Year 10 Mathematics – Foundation

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

Perimeter & Area, Expressions & Formulae, Number & Pattern Sequences

Grammar

Students will develop their knowledge of area and perimeter of shapes, this is further developed through more complex compound shapes, these techniques are also applied in a problem solving way very often involving money calculations of cost.

Students consolidate and extend their knowledge of algebraic expressions and formulae, learn to manipulate these through combining expression, multiplying and dividing along with changing the subject of formulae to find different quantities.

Students will here apply their understanding of arithmetic sequences to a number of given situations including practical problems, this is then further developed to incorporate an understanding of Quadratic and geometric sequences.

Dialectic

Students further develop their knowledge through problem solving and practical applications of area and perimeter.

Students become confident in algebraic manipulation and through further problem solving recognise which techniques should be applied when.

Students apply their gained knowledge to practical sequences through patterns and described situations, students also investigate other types of sequences that occur naturally.

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...

Perimeter and Area

Area of common shapes
Perimeter of common shapes
Area and perimeter of compound shapes

Algebraic expressions and formulae

Forming algebraic expressions
Simplifying algebraic expressions
Solving equations

Number and Pattern sequences

Continuing linear sequences
Calculating the Nth term for sequences
Finding a missing number in a sequence
Fibonacci sequences

How can I use this Maths in “Real-life”?

Area and perimeter is important in calculation of costs for many different applications pointing these out as opportunities arrive is very useful to make maths real for students.

Equations and formula form the basis of many things and are used continuously in desgin on buildings, finance and commerce plus, science and numerous other applications. Pointing this out to Students when opportunity arrives can help students understand the need to learn about what can sometimes seem an abstract topic.

Sequences are used to make predictions about situations in the future. For example if I’m given £1 more pocket money every month, how much will I earn over 5 years?

Fibonacci sequences occur naturally – e.g. the number of petals on flowers, spiral on a shell, number of branches on a tree.

Autumn Term 2

Statistics – Representing & Interpreting Data, Forming & Solving Linear Equations, Working with Decimals &
Fractions

Grammar

Students develop their investigational skills through interrogation of data using different statistical techniques, from calculation of averages extending into more complex measures, students learn to represent data in appropriate charts and tables.

Students will develop further their solving equations techniques to incorporate more complex equations, simultaneous equations both linear and when one is quadratic, and learn how and when to apply techniques to problem solving.

Students learn how to inter-change decimals and fractions, how to work with reoccurring decimals and develop strategies to solve problems that contain decimals and fractions.

Dialectic

Students are given opportunities to practice the skills acquired through comparing a number of sets of data and develop an understanding of which techniques are better employed for different types of data.

Students are given opportunities to apply the methods learnt for solving equations to real life problems in which they further enhance their ability to employ equations to solve given problems.

Through numerous differing problems students consolidate and extend the use of fractions and decimals in real world situations.

Rhetoric

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

Statistics – representation and interpretation

Drawing bar charts, pie charts, scatter diagrams
Calculating averages form grouped data

Solving Linear equations

Solving equations with unknowns one side, both sides or with brackets
Solving equations with brackets

Working with Fractions

Add, subtract, multiply and divide fractions and mixed numbers with and without a calculator

How can I use this Maths in “Real-life”?

Comparing any kind of data in real life. e.g. comparing heights of 2 groups of people. Identifying the spread of shoe sizes to know how many of each size a shop should order.
Scatter diagrams are used to identify a relationship between 2 things and make predictions. E.g. Is there a link between time spent watch TV and exam performance?

People solve equations everyday without realise they are equations. For example working out someone’s ages if they are 10 years older than you, calculating the amount of profit they will make if they make a certain number of sales.

Anything that involves calculating with numbers that aren’t whole can be done easier using fractions e.g. engineers that need exact measurements when measuring or calculating.

Spring Term 1

Percentage Calculations Ratios, Proportion & Best Buys, Similarity & Congruency

Grammar

Student study rates of change in this section which incorporates but is not limited to the rate of change of velocity, this is through interpretation of velocity time graphs developing appropriate techniques.

Students study speed calculations and distance time graphs, then moving on to calculate other compound measures.

Students firstly gain a full understanding of when shapes are congruent and when they are similar, through problem solving they develop proofs of congruency, and through geometric shapes use similarity to determine lengths, areas and volumes.

