and dividing with standard form. Prime factor decomposition. LCM and HCF |
Topic 1: Algebraic Manipulation Learning question: Key Knowledge: Consolidation of manipulation of algebraic expressions including combining like terms, expanding brackets, common factor factorising, substitution and expanding double brackets. Topic 2: Lines, Angles and Shapes Learning question: Key Knowledge: Consolidation of missing angles in triangles, quadrilaterals, parallel lines and polygons. |
Topic 1: Fractions & Percentages Learning question: Key Knowledge: Consolidation of 4 rules with mixed numbers. Converting between FDP. Percentages and fractions of amounts. Percentage increase and decrease. Percentages in context. Topic 2: Ratio & Proportion Learning question: How can ratio be used to solve problems? Key Knowledge: Simplifying and calculating with ratio. Map scales. Exchange rates. |
Topic 1: Equations Learning question: Key Knowledge: Identifying expressions, equations, identities and formulae. Function machines to write equations, Solve equations with 2 steps and the variable on both sides of the equation. Form and solve equations. Change the subject of an equation or formula. Topic 2: Length, Area & Volume Learning question: How can I find the surface area and volume of prisms? Key Knowledge: Consolidation of area and perimeter including circles. Volume of cuboids, prisms and cylinders. |
Topic 1: Statistics 1 Learning question: How can I collect, analyse and display data? Key Knowledge: Types of data. Sampling methods. Averages and range. Bar charts, pictograms and stem and leaf diagrams. Reading tables, charts and timetables. Scatter graphs. Spearman’s Rank. Frequency polygons. Time series graphs. Moving averages. |
Topic 1: Probability Learning question: Key Knowledge: Listing outcomes. Mutually exclusive events. Sample space diagrams. Relative frequency and expectation. Frequency tree. Probability trees and Venn diagrams. Topic 2: Transformations Learning question: Key Knowledge: Reflection, Rotation, translation and enlargement. |
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Building and revisiting
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Overview: The topics in the Year 9 Foundation curriculum follow a similar pattern to years 7 and 8 and aim to consolidate all the skills learned so far and extend to more complex questions, algebra and real life situations. Year 9 sets the foundation for the GCSE curriculum in year 10. Additionally, all students will begin to study for the GCSE Statistics examination they will take in the Summer of Year 10. Topics and Key Skills are revisited every lesson through Recall 5s and through retrieval SPARX homework. |
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Students consolidate their knowledge of place value, decimals, powers and root from Year 7&8 using index laws with both numbers and variables. They apply their knowledge of these in order to multiply and divide with standard form and find the HCF and LCM of two or more numbers. |
Students consolidate their understanding of the basic manipulation of algebra from Year 7&8 working with more complex questions. They use their knowledge of angle rules to calculate missing angles in a variety of circumstances and interleave their algebra skills in order to solve problems. |
Students consolidate their understanding of the 4 rules of number with mixed numbers and fractions. Students find fractions and percentages of amounts with and without a calculator and begin to explore percentages in context. They use their knowledge of ratio to work with scale drawings, recipes and exchange rates. They begin to explore the concept of inverse proportion. |
Students explore the difference between expressions, equations, identities and Formulae. They continue to solve linear expressions involving more complex questions and change the subject of a formula where the variable subject is in the denominator. They develop their understanding of the volume of a cuboid to calculate the volume of a prism or cylinder. |
Students begin to study for the GCSE Statistics examination. They investigate what types of data exist, how it can be collected, displayed and analysed. They develop the skills learned in Year 7&8 and are introduces to the estimated averages from grouped data, interpolation, extrapolation, Spearman’s Rank, Frequency Polygons and Moving Averages. |
Students explore the probability topics from the GCSE Statistics curriculum deepening their understand of the concepts developed in year 7&8 as well as exploring frequency trees and probability trees for dependent events. They consolidate their knowledge of transformations on a coordinate grid. |
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Assessment |
RAP x 2: 15 Skills Retrieval Test in final week |
RAP x 2: 15 Skills Retrieval Test in final week |
RAP x 1: 15 Skills Retrieval Test in final week Mid Year KASTS |
RAP x 2: 15 Skills Retrieval Test in final week |
RAP x 2: 15 Skills Retrieval Test in final week |
RAP x 1: 15 Skills Retrieval Test in final week End of Year Assessment |
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HT1 |
HT2 |
HT3 |
HT4 |
HT5 |
HT6 |
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Year 9 Higher |
Topic 1: Place Value, Integers, Decimals, Powers and Roots Learning question: Key Knowledge: Topic 2: Factors, Multiples and Standard Form Learning question: Key Knowledge: |
Topic 1: Algebraic Manipulation Learning question: Key Knowledge: Consolidation of manipulation of algebraic expressions expansion and factorisation. Factorising quadratics including difference of 2 squares. Change the subject of a formula with the variable on both sides. Solve simple linear simultaneous equations. Topic 2: Sequences, Functions and Graphs Learning question: Key Knowledge: Topic 3: Ratio & Proportion Learning question: How can ratio be used to solve complex problems? Key Knowledge: Consolidation of ratio. Map scales. Exchange rates. |
Topic 1: Fractions & Percentages Learning question: What is interest and depreciation? Key Knowledge: Topic 2: Angles Learning question: How can I solve angle problems in polygons? Key Knowledge: Consolidation of angles in shapes and on parallel lines. |
Topic 1: Area Review Learning question: How do I calculate the area of a compound shape? Key Knowledge: Topic 2: Pythagoras Learning question: How are the sides of right angles triangles related? Key Knowledge: The Pythagorean theorem Midpoint and plotting coordinates. Length of a line segment. Topic 3: Circles Learning question: How do I calculate the area of sectors and length of arcs? Key Knowledge: Consolidation of area and circumference of circles. Arc length. Area of sectors.
