# Mathematics

*Anyone can be a Mathematician!*

Head of Mathematics, Mrs C Brown, c.brown@glynschool.org

### Why study this subject?

Mathematical thinking is important for all members of a modern society as a habit of mind for use in the workplace, business and financial worlds, and for personal decision-making. Mathematics is fundamental to national prosperity in providing tools for understanding science, engineering, technology and economics. It is essential in public decision-making and for participation in the knowledge economy.

Mathematics equips students with uniquely powerful ways to describe, analyse and change the world. It can stimulate moments of pleasure and wonder for all students when they solve a problem for the first time, discover a more elegant solution, or notice hidden connections. Students who are functional in Mathematics and financially capable are able to think independently in applied and abstract ways, can reason, solve problems and assess risk. Mathematics is a creative discipline. The language of Mathematics is international. The subject transcends cultural boundaries and its importance is universally recognised. Mathematics has developed over time as a means of solving problems and also for its own sake.

### Year 7 sequence of lessons

**Half Term 1 **- Algebraic thinking Sequences, Algebraic notation, Equations and equivalence

In the first half term students are taught in mixed ability classes. We find that the key skills in algebra can be challenging and accessible to all students at the same time. A lot of the skills taught are key to access algebra and will be interleaved in the following years schemes of learning. It is imperative that students also understand the essence of algebra. This is initially done through making links between number topics such as sequences and linking it with the unknown. Calculator skills are also taught throughout.

Students are introduced to the concepts of constant rates of change (leading to understanding proportion).

**Half Term 2 **- Place Value and Proportion, Place Value and ordering, Fractions decimals Percentages

Students have the opportunity to consolidate their understanding and make sure that any misconceptions on place value is addressed. This is a key building block for all the operations and to understand fractions decimals and percentages. Students at the higher end will be challenged by problem solving and making links to other topics. Reasoning and proportional understanding skills to be developed throughout. Proportional understanding will be further developed using pie charts.

**Half Term 3 **- Applications of number, addition and subtraction, multiplication and division, fractions and percentages

Students revisit the four operations with an emphasis on most efficient methods, choosing when to do mental, written or calculator methods, fluency and problem solving. A series of topics is linked to multiplication and division aiming to revisit key concepts and build link, including proportional reasoning. Such topics are: factors and multiples, perimeter and area of basic shapes, order of operations and equations will also be taught.

**Half Term 4 **- Directed numbers, add and subtract fractions

Students work on all four operations with negative numbers, \in the primary students have a limited experience with negative numbers so this block will help them deepen their understanding. As well as exploring negative numbers the topic provides opportunities for reviewing the order operations, substitution and solving equations. Students will use multiple operations in the same question

This topic builds on the topics of fractions, decimals, percentages taught in the autumn term. Students will get to use equivalent fractions in the context of addition and subtraction.

**Half Term 5 **- Line and angles, drawing, measuring and construction,v angles and geometric reasoning

Students are given opportunities to develop their skills at using geometrical equipment such as protractors and pairs of compasses. A number of students struggle with constructions so it is helpful to expose them to this topic early on so that they have plenty of opportunities to develop these skills. This unit also gives students a change from number, helping to maintain their engagement late in the year. By this point in the year, students are equipped with number skills that can be applied to angle and geometric reasoning questions. Proportion will interleaved. Names and properties of triangles, quadrilaterals and other polygons will be covered. Students use angle facts to start making chains of geometric reasoning.

**Half Term 6 **- Probability, coordinate system, reasoning with number

Students are introduced to probability for the first time. The basics are taught in order for students to become familiar with the terms and language used in probability. This will be built on in future years. FDP will be used accordingly, forming and solving equations, adding and subtracting fractions.

Building on the knowledge of KS2 students will look at straight lines and their equations. They will be introduced to concepts of gradient and intercept but the focus is to produce lines from their equations. They will make links with sequences and their graphs.

Students will review and extend mental strategies to consolidate their KS2 and extend their understanding of numbers.

