Year 9 Mathematics

Curriculum Intents

Across our Mathematics curriculum we aim for students to become fluent in the core concepts of mathematics and reason mathematically in order to solve problems. With spaced retrieval and interleaving topics, students are encouraged to explore and deepen their knowledge of connections between topics. It is our aim to equip students with the mathematical skills they will need beyond school and to pique their interest in the subject in the hope they continue to study mathematics further.

How

Mathematics is an integral part of the curriculum where students can learn a number of logic skills and the ability to approach problems in numerous ways. The topics within mathematics are closely linked and our curriculum requires constant interweaving with careful sequencing to allow students to progress through their journey studying mathematics. Our mathematics curriculum allows students to build on the core concepts of mathematics:

– Number
– Algebra
– Ratio, Proportion and Rates of Change
– Geometry & Measure
– Statistics & Probability

So that they can appreciate the interlinking of topics in mathematical problems and the complexity of the subject. Students are encouraged to try a range of problems and challenge themselves through the curriculum. Our subject is one that confidence is key in and we encourage students to be positive about it and explore how mathematics can open doors to many varied careers.

Why

Our curriculum is designed to build on core concepts of mathematics in Year 7 & 8 in order to give students the foundation to build up their declarative knowledge. Our worked examples & use of ‘your turn, my turn’ allowed students to apply their declarative knowledge (facts & formula) and focus on the procedural element of mathematics. Misconceptions are regularly addressed through the use of diagnostic questions in class & homework. Across the curriculum there is interleaving of topics to ensure students are learning new concepts where prior knowledge of these has been recently revisited in the scheme of learning. Topics are covered in depth to allow time for students to also focus on problem solving. Students are therefore given the ‘tools’ they need to approach multi-step problems in order to demonstrate their conditional knowledge. There is ample time for spaced retrieval and all classes complete regular low stakes quizzes to promote recall and revision of topics. Regular mid stakes & summative assessments take place to check students progress and identify any gaps in knowledge which need addressing.

Autumn Term 1

Ratio and Proportion 3

Grammar

Students will consolidate their work on fractions and ratios. They will be shown methods to calculate percentage change, solve problems involving direct & inverse proportion. They will be taught to work with compound units

Dialectic

Students will solve problems involving proportion & ratio. They will construct and interpret conversion graphs and distance/time graphs. They will also solve a range of problems with compound measures being careful with consistency of units

Rhetoric

Students will work peer to peer and peer to class to share ideas and examples of their working. They will be assessed using low stakes quizzes and diagnostic questioning.

In school...
How can I support this unit at home...

This unit will begin with working and calculating with fractions. This will include converting between fractions, decimals and percentages. They will move on to calculating a percentage increase or decrease and the percentage change given old and new values. Students will then look at ratios – simplifying, sharing in a given ratio and solving problems involving ratios. They will solve a range of proportion problems.

This will include calculating “best buys” and problem solving using these relationships, including recipe style questions and other proportional relationships such as calculating rates of pay. Students will then look at compound measures and applying these in problem solving contexts with a focus on “real world examples” and emphasis on units and correct terminology. This will focus on speed, distance time relationships.

Talk about time in decimal and analogue form. Use situations such as interest rates for borrowing and saving, business plans and percentage profit for percentages and percentage change. Timetables, travelling and cooking for working with time.

Use ratio in the home to look at relationships and aspects of ratio (photograph size/screen sizes). When shopping look at prices/offers that use percentages and work out the savings.

When cooking use recipes to scale up or down a recipe, if it is for 4 people how much do you need of each ingredient for 8? If it is for 6 how will I know how much of each ingredient for 4 people? Use conversion graphs to change UK pounds to Euros or dollars. Use journeys to understand the relationship between speed, distance and time.

Autumn Term 2

Angles and Shapes 2

Grammar

In this unit students learn new content and revisit previous learning. Trigonometry, and circle theorems will be new to all students. Angles in parallel lines, angles in polygons, bearings, Pythagoras and trigonometry may be new to students.

Dialectic

Students will manipulate increasingly complex algebraic expressions and equations
Students will apply their knowledge to problem solving. Students will understand the importance of working with exact values rather than rounded decimals.

Rhetoric

Students will work peer to peer and peer to class to share ideas and examples of their working. They will be assessed using low stakes quizzes and diagnostic questioning.

In school...
How can I support this unit at home...

The second unit in year 9 is an extension of the year 7 unit of angles and shapes as well as the Pythagoras portion of the year 8 unit of area and volume. It continues to allow for students to consolidate their learning from year 8, while pushing on with each of the topics within the unit.

This unit offers a lot of opportunity for students to learn new content while also revisiting previous learning. Trigonometry, and circle theorems will be new to all students. Angles in parallel lines, angles in polygons, bearings, and pythagoras may be new to students depending on what they were able to cover in year 7 and 8.

