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.
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
This term builds on Year 8 content. It is focused on two strands:
- Reasoning with Number, and
- Reasoning with Algebra.
Reasoning with Number
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 students 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, students relate these to fractions and decimals, extending their learning in Year 8. All students 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.
Students 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.
Reasoning with Algebra
Students 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 students rearrange formulae. Higher strand students will also consider inverse relationships and perpendicular lines.
Students 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.
Spring Term
Learners will work on two strands:
- Constructing in 2/3 Dimensions, and
- Reasoning with Geometry.
Constructing in 2/3 dimensions
This is the first time students have studied 3D shapes formally at KS3, students explore surface area, volume, plans and elevations.
Learners also build on their knowledge of constructions from previous years to look at the idea of a locus and the standard constructions using a straight edge and a pair of compasses. Congruence is also explored.
Reasoning with geometry
Building on their study of line symmetry and reflection in Year 8, students now look at rotational symmetry and rotation, as well as translations described in vector form.
Students also revise squares and square roots in preparation for their study of Pythagoras’ theorem. Students explore the theorem in a variety of contexts.
Summer Term
Towards the end of the year, the summer term focusses on two strands:
- Reasoning with Proportion and,
- Representations.
Reasoning with Proportion
Students develop their knowledge of transformations to include enlargement, learning the mathematical meaning of the word similar. You can link back to other transformations as necessary. If appropriate students can move onto negative scales and factors. All students should experience finding unknown sides in similar shapes and this can be extended to formal similar triangles problems.
Building on students’ experience in previous years, here 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. Students also revisit ‘best buy’ comparing unit pricing from earlier in the year with the alternative methods such as using scale.
Students 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. Students go on to explore flow problems such as how long it will take to fill/empty tanks of different shapes at different rates. Students following the Higher strand will also look at converting compound units such as m/s to km/h. You could also include metric and imperial conversions here if desired.
Representations
In representations, learners build on their learning in Year 7 and 8 to calculate the probabilities of single and combined events. A key focus is the introduction of the idea of independent events and the use of multiplication rules for these.
In the final topic of the year, Algebraic Representation, students extend their knowledge of graphs to look at interpretation and creation of different types of graphs. Students explore and plot quadratic, reciprocal and exponential graphs.
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.