Mathematics
Year 10 Rationale
The Harrow High School Mathematics department follows a tailored version of the White Rose Maths scheme of work. The White Rose Maths approach is to learn by making connections through carefully sequenced examples and questions.
The curriculum is highly adaptive. Teachers assess prior knowledge before each unit and tailor their lessons accordingly. Basics are revised if necessary, and if time permits, learners are accelerated onto higher maths and further maths.
In general, the scheme follows the structure outlined in Key Ideas in Teaching Mathematics (2013); a strong foundation in numerical and algebraic reasoning is built on with other more sophisticated types of reasoning as KS4 progresses. Each unit, and each lesson within each unit, is carefully sequenced to ensure all necessary prior knowledge is taught and understood.
AUTUMN TERM
In the Autumn term, learners cover two strands of content:
- number, and
- proportion.
Learners have ample opportunities to revise and consolidate key concepts and processes from Key Stage 3, and develop their knowledge into Key Stage 4.
Learners begin with revision of the fundamental skills needed to succeed at their GCSE:
- Calculations with integers, decimals and fractions
- Rounding and limits of accuracy
- Ratio and proportion problems
- Factors, multiples and primes
- Percentages
- Laws of indices and roots
- Inverse proportion and compound measures
This is covered through intelligent inquiry and explicit instruction. Where learners have strong prior knowledge, we are able to extend these into related higher topics such as bounds, surds, fractional indices and proportion equations.
Spring Term
In the Spring term, learners study:
- algebraic techniques, and
- statistics.
Key building blocks are revisited:
- Simplifying algebraic expressions
- Solving linear equations
- Representing and solving inequalities
- Using units of measurement
- Collecting and representing data
- Analysing, describing and interpreting data
- Probability
Algebra is taught as a generalisation of number and relies on strong number concepts from Autumn. For students who have retained most of what was taught at Key Stage 3, this can be extended into higher tier and further maths by looking at, for example, expanding triple brackets and the binomial expansion.
The study of measure and statistics relies on a good understanding of number and proportion. As learners build diagrams, convert units and make observations with statistics, they are using the proportional reasoning developed in the Autumn. Learners who are attaining highly will study higher content such as histograms and conditional probability
Summer Term
The remainder of Year 10 is split into two strands:
- more advanced algebra, and
- geometry.
Learning continues to increase in formality. Learners are expected to build chains of reasoning and proofs in both algebraic and geometric contexts. The key concepts of form, communication and self-validation are emphasised.
The following topics are revisited:
- Linear sequences
- Expanding and factorising brackets
- Using and rearranging formulae
- Angle problems
- Congruent and similar shapes
- Areas of 2D shapes
Learners are expected to revise and make enough progress to solve quadratic and simultaneous equations, and calculate with arcs and sectors. Students with stronger prior knowledge will be extended further, looking at quadratic sequences and simultaneous equations, circle theorems and congruence proofs.
By the end of Year 10, learners should have excellent knowledge of number, ratio, proportion, statistics, probability and geometry. These will be built on in Year 11 when learners study graphs, functions, vectors and transformations.