Mathematics
Year 8 Rationale
The Harrow High School Mathematics department follows the White Rose Maths scheme of work. The White Rose Maths approach focusses on developing skills and reinforcing competency in all areas, whilst providing opportunities to build reasoning and problem-solving into each lesson, with delivery of the curriculum focused on depth rather than acceleration.
We have adapted the scheme in places to ensure the pace and order of topics allows maximum progress and enjoyment for all learners at HHS.
Autumn Term
We begin the autumn term with two strands:
- Developing Number, and
- Proportional Reasoning.
The Developing Number units provide an accessible start to the year for all learners and allow a solid number foundation to be consolidated before applying concepts to the more abstract concepts covered in Year 8. The Prime Numbers and Proof topic allows learners to revisit key number concepts from Year 7 and allows teachers to identify any weaknesses in number skills.
Learners then move on to Indices and Standard Form. Before exploring the ideas behind the addition and subtraction laws of indices (which will be revisited when standard form is studied next term), the groundwork is laid by making sure students are comfortable with expressions involving powers, simplifying e.g. 3x²y x 5xy³. The higher strand also looks at finding powers of powers.
The Proportional Reasoning units focus initially on the meaning of the ratio and the various models that can be used to represent ratios. Based on this understanding, it moves on to sharing in a ratio given the whole or one of the parts, and how to use e.g. bar models to ensure the correct approach to solving a problem. After this we look at simplifying ratios, using previous answers to deepen the understanding of equivalent ratio rather than ‘cancelling’ purely as a procedure. We also explore the links between ratio and fractions and understand and use pi as the ratio of the circumference of a circle to its diameter.
Students now work with the link between ratio and scaling, including the idea of direct proportion, linking various form including graphs and using context such as conversion of currencies which provides rich opportunities for problem solving Conversion graphs will be looked at in this block and could be revisited in the more formal graphical work later in the term. Links are also made with maps and Scales, and with the use of scale factors to find missing lengths in pairs of similar shapes. Students will have had a little experience of multiplying and dividing fractions in Year 6; here we seek to deepen understanding by looking at multiple representations to see what underpins the (often confusing) algorithms. Multiplication and division by both integers and fractions are covered, with an emphasis on the understanding of the reciprocal and its uses.
Spring Term
There are two strands during the spring term:
- Representations, and
- Algebraic Techniques.
Building on their knowledge of coordinates from KS2, students look formally at algebraic rules for straight lines, starting with lines parallel to the axes and building up to the more general form in Working in the Cartesian Plane. When considering representations of data, students are introduced formally to bivariate data and the idea of linear correlation They extend their knowledge of graphs and charts from KS2 to deal with both discrete and continuous data. Students also building on tehri probability knowledge from Year 7, focussing on sample spaces and the use of tables to represent these.
In Algebraic Techniques, building on their understanding of equivalence from Year 7, students explore expanding over a single bracket and factorising by taking out common factors. All students will revisit and extend their knowledge of solving equations, now to include those with brackets and potentially, with unknowns on both sides. Bar models are used as a tool to help students make sense of the maths. Students will also learn to solve formal inequalities for the first time, learning the meaning of ‘solution set’ and exploring the similarities and differences compared to solving equations. Emphasis is placed on both forming and solving equations rather than just looking at procedural methods of finding solutions.
Moving on to sequences, this short block reinforces students' learning from the start of Year 7, extending this to look at sequences with more complex algebraic rules now that students are more familiar with a wider range of notation. The higher strand includes finding a rule for the nth term for a linear sequence, using objects and images to understand the meaning of the rule.
Summer term
To end the year for the summer there are two strands:
- Developing Geometry, and
- Reasoning with Data.
The Developing Geometry blocks build on KS2 and Year 7 understanding of angle notation and relationships, extending all students to explore angles in parallel lines and thus solve increasingly complex missing angle problems. Links are then made to the closely connected properties of polygons and quadrilaterals. The use of dynamic geometry software to illustrate results is highly recommended, and students following the higher strand will also develop their understanding of the idea of proof. They will also start to explore constructions with rulers and pairs of compasses. This key block may take slightly longer than two weeks and the following blocks may need to be adjusted accordingly.
Students following the Higher strand will have met the formulae for the area of a trapezium in Year 7; this knowledge is now extended to all students, along with the formula for the area of a circle. A key aspect of the unit is choosing and using the correct formula for the correct shape, reinforcing recognising the shapes, their properties and names and looking explicitly at compound shapes.
The end of the year, students work on Reasoning with Data. Much of the statistics content in KS3 is a continuation of that studied at primary school. A particular focus is using charts to compare different distributions. We also explore when graphs may be misleading, an important real-life consideration.
Students move on Measures of Location, having already met median and mean earlier in KS3. This block introduces mode and also looks at when and why each average should be used. We also consider outliers, considering what effect these have on all the measures studied, and whether they should be included or excluded in our calculations.
Knowledge organisers
A knowledge organiser is an important document that lists the important facts that learners should know by the end of a unit of work. It is important that learners can recall these facts easily, so that when they are answering challenging questions in their assessments and GCSE and A-level exams, they are not wasting precious time in exams focusing on remembering simple facts, but making complex arguments and calculations.
We encourage all learners to use them by doing the following:
- quiz themselves at home, using the read, write, cover, check method.
- practise spelling key vocabulary
- further researching people, events and processes most relevant to the unit.