### Year 8 sequence of lessons

**Half Term 1 **- Reasoning with numbers & basic algebra skills

Extending Year 7 knowledge by linking LCM and HCF with algebraic understanding (with a focus on bigger numbers, prime factorisation and real life problems.)

Progression of year 7 algebraic skills at a greater depth (i.e. from one-step solving equations in year 7 to two-step solving equations in year 8).

Expanding brackets is also taught in year 8 linking this with solving equations.

**Half Term 2 **- Developing geometry

Students covered area as an application of multiplication and division. Area is reviewed here in its own right to ensure students are proficient at what was covered in year 7, while adding areas of trapeziums, circles and compound shapes.

Having just studied algebra skills, shape and space provides good opportunities for students to apply these skills in a different context. More difficult angle topics such as parallel lines and polygons are included here as students have covered the basics.

**Half Term 3 **- Representations

Finding the nth term is taught with knowledge of sequences work, algebraic notation and substitution taught in year 7.

Students build on the unit working with Coordinates in year 7. Now they will work out the equation of a straight line and compare that to the nth term used in sequences just before.

The topic also lays the foundation for the introduction into proportional reasoning with straight lines.

**Half Term 4 **- Proportional reasoning#

The topic focuses on developing the understanding of ratio. Sharing into a ratio given the whole or parts and problem solving. It builds on multiplication skills, links with FDP, multiplicative relationships, links to graphs, links to scale factors. Deepens understanding of equivalent ratios. Develops understanding of ratio, scale diagrams and mapsI Interleaving with graphs and solve problems with direct proportion.

**Half Term 5 **- Developing number

Revisit fractions and percentages to deepen understanding. Students calculate percentage increase and decrease using a variety of methods. They solve problems in a variety of contexts. Link to ratio and proportion taught in the previous half term.

**Half Term 6 **- Three dimensional shapes and handling data cycle

Students have covered area of 2D shapes previously which is necessary for volume and surface area of 3D shapes. Students construct nets and use the language of faces, vertices and edges. They identify 2D shapes within 3D shapes, work out the volume and surface area of cubes, cuboids and prisms.This is an opportunity to revisit areas, rounding and estimation as well as conversion of units. Again, as algebra has been covered previously, students are able to apply algebra to volume and surface area questions to find missing lengths.

Students are introduced to key terminology with data, and these are linked to basic data that they were taught in KS2, revisiting methods of collecting data in order to analyse and represent graphically.

Students should have been introduced to Averages in KS2. This reintroduces the topic and expands to include averages for grouped data and which average is appropriate to make comparison between distributions..

Students build on what they learnt in Year 7 extending their understanding to calculate the probability of two events by listing outcomes using a sample space diagrams. Students also calculate probabilities using tables and venn diagrams.

### Year 9 sequence of lessons

**Half Term 1 **- Constructions in 2D and reasoning with proportion

Students revisit constructions of triangles which they have seen previously in year 7 and extend the topic to bisectors angle construction and perpendiculars. Students explore and understand congruent triangles through constructions.

Constructions are a prerequisite for Loci to be taught in Year 10.

In proportional reasoning students enlarge shapes, understand the difference between congruence and similarity, find missing lengths in similar triangles.

**Half Term 2 **- Standard form, compound measures, rounding and estimation

Students are taught standard form for the first time. It’s an application of indices and an introduction to the concept of negative indices. Students can express very large and very small numbers in a more manageable form.

Students use rounding to estimate numerical expressions and appreciate any misconceptions with rounding in real life.

Compound measures, speed, density.

Pythagoras’ theorem.

**Half Term 3 **- Reasoning with geometry

Students review key angle facts taught in year 7, angles in parallel lines and angles in polygons taught in year 8. The aim is to use algebraic skills to find angles and chains of reasoning to evaluate angles

Students explore rotations and translations. They look at rotational symmetry of shapes, rotate shapes, translate points and shapes. They are introduced to the concept of invariance in the context of transformations.

**Half Term 4 **- Reasoning with algebra

Students review and progress from two-step equations to three-step with the unknown on both sides. The unit Includes solving with brackets and inequalities. Forming equations and problem solving in contexts seen before like areas, angles, probability. Students revisit straight line graphs taught in year 8 and solve equations using the graphs. As an extension students can look at solving simultaneous equations graphically.

