# 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.

## Autumn Term

We begin the autumn term with two strands:

• proportional reasoning and
• representations.

The unit focusses 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, for example, 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. Learners following the higher strand also look at gradients in preparation for next half-term.

Learners now work with the link between ratio and scaling, including the idea of direct proportion, linking various forms 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 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. Learners 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. Links between fractions and decimals are also revisited. Learners following the higher strand will also cover multiplying and dividing with mixed numbers and improper fractions.

## Spring Term

There are two strands during the spring term:

• algebraic techniques and
• developing number.

Building on their understanding of equivalence from Year 7, learners will explore expanding over a single bracket and factorising by taking out common factors. The higher strand will also explore expanding two binomials. All learners will revisit and extend their knowledge of solving equations, now to include those with brackets and for the higher strand, with unknowns on both sides. Bar models will be recommended as a tool to help learners make sense of the maths.

Learners 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. This short block reinforces 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. Before exploring the ideas behind the addition and subtraction laws of indices (which will be revisited when standard form is studied in the summer term), the groundwork is laid by making sure learners are comfortable with expressions involving powers, simplifying e.g. 3x²y x 5xy³. The higher strand also looks at finding powers of powers.

## Summer term

To end the year for the summer there are two strands:

• developing geometry, and
• reasoning with data.

This block builds 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 learners 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.

Learners 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 learners, 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 teaching of reflection is split from that of rotation and translation to try and ensure students attain a deeper understanding and avoid mixing up the different concepts. Although there is comparatively little content in this block, it is worth investing time to build confidence with shapes and lines in different orientations. Learners can revisit and enhance their knowledge of special triangles and quadrilaterals and focus on key vocabulary such as object, image, congruent, etc.

Rotation and translations will be explored in Year 9.

## 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.