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Topic 1: Linear Graphs Learning question: How can I find the equation of a linear graph given two coordinates on the line? Key Knowledge:
Topic 2: The Data Cycle
Learning question:
Key Knowledge: Types of data. Sampling. Capture-recapture. Averages and range from a list. Stem and leaf. Quartiles and IQR. Averages from a table. Linear interpolation. Presenting data. Scatter Graphs. Pie Charts. Correlation and line of best fit. Time series graphs. |
Topic 1: Probability Learning question: Key Knowledge: Topic 2: Learning question: Key Knowledge: Invariance. Negative and fractional enlargement. |
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Building and revisiting
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Overview: The topics in the Year 9 Higher curriculum follow a similar pattern to years 7 and 8 and aim to consolidate all the skills learned so far and extend to more complex questions, algebra and real life situations. Year 9 sets the foundation for the GCSE curriculum in year 10. Students are introduced to Surds and more complex percentages problems, as well as the nth term of quadratic sequences and more complex linear equations topics. Additionally, all students will begin to study for the GCSE Statistics examination they will take in the Summer of Year 10. Topics and Key Skills are revisited every lesson through Recall 5s and through retrieval SPARX homework.. |
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Students consolidate prior learning with place value, powers and roots and work with fractional and negative indices. They use their knowledge of indices rules to add, subtract, multiply and divide standard form. Students are introduced to the concept of a surd, simplifying and multiplying them. |
Students consolidate their knowledge of solving linear equations and changing the subject of an equation. They develop their knowledge of linear nth term to find the nth term quadratic sequences. Students use their knowledge of ratio and proportion to solve problems with maps scales, exchange rates and more complex ratio problems in context. Students solve simple linear simultaneous equations. |
Students consolidate their knowledge of fractions and percentages from Year 7&8, converting between fractions and recurring decimals, finding reverse percentages and calculating interest and depreciation. They use their angles knowledge to calculate missing angles in a variety of shapes and situations including the use of algebra. |
Students consolidate their knowledge of area of shapes and find the area and perimeter of compound shapes including trapeziums. They convert between metric units of area. Students develop their work on Pythagoras from Year 8 and use it to calculate the length of a line segment. Students use their knowledge of area and circumference of a circle to find arc lengths and the area of sectors. |
Students consolidate their knowledge of linear graphs and begin to be able to name graphs given points on the graph, the gradient and/or the y-intercept. Students begin to study for their GCSE Statistics Examinations reviewing statistics and probability topics from years 7&8 as well as being introduced to concepts such as quartiles, IQR, Linear Interpolation and the equation for a line of best fit. |
Students review their probability work from Year 7&8 and extend their knowledge to understand set notation and conditional probability as well as the product rule for counting. They consolidate their understanding of transformations, combining single transformations, and introduced to the concept of invariance. |
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Assessment |
RAP x 2: 15 Skills Retrieval Test in final week |
RAP x 2: 15 Skills Retrieval Test in final week |
RAP x 1: 15 Skills Retrieval Test in final week Mid Year KASTS |
RAP x 2: 15 Skills Retrieval Test in final week |
RAP x 2: 15 Skills Retrieval Test in final week |
RAP x 1: 15 Skills Retrieval Test in final week End of Year Assessment |
KS4 Curriculum Overview
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Year 10 Foundation
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Topic 1: Learning question: Key Knowledge: Topic 2: Learning question: Key Knowledge: Consolidation of algebraic manipulation. Substitute into expressions with brackets and indices. Expansions and factorisation. Factorise quadratics. Solve quadratics by factorising. |
Topic 1: Shape, Area & Volume Learning question: What is congruency and similarity in shape? Key Knowledge: Area and perimeter. Area of trapeziums. Convert between metric units of area and volume. Nets. Surface area and volume of prisms. Identify congruent and similar shapes. Topic 2: Learning question: Key Knowledge: Topic 3: Learning question: Key Knowledge: Area and circumference of circles. Area of a sector. Volume and surface area of cylinders, cones, pyramids and spheres. |