Year 9 continues to build on the calculator work completed during year 8 and within this unit with Pythagoras and Trigonometry this becomes even more important. This will also provide an opportunity to reinforce rounding.

Angles problems crop up in various design solutions and in navigation. Use navigation of ships and planes, and map skills for bearings. Carpentry and construction problems use pythagoras and trigonometry. Calculate heights of natural objects and angles of inclination/declination by using Pythagoras and trigonometry.

Spring Term 1

Algebra 5

Grammar

Students will learn to expand and factorise. Triple brackets and completing the square will be brand new to all students whereas the concepts of expanding and factorising and index laws will be new to other students at various difficulties. Higher ability will be introduced to Surds.

Dialectic

Students will manipulate increasingly complex algebraic expressions and equations.
Students will apply their knowledge to problem solving. Students will understand the importance of working with exact values rather than rounded decimals.

Rhetoric

Students will work peer to peer and peer to class to share ideas and examples of their working. They will be assessed using low stakes quizzes and diagnostic questioning.

In school...
How can I support this unit at home...

The third unit in year 9 covers algebraic manipulation, continuing to expand on the work covered in year 7 and 8, as well indices and surds, also continuing to expand on work covered in year 8.

This unit offers a lot of opportunity for students to learn new content while also revisiting previous learning. Triple brackets and completing the square will be brand new to all students, whereas the concepts of expanding and factorising will be new to other students at various difficulties.

Surds will also be a brand new topic for students to encounter for the higher ability students while index laws will also be introduced to some for the first time.

Look at mathematical and scientific formulae in a range of settings such as construction, engineering, business.

Spring Term 2

Probability 2

Grammar

Students revisit calculations with fractions and extend to algebraic fractions.

They will use a variety of probability diagrams and apply conditional probability to these diagrams. Students will be introduced to the product rule for counting.

Dialectic

Students will solve probability problems by modelling using an appropriate diagram or list. They will show how different conditions affect probabilities of given outcomes.

Rhetoric

Students will work peer to peer and peer to class to share ideas and examples of their working. They will be assessed using low stakes quizzes and diagnostic questioning.

In school...
How can I support this unit at home...

The fourth unit in year 9 covers fraction operations and probability. This builds directly on the work covered in year 7 during the corresponding unit. Due to the two-year gap between the unit students will need opportunities to recap previously learned content while still having a lot of new content to cover.
The fractions work goes through four operations of fractions, then onto mixed numbers, and then finally algebraic fractions allowing all students to see new content.

The probability will also be built on with some students now seeing a variety of probability diagrams, including probability trees and Venn diagrams, for the first time. Those that have already seen this in year 7 will now move on to apply conditional probability to these diagrams. Students will also expand their work on listing outcomes to the product rule for counting.

Discuss risk and chance in different contexts such as insurance, business plans, risk assessments.

Summer Term 1

Algebra 6

Grammar

Students will continue to improve their algebra skills. They will learn about sequences, straight line graphs and solving equations in more depth than year 8.

Dialectic

Students will be able to describe the difference between equations, expressions and formulae. They will identify the different types of sequences and be able to find the nth term for them.

Rhetoric

Students will work peer to peer and peer to class to share ideas and examples of their working. They will be assessed using low stakes quizzes and diagnostic questioning.

In school...
How can I support this unit at home...

The fifth unit in year 9 covers solving equations, straight line graphs and sequences. They will have knowledge of algebraic notation and how to apply it in different situations. They will use their knowledge to solve and understand problems and become fluent in the correct terminology.

Look at sequences in real life, including Fibonacci in nature. Use straight line graphs to model situations and use them to make predictions. Form equations to help solve real life problems.

Summer Term 2

Transformations and Constructions

Grammar

Students will deepen their understanding of reflection, rotation, translation and enlargement and how to combine these. They will also learn how to construct triangles and bisectors.

Dialectic

Students will be able to describe transformations using the key notation and investigate what happens if more than one combination is done. They will be able to determine the minimum information needed to construct a triangle.

Rhetoric

Students will work peer to peer and peer to class to share ideas and examples of their working. They will be assessed using low stakes quizzes and diagnostic questioning.

In school...
How can I support this unit at home...

The sixth unit in year 9 covers transformations, including rotation, reflection, translation and enlargment, and constructions. This will build on previous transformation knowledge they have learnt and will extend into fractional and sometimes negative scale factors. They will also looks at what happens if more than one of these transformations is done and use the correct terminology to describe them.

They will also look at constructing triangles and bisectors and using this to solve loci problems.

Look at constructions in real life and why it’s important to be able to draw accurate diagrams. Use loci problems to solve real life style problems like where to place satellites so all areas can be covered.

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