# Mathematics

#### Year 9 Rationale

The Harrow High School Mathematics department follows a tailored version of White Rose Maths scheme of work for Year 9.  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

This term builds on Year 8 content. It is focused on two strands:

• reasoning with algebra, and
• constructing in 2- and 3-dimensions.

Learners build plotting simple line graphs. They now study y=mx+c, as the general form of the equation of a straight line, interpreting m and c in abstract and real-life contexts and reducing to this form in simple cases. This will be explored further in the next block when learners rearrange formulae. Higher strand learners will also consider inverse relationships and perpendicular lines.

Learners revisit and extend their knowledge of forming and solving linear equations and inequalities, including those related to different parts of the mathematics curriculum. They also explore rearranging formulae, seeing how this links to solving equations and reinforcing their understanding of the difference between equations, formulae, identities and expressions. This is a good opportunity to practise non-calculator skills if appropriate.

Reasoning is encouraged throughout the White Rose Maths scheme of learning and this block allows time for direct teaching of this. The opportunity is taken to revisit primes, factors and multiples, which provides a wealth of opportunity to make and test simple conjectures. As well as testing given conjectures, learners should be encouraged to create and test their own. An example given in the block is through looking at relationships in a 100 square; another great source of patterns is Pascal's triangle.

Learners also develop their algebraic skills through developing chains of reasoning and learning how to expand a pair of binomials, which higher strand students met in Year 8.

## Spring Term

Learners will work on two strands:

• reasoning with number, and
• reasoning with geometry.

Learners will develop their knowledge of the number system to include rational and real numbers, with the higher strand also looking at simple surds. The block provides plenty of opportunity for learners to revisit and practise their number skills both with and without a calculator as necessary. Standard form and HCF/LCM are also revisited.

Building on their revision of fractions in the last block, learners relate these to fractions and decimals, extending their learning in Year 8. All learners will look at ‘reverse’ percentage problems with higher attainers stretched by looking at repeated percentage change. Both calculator and non-calculator methods are encouraged, with the use of decimal multipliers again key.

Learners practise their number skills in various financial contexts in this block.  The language of financial mathematics, already introduced in Years 7 and 8, is further developed. Simple ideas of tax and wages are introduced, and the percentages studied in the last block are applied in various contexts including simple and compound interest.

## Summer Term

Towards the end of the year, the summer term focusses on two strands:

• reasoning with proportion and,
• representations and revision.

Learners develop their knowledge of transformations to include enlargement, learning the mathematical meaning of the word 'similar'. This can link back to other transformations as necessary. If appropriate learners can move onto negative scales and factors. All learners should experience finding unknown sides in similar shapes and this can be extended to formal similar triangles problems and trigonometry in the 30/60/90 triangle. General trigonometry is introduced at the start of Year 10.

Building on learners’ experience in previous years, in the summer term of Year 9 they solve all types of ratio problems and make the links with direct proportion and graphs. Students formally study inverse proportion for the first time, and if following the higher strand, they also look at graphs of inverse relationships. If appropriate, students could also look at more complex problems involving algebra. Learners also revisit ‘best buy’ comparing unit pricing from earlier in the year with alternative methods such as using scale.

Learners develop their knowledge of inverse relationships to explore speed, distance and time in detail. They also look at graphs and the link between the speed/distance/time formula and density/mass/volume. Learners go on to explore flow problems such as how long it will take to fill/empty tanks of different shapes at different rates.n

Learners following the higher strand will also look at converting compound units such as m/s to km/h. Metric and imperial conversions can also be included here if desired.

## 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.