Topic 1: Equations & Inequalities Learning question: Key Knowledge: Consolidation of solving and rearranging equations. Representing inequalities on a number line. Solving inequalities. Error interval and truncation. Solve simultaneous equations. Topic 2: Sequences and nth term Learning question: Topic 3: Learning question: Key Knowledge: Index numbers. RPI, CPI and GDP. Rates of change. Cumulative frequency Curves. Boxplots. Outliers and skew. Key Knowledge: Consolidation of nth term of linear sequences. Nth term from diagrams. Use a formula to find the terms of a quadratic sequence. Geometric sequences. |
Topic 1: Analysing Data (Stats Revision) Learning question: Key Knowledge: Topic 2: Probability (Stats Revision) Learning question: Is probability an accurate way to predict events? Key Knowledge: Listing outcomes. Mutually exclusive events. Sample space diagrams. Relative frequency and expectation. Frequency tree. Probability trees and Venn diagrams. |
GCSE Stats Revision & Exam Practice |
GCSE STATS EXAM Topic 1: Linear Graphs Learning question: What is the general equation of a linear graph? Key Knowledge: Midpoints. Horizontal and vertical graphs. Plot linear graphs using a table. Find the gradient of a line. The general equation of a line. Parallel lines. Topic 1: Constructions and Loci Learning question: How can constructions help to solve real life problems? Key Knowledge: Constructing triangles, angles and bisectors. Loci. Scale drawings. Bearings. Elevations. Isometric drawings. |
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Building and revisiting
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Overview: Year 10 is the beginning of the GCSE Curriculum for all students and builds upon the foundations built in KS3. Additionally, all students will complete their course of study for the GCSE Statistics examination they take in the Summer. Topics and Key Skills are revisited every lesson through Recall 5s and through retrieval SPARX homework.. |
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| Students consolidate their understanding of how FDP are linked and use a decimal multiplier to increase and decrease an amount by a given percentage. They find percentage change, reverse percentages, interest and depreciation. They further consolidate their algebra skills from KS2 and explore the link between factorising and expanding. They factorise and solve simple quadratic equations. | Students consolidate their KS2 knowledge of area, perimeter and volume. They calculate the area and volume of more complex shapes and explore the nets and characteristics of simple 3d shapes. They identify congruent and similar shapes. Students revisit their work on Pythagoras from Year 8 and solve questions in context. | Students are introduced to the concept of inequalities and apply their understanding of how to solve an equation to them. They represent inequalities on a number line and solve simple simultaneous equations. Students continue to work with linear sequences and nth term and use the nth term of a quadratic sequence to find the terms in the sequence. They are introduced to the concept of a geometric sequence and explore Fibonacci sequences. | Students are introduced to the concept of Skew, index numbers, RPI, CPI and GDP. They plot and interpret cumulative frequency polygons and explore the relationship between these and boxplots. They begin to consolidate the Statistics knowledge gained in Year 9 and 10 in advance of their GCSE Statistics examination. | Students consolidate their data and probability knowledge gained in the last 4 years in order to revise for their GCSE Statistics Examination and sit a mock exam preparation. | Students sit their GCSE Statistics examination. Students will further their understanding of linear graphs calculating the gradient of a line, given two coordinate and using y = mx + c to draw and name lines. They will identify parallel lines from the equation of a line. Students further explore the construction of common shapes and angles and use these skills to draw Loci. They work with maps and scales and draw accurate drawings of 3d shapes using isometric paper as well as elevations. | |||||||
| Assessment |
RAP x 2: 15 Skills Retrieval Test in final week |
RAP x 2: 15 Skills Retrieval Test in final week |
RAP x 1: 15 Skills Retrieval Test in final week Mid Year KASTS |
RAP x 2: 15 Skills Retrieval Test in final week Mock Examination |
RAP x 1: 15 Skills Retrieval Test in final week |
RAP x 1: 15 Skills Retrieval Test in final week End of Year Assessment |
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| Year 10 Higher |
Topic 1: Compound measures Learning question: Key Knowledge: Topic 2: Solving quadratics and inequalities Learning question: Key Knowledge: Topic 3: Congruent and Similar Shapes Learning question: Key Knowledge: Topic 4: Real life graphs Learning question: What are the characteristics of velocity and speed graphs? Key Knowledge: |