Students rearrange formulae using skills from solving equations and linking function machines learnt from Year 7.

**Half Term 5 **- Developing number, percentages, maths and money

Students will revisit percentage increase and decrease. Students will calculate percentage change and consider problem solving in financial contexts such as interest rates and best buys As an extension students will look at reverse percentage problems. The unit revisits and links fractions, percentages and proportions.

**Half Term 6 **- Measures of location and dispersion

This unit builds on the knowledge and skills learnt in year 8 with averages, by extending finding averages within frequency tables. It is also an opportunity to revisit the topic to ensure full understanding of measures of average and spread. New concepts of quartiles and box plots are introduced, to enable students to compare data sets and extend their understanding of using averages and ranges. Problem solving is now brought in so students can apply their knowledge and skills.

### Year 10 sequence of lessons

**Half Term 1 **- Accuracy and estimation and similarity and trigonometry

Students revisit rounding and estimation first taught in year 7 and interleaved in year 8 and 9 within shapes. They develop an understanding of error intervals and they use inequalities to represent these. Students look at surds as an extension topic.

Students review similarity covered in year 9 and use the concept to build on Trigonometry which is taught for the first time and is considered a special case of similarity.It is introduced early in the year so it can be revisited when bearings are taught later in the year.

Constructions are reviewed through the study of loci.

**Half Term 2 **- Developing algebra, sequences, equations & quadratics

Students practice expanding single and double brackets, factorise single brackets,factorise quadratics in the form x^2 + bx +c. They review solving equations and learn how to solve quadratic equations. They plot quadratic graphs and solve equations graphically.

Students learn how to form and solve simultaneous equations. Students study quadratic sequences at the Higher tier only.

**Half Term 3 **- Proportions and proportional change

Use ratio in a variety of contexts and make links fractions

Revisit fractions, decimals and percentages.Percentage change, simple and compound interest. Evaluate exponential change (growth and decay).

**Half Term 4 **- Geometry

Volume and SA with Revisit circles, calculate volume and SA of cylinders and cones.

Angles and bearings

Revisit angle facts. Understand and use bearings.

Vectors

- Understand vector notation
- Vector arithmetic
- Vectors and translations

**Half Term 5 **- Data

Review Collecting, representing and interpreting data.

- -time series
- -sampling
- -Correlation and line of best fit
- Frequency polygons

Probability 3

- Work with mutually exclusive and independent events
- Tree diagrams
- Venn diagrams

**Half Term 6 **- Using Number

This is a half term where teachers plan revision lessons on the topics below. It is at the end of the year to help plan more efficiently since the teacher knows the strengths and areas for improvement of the class.

Non calc methods

Revisit Four operations with integers, decimals fractions with and without context

Exact values

Types of numbers & sequences

Indices and roots

- Revisit Factors, prime factorisation
- Revisit arithmetic and geometric sequences
- Work out powers and roots
- Revisit Rules of indices
- Revisit Standard form

### Year 11 sequence of lessons

**Half Term 1 **- Algebra and geometric reasoning

Students review quadratics and quadratic equations from year 10. At the higher tier students learn how to solve quadratics using the quadratic formula, by completing the square and further develop their understanding of quadratic graphs.

Solving inequalities is revisited. Students represent solutions on a number line. Higher tier students learn how to solve inequalities with two variables graphically and quadratic inequalities.

Students revisit Volume and surface taught in year 8 along with those of pyramids, spheres, cones and compound shapes.

Circle theorems are taught to the Higher tier only.

**Half Term 2 **- Probability and trigonometry

- Systematic listing
- Probability
- Trigonometry

**Half Term 3 **- Functions and graphs

- Functions
- Graphs and transformations

Higher only

- Area and gradient of a curve -Equation of circle & tangent
- Iteration
- Histograms

**Half Term 4 **- Proof

- Proof
- Algebraic fractions
- Proof with vectors

**Half Term 5 **- Exam preparation (H/F)