Year 7
Algebraic Thinking
- Sequences
- Understand and use algebraic notation
- Equality and equivalence
We begin in Year 7 by looking at sequences, and identifying patterns. Having a solid foundation of algebra notation allows us to describe these patterns and generalize problems.
Place value and Proportion
- Place value and ordering integers and decimals
- Fraction, decimal and percentage equivalence
Having used Algebra to generalize problems we go back and look more closely at the number line and place value. We investigate how numbers are written using place value and explore the number line between integers into decimals and fractions. Having a secure understanding of the equivalence between decimals, fractions and percentages allows us to be able to interchange between them.
Applications of Number
- Solving problems with addition & subtraction
- Solving problems with multiplication and division
- Fractions & Percentages of amounts
Using the knowledge of place value we then explore written arithmetic techniques to add, subtract, multiply and divide both integers and decimals. This then leads us into finding fractions and percentages of amounts.
Directed Number
- Operations and equations with directed number
Continuing with number, we extend the number line below zero and explore what happens when using negative numbers in arithmetic. This is then linked back to the first topic of the year and we incorporate negative numbers into algebraic expressions, linking the two topics together.
Fractional Thinking
- Addition and subtraction of fractions
Extending our knowledge of the number line even further and alongside our arithmetic methods, we look at how fractions are represented and how we can add and subtract fractions. There is the opportunity here to work with algebraic fractions, again creating the link between number and algebra.
Lines and Angles
- Constructing, measuring and using geometric notation
- Developing geometric reasoning
Taking the idea of a number line, we explore the idea of measurement, focusing on angles and lengths. By combining lines and angles we can create and explore the properties of many different polygons and develop the idea of geometric reasonings. Using a protractor, compass and ruler we can extend our knowledge of shapes to construct accurate drawings of different polygons.
Reasoning with Number
- Developing number sense
- Sets and probability
- Prime numbers and proof
Having spent a large amount of Year 7 focusing on the number system, we finish the year by bringing it all together and focusing on developing number sense, mental arithmetic techniques and ‘tricks’ to build fluency and confidence when working with numbers. Finally we explore different types of numbers e.g. primes and how we can represent them as sets.
Year 8
Proportional Reasoning
- Ratio and Scale
- Multiplicative change
- Multiplying and dividing fractions
Year 8 begins with a focus on proportion, and multiplicative change. This includes ideas like ‘4 apples cost £30, how much does 12 apples cost?’ and being able to scale recipes and converter money into different currencies.
Having focused on the addition and subtract of fractions in Year 7, we now explore multiplication and division of fractions as part of proportion.
Representations
- Working in the Cartesian Plane
- Representing data
- Tables and Probability
This topic focuses on different areas of representation, to begin we look at plotting coordinates and how we describe a point in space. As in Year 7 we then look for patterns in coordinates and identify lines, using algebra to create rules and equations for these lines.
The next focus is being able to represent data and again, identify patterns and relationships using scatter graphs and tables.
And finally, we explore the idea of probability and the chance of something happening.
Algebraic techniques
- Brackets, equations and inequalities
- Sequences
- Indices
Building on the ideas covered in the Year 7 Algebraic thinking topic, here we look more closely at algebraic notation and manipulation, including explaining brackets and factorising, all fundamental skills of algebra. The idea of using algebra to generalize the world around us allows us to form and solve a variety of equations to solve problems. In Year 7 we looked at sequences, and the term to term rule but with greater algebra skills we are now able to describe the position to term rule for a linear sequence.
Developing Number
- Fractions and percentages
- Standard index form
- Number sense
Expanding on the work covered in Year 7 on the number line, we build fluency and confidence in using percentages. We encourage the use of a calculator and calculator techniques, particularly in finding percentages of amounts, and calculating percentage increase and decrease. This is a topic that comes up in many different subjects, such as the sciences, geography and psychology.
Having an awareness of the size of numbers is important, and here we look at huge and tiny numbers using standard form and idea of powers of 10, fundamental for scientists as well as mathematicians.
Developing Geometry
- Angles in parallel lines in polygons
- Area of trapezium and circles
- Line symmetry and reflection
Looking back at the lines and angles topic in Year 7 we now develop those ideas of geometry and begin by exploring properties of angles. Focusing on interior and exterior angles of polygons as well angles on parallel lines.
We then look more closely at the whole shape, and how we calculate the space it takes up (area), and if there is any symmetry.
Reasoning with Data
- The data handling cycle
- Measures of location
Year 8 finishes with a look at the data handling cycle, starting with how we collect data, how it can be represented to make it clear to read and finally how we can analyze it and draw conclusions.
Year 9
Reasoning with Algebra
- Straight line graphs
- Forming and solving equations
- Testing conjectures
Linking to the idea of representation in Yr 8 and the use of coordinates to plot a point in 2D space, we develop the idea that a line is a set of coordinates that follow a rule and use algebra to create equations in form y = mx + c to describe these lines.
Having created equations, we then look at being able to solve them, recapping some of the algebra manipulation from Year 8 including expanding brackets.
Constructing a 2 and 3 Dimensions
- Three-dimensional shapes
- Constructions and congruence
Returning to Geometry, we build on our knowledge of 2D shapes and explore the world of 3D, looking closely at the properties of 3D shapes.
Having worked on constructions in Year 7 and the use of a protractor and compass, we return to the idea of constructions and look at loci, and its use in the real world.
Reasoning with Number
- Number
- Using percentages
- Maths and money
Building on the work with number in Year 7 & 8 students explore different types of numbers from surds, to factors and multiples as well becoming more fluent and confident in working with fractions and percentages.
Often students struggle to see where their number skills may be useful in real life, so we take the opportunity to apply their skills in real life situations including VAT, compound interest, wages & taxes, exchange rates and best buys. Real life maths that helps us in everyday life.
Reasoning with Geometry
- Deduction
- Rotation and translation
- Pythagoras’ Theorem
Once again we return to geometry, and consolidate our knowledge on angles and look at transforming shapes by rotations and translation, making the link to art and idea of tessellation.
The use of Pythagoras is vast within so many different areas of life, from engineering to builders creating a right angle. We explore how Pythagoras discovered his theorem and how to apply it to solve a range of problems.
Reasoning with Proportion
- Enlargement and similarity
- Solving ratio & proportion problems
- Rates
In year 8 students studied proportion and multiplicative change, here we build on that knowledge with the idea of enlargement and similar shapes. The idea of proportion links to both number and geometry.
Representations
- Probability
- Algebraic representations
In this topic we look at probability from Year 8 and extend the understanding of experimental and theoretical chance to more than one event, using tree diagrams.
Finally, we look back at work from earlier in the year on coordinates and straight lines and explore non-linear graphs, including quadratics, reciprocals and price wise functions.