Topic 1: Learning question: What is the relationship between the angles and sides of right angled triangles? Key Knowledge: Topic 2: New Stats 1 Learning question: What is the relationship between cumulative frequency graphs and box-plots. Key Knowledge: Consolidation of probability. Binomial distribution. IQR. Cumulative frequency. Boxplots. Topic 3: New Stats 2 Learning question: What is standard deviation? Key Knowledge: Geometric and weighted mean. Standard deviation of discrete data. Chain based index numbers. RPI, CPI and GDP. Rates of change. Population pyramids. |
Topic 1: New Stats 3 Learning question: Key Knowledge: Topic 1: New Stats 4 Learning question: Key Knowledge: |
Topic 1: Volume and Surface Area Learning question: Key Knowledge: Topic 2: Surds Learning question: Key Knowledge: |
Topic 1: Proportion Learning question: What is direct and indirect proportion? Key Knowledge: Direct and inverse proportion. Topic 2: Algebraic Fractions Learning question: Key Knowledge: GCSE Stats Revision & Exam Practice |
GCSE Stats Exam Topic 1: Vectors Learning question: Key Knowledge: Column vectors. Vector geometry. Topic 2: Circle Theorems Learning question: Key Knowledge: Circle theorems. Topic 3: Learning question: Key Knowledge: Constructing triangles, angles and bisectors. Loci. Scale drawings. Bearings. Elevations. Isometric drawings. |
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Building and revisiting
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Overview: Year 10 is the beginning of the GCSE Curriculum for all students and builds upon the foundations built in KS3. Additionally, all students will complete their course of study for the GCSE Statistics examination they take in the Summer. Topics and Key Skills are revisited every lesson through Recall 5s and through retrieval SPARX homework. |
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| Students are introduced to the concept of compound measures and study speed, density and pressure. They develop their knowledge of solving equations using factorisation, completing the square and the quadratic formula to solve quadratic equations. They further investigate what it is to be congruent and similar using rules for triangles and in 3d shape. Students study real life graphs including distance/time graphs and velocity/time graphs. | Students review Pythagoras and are introduced to the concept of trigonometric ratios in right angled triangles. They sketch trigonometric graphs and memorise exact trig values. Students further their statistics knowledge, studying topics such as Binomial distributions, Cumulative frequency, boxplots, outliers, geometric and weighted mean and chain based index numbers. They are introduced to the concept of standard deviation and use it to analyse data. | Students continue to work on statistics and are introduced to topics such as Population Pyramids, Histograms, Choropleth Maps, Spearman’s Rank, PMCC and SRCC, Moving averages, Normal Distributions, Standardised scores and Quality assurance. | Students convert between metric units of volume and calculate the volume and surface area of prisms, pyramids, cylinders, cones, frustums, spheres and hemispheres. They review their work on surds from year 9 and use it to rationalise the denominator of a fraction. | Students investigate the concepts of direct and inverse proportion. They work with fractions that involve algebra simplifying, multiplying, dividing, adding and subtracting them. The solve algebraic fractions and begin to revise for their GCSE Statistics examination. | Students sit their GCSE Statistics examination. They work use column vectors diagrammatically and calculate with them. Students are introduced to Circle theorems and use them to solve contextual problems including algebra. Students use mathematical tools to construct accurate drawing and use loci to solve real life problems. They draw scale drawings, isometric drawing and elevations. | |||||||
| Assessment |
RAP x 2: 15 Skills Retrieval Test in final week |
RAP x 2: 15 Skills Retrieval Test in final week |
RAP x 1: 15 Skills Retrieval Test in final week Mid Year KASTS |
RAP x 1: 15 Skills Retrieval Test in final week Mock Examination |
RAP x1: 15 Skills Retrieval Test in final week |
RAP x 1: 15 Skills Retrieval Test in final week End of Year Assessment |
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Year 11 Foundation
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Topic 1: Ratio, Proportion and Compound Measures Learning question: Key Knowledge: Consolidation of order of operations and Ratio. Best buys. Speed. Distance and velocity time graphs. Pressure. Density. and depression. Exact Trig values. Topic 1: Vector Notation Learning question: What do column vectors represent? Key Knowledge: Column vector notation. Adding and subtracting column vectors. Multiplying vectors by a scalar. |