Dialectic

The techniques learnt are now transferred to a number of different situations involving rates of change and these are used to solve real situations.

Students are challenged to apply their gained knowledge to develop their own distance time graphs for described situations and through problem solving to determine required parameters.

Students are challenged to use congruency and similarity in detailed proofs requiring a methodical and logical approach to derive a mathematical proof.

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...

Ratio and proportion – ratio

Simplifying ratios
Converting between ratio and fractions
Dividing into given ratios

Speed and Proportion

Calculating speed, distance or time given 2 out of the 3

Similarity and Congruency

Identify congruent shapes
Calculate missing lengths of similar shapes

Anything that involves calculating with numbers that aren’t whole can be done easier using fractions e.g. engineers that need exact measurements when measuring or calculating.

Calculating how long a journey will take if you know how far away it is and roughly what speed you are travelling.
Calculating what speed you need to run if you want to finish a marathon in 3 hours.

Similar Triangles are very useful for indirectly determining the sizes of items which are difficult to measure by hand. Typical examples include building heights, tree heights, and tower heights.

Spring Term 2

Powers and Standard Form, Right Angled Triangles

Grammar

Students develop their understanding of basic powers and progress to look at the more complex index laws. Students learn to inter-convert between standard form and normal form and problem solve with numbers written in standard form.

This section covers the techniques students need for working with right-angled triangles namely Pythagoras and trigonometry, once students have a grasp on the fundamentals they begin then to investigate more complex problems.

Dialectic

Through a number of different tasks students make links between the basic and more complex index laws and when they need to apply them in order to progress through a problem or calculation.

Through extended problems students combine all techniques learnt to complex problems they must reduce to right angled triangles many of which contain several calculations to arrive at a solution.

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...

Powers and Standard form

Using indices laws to simplify expressions
Convert to and from standard form

Right-angled triangles

Pythagoras
Trigonometry

Scientists use standard form to do calculations in space or with atoms as the numbers are really large or small numbers.

Pythagoras and trigonometry is used in many industries including building trade, Engineering, architecture and many scientific disciplines. How high will a sloped ceiling be if I make the angle of elevation 40 degrees?

Summer Term 1

Volume & Surface Area of Prisms, Probability of Events

Grammar

Building on the previous section of area students now look at 3D shapes and how they calculate surface area and volume. This is done mainly in context in which students perform calculations to problem solve.

Students will learn how to describe the probability of an event and also use Sample space diagrams, Venn diagrams and listing methods to ascertain the number of possible outcomes for a specific event.

Dialectic

Through opportunities presented students are challenged to apply basic volume and surface area techniques earnt to complex real life and algebraic problems.

Knowing which diagram is appropriate to which situation requires carful consideration of problems presented, then applying those techniques students solve a number of different probability situations.

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...

Volume and surface area of Prisms

Volume of prisms including cylinders
Surface area of prisms including cylinders

Probability of events

Probability calculations
Frequency Trees
Probability Tree diagrams

Calculating how much cardboard will be needed to make a box.
Calculating how many tins of pain will be needed to paint a room in a house.

Probability is widely used in all sectors in daily life like sports, weather reports, blood samples, predicting the sex of the baby in the womb, congenital disabilities, statics, and many more.

Summer Term 2

Sectors, Pyramids, Cones and Spheres, Transformation

Grammar

Students problem solve with the more complex 3D shapes of Spheres, Cones and Pyramids, this section also brings in the techniques learned in the right angled triangles section. Here students learn to combine a number of previously learnt techniques.

Students study the concepts of transformations of shapes and learn to recognise when and which transformations have been applied. Students learn to determine which single transformation maps a shape on to a given image

Dialectic

Students are challenged to bring together a number of techniques taught in more complex problems some of which will be through practical real life problems

Students are given opportunities to analyse different transformations and deduce properties about the image once a transformation has been applied

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...

Volume and surface area of Cones, Spheres and Pyramids

Volume of Pyramids, Cones and Spheres
Surface area of Pyramids, Cones and Spheres

Transformation

Reflections
Rotations
Translations
Enlargements
Combined transformations

There are many examples of cones, spheres and pyramids in real life – ice cream cones, megaphone, traffic cones, Christmas trees, footballs.

Mass production of shoes and spectacle frames. flipping images on a computer. the mirror images of the chemical structure of the sugar molecules, glucose (in sugarcane) and fructose (in fruit).

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