Mathematics
Year 7 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
In the Autumn term, learners will cover two strands:
- Algebraic Thinking, and
- Place Value and Proportions.
Starting with these topics allows learners to consolidate and develop their learning from primary school whilst also deepening their understanding and linking their knowledge to new content.
Rather than rushing to find rules for the nth term, the scheme of work spends time exploring sequences in detail, using both diagrams and list of numbers. Calculators are used throughout so the number skills are not a barrier to finding the changes between terms or subsequent terms. Sequences are treated more formally later in this unit.
In Algebraic Notation, there is a focus on developing a deep understanding of the basic algebraic forms, with more complex expressions being dealt with later. Function machines are used alongside bar models and letter notations, with the time invested in single function machines and the links to inverse operations before moving on to series of two machines and substitution into short abstract expressions.
Towards the end of Autumn, students are introduced to forming and solving linear equations, building on their study of inverse operations. The equations met will mainly require the use of a calculator, both to develop their skills and to ensure understanding of how to solve equations rather than spotting solutions. The unit finishes within consideration of equivalence and the difference between this and equality, illustrated through collecting like terms.
In the Place Value unit, students explore integers up to one billion and decimals up to hundredths. Using and understanding number lines is a key strategy explored in depth, and will be useful for later work on scales and axes.
Spring Term
The focus for the Spring term is on three strands:
- Application of Number,
- Directed Number, and
- Fractional Thinking.
It builds on the formal methods of addition and subtraction students developed at key stage 2. All students will look at this in the context of interpreting and solving problems, for those for whom these skills are secure, there will be even more emphasis on this. Problems will be drawn from the contexts of perimeter, money, interpreting bar charts and tables and looking at frequency trees; we believe all these are better studied alongside addition and subtraction rather than separately. Calculators should be used to check and/or support calculations, with significant figures and equations explicitly revisited.
The rest of the term is dedicated to the study of multiplication and division, allowing for the student to form and solve two-step equations both with and without a calculator. Unit conversions will be the main context as multiplication by 10, 100 and 1000 are explored. As well as distinguishing between multiples and factors, substitution and simplification can also be revised and extended. Again, the emphasis will be on solving problems, particularly involving areas of common shapes and the mean. Choosing the correct operation to solve a problem will also be a focus. There will also be some exploration of the order of operations, which will be reinforced alongside much of this content next term when studying directed numbers.
Students will only have a limited experience of directed number at primary school, so the Directed Numbers unit is designed to extend and deepen their understanding of this. Multiple representations and contexts will be used to enable students to appreciate the meaning behind operations with negative integers rather than relying on a series of potentially confusing ‘rules’.This block also provides valuable opportunities for revising and extending earlier topics, notably algebraic areas such as substitution and the solution of equations.
The Spring term ends with an introduction to fractions, decimals and percentages which lays important foundations of upcoming fractions topics. Building on the work on decimals from Place Value, the key focus for this block is for students to gain a depp understanding of the links between fractions, decimals and percentages so that they can convert fluently between those most commonly seen in real-life.
Summer Term
There are three strands for the summer:
- Fractional Thinking,
- Lines and Angles, and
- Reasoning with Number.
The term begins with students continuing their work on fractions, further deepening their understanding of the uses of fractions. Learners begin by finding fractions and percentages of quantities and the links between the two, followed by deepening their understanding of equivalent fractions in order to eventually add and subtract any pair of fractions.
In Lines and Angles, students will build on their KS2 skills using rulers, protractors and other measuring equipment to construct and measure increasingly complex diagrams using correct mathematical notation. This will include three letter notations for angles, the use of hatch marks to indicate equality and the use of arrows to indicate parallel lines. Pie charts will be studied here to gain further practice at drawing and measuring angles.
The Developing Geometric Reasoning block covers basic geometric language, names and properties of types of triangles and quadrilaterals, and the names of other polygons. Angles rules will be introduced and used to form short chain reasoning.
The term ends with Sets and Probability which provides opportunities to revisit earlier learning such as FDP equivalence where students also learn about sets, set notation and systematic listing strategies.
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.