Topic 1: Quadratic and Cubic Graphs Learning question: Key Knowledge: Plot quadratic graphs. Characteristics of quadratics graphs. Cubic and reciprocal graphs. Topic 2: Simultaneous equations Learning question: How do I solve equations with 2 variables? Key Knowledge: Topic 3: Congruence, Similarity and Transformations Learning question: What makes shapes congruent? Key Knowledge: Congruent shapes. Similar shapes and triangles. Reflection, Rotation, Enlargement and Transformation. Topic 4: Pythagoras & Trigonometry Learning question: How are the angles and sides of right angled triangles related? Key Knowledge: Pythagoras in context. Trigonometric ratios in right angled triangles. Elevations |
Revision and Exam Practice | Revision and Exam Practice | GCSE Maths Exam | |
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Building and revisiting
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Overview: In Year 11, students complete their study for the GCSE Mathematic curriculum and begin a course of revision and exam practice. Their revision curriculum is set but adapted according to the QLA undertaken after each mock examination. Topics and Key Skills are revisited every lesson through Recall 5s and through retrieval SPARX homework. |
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| Students consolidate their understanding and ratio and proportion and explore compound measure of speed, density and pressure. They use and calculate with column vectors. | Students explore the shape and characteristics of quadratic, cubic and reciprocal graphs and plot them using a table of values. They consolidate their knowledge of transformations and calculate missing sides and angles of right angled triangles. | Students follow a revision and exam practice course of study ahead of their GCSE exam. | Students follow a revision and exam practice course of study ahead of their GCSE exam. | Students sit their GCSE Mathematics Examination | ||
| Assessment |
RAP x 1 Mock Examination |
RAP x 2 Congruence & Similarity Pythagoras |
Marked and self marked past papers |
Marked and self marked past papers Mock Examination |
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| HT1 | HT2 | HT3 | HT4 | HT5 | HT6 | |
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Year 11 Higher
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Topic 1: Further Trigonometry Learning question: What is the relationship between angles and sides of triangles that are not right-angled? Key Knowledge: Sine rule. Cosine rule. Trig and Pythagoras in 3d shape. Area of a triangle. Topic 2: Further Graphs Learning question: Key Knowledge: |
Topic 1: Functions Learning question: Key Knowledge: Topic 2: Circle Tangents Learning question: Key Knowledge: Topic 3: Transforming Graphs, Gradient and Area Under Curves Learning question: Key Knowledge: Topic 4: Learning question: Key Knowledge: Constructing triangles, angles and bisectors. Loci. Scale drawings. Bearings. Elevations. Isometric drawings. |
Revision and Exam Practice | Revision and Exam Practice | GCSE Maths Exam | GCSE Maths Exam |
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Building and revisiting
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Overview: In Year 11, students complete their study for the GCSE Mathematic curriculum and begin a course of revision and exam practice. Their revision curriculum is set but adapted according to the QLA undertaken after each mock examination. Topics and Key Skills are revisited every lesson through Recall 5s and through retrieval SPARX homework. |
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| Students extend their understanding of triangle trigonometry to those which are not right angled. They use the sine and cosine rules to calculate sides and angles including those in 3d shapes. Students study real life graphs including distance/time graphs and velocity/time graphs. Students study and plot quadratic, cubic and reciprocal graphs. They are introduced to iterations.. Students sketch simple graphs of circles and extend their understanding of inequalities to include linear and quadratic inequalities and their regions. Students expand triple brackets and solve linear and quadratic simultaneous equation both algebraically and graphically. | Students complete their GCSE course studying functions. They are introduced to exponential graphs and the concept of the transformation of graphs. They calculate an estimate for the area under a curve and the gradient at a point on a curve. They further their knowledge of the equation of a circle by calculating tangents to a point on a circle. Students use mathematical tools to construct accurate drawing and use loci to solve real life problems. They draw scale drawings, isometric drawing and elevations. | Students follow a revision and exam practice course of study ahead of their GCSE exam. | Students follow a revision and exam practice course of study ahead of their GCSE exam. | Students sit their GCSE Mathematics Examination | ||
| Assessment |
RAP x 1 Mock Examination |
RAP x 2 Functions Transformations of graphs |
Marked and self marked past papers |
Marked and self marked past papers Mock Examination |
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