Year 11 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

Linear Equations, Statistics Representation & Interpretation, Constructions & Loci

Grammar

Students will review and extend work on solving equations from previous years. They will also learn how to construct equations from word problems.
Students will learn about the different ways to represent data and which is the most appropriate to use in different situations. They will look at analysing real life data using these graphs.
Students will further their knowledge on constructions and learn how to construct different triangles and bisectors

Dialectic

Students given the opportunity to compare different types of equation and which method is the most appropriate. They are encouraged to check their answer is correct using substitution.
Students will apply the acquired statistical techniques to analyse data and interpret statistical differences between two or more sets of data.
Students will be able to determine the minimum information needed to construct a triangle. They will be able to solve loci problems and identify which construction is needed.

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...

Linear Equations

In this section students study solving equations with 1, 2 and 3 steps, brackets, fractions and unknowns both sides

Statistics Representation & Interpretation

In this sections, students will learn how to draw and interpret bar charts, pie charts, pictograms.

Constructions & Loci

In this section, students will learn how to construct triangles, perpendicular bisectors, angle bisectors and solve loci problems using compasses and ruler

People solve equations everyday without realising 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.

Analysing real life data

Engineers use loci to decide where to lay pipes or place satellites so they reach everywhere.

Autumn Term 2

Ratio Proportion & Rates of Change, Powers & Standard Form, Transformations & Congruency

Grammar

Students will learn how to solve ratio problems. Also problems involving direct proportion, best value when comparing same items of different sizes, changing recipes by scaling up or down.
Students will review and extend their knowledge of numbers and algebraic terms raised to whole number, and simplify expressions using multiplication and division of powers. Students will be able to write numbers in standard form.
Students will deepen their understanding of reflection, rotation, translation and enlargement and how to combine these.

Dialectic

Students apply algebraic techniques to solve problems involving direct and indirect proportion, this is through given problem based scenarios and further develops their thinking skills.
Students will further develop their confidence in applying the learnt algebraic techniques to more complex situations incorporating many transferable skills.
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...

Ratio, Proportion & Rates of Change

Simplifying and sharing into ratios, solving direct and inverse proportion problems including best buys and recipe questions

Powers & Standard Form

Simplifying expressions involving indices
Converting to and from standard form

Transformations & Congruency

How to carry out and describe rotations, reflections, translations, enlargement

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

Scaling recipes up and down for a different number of people

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

Transformations are seen everywhere in real life – when looking in a mirror, a spaceship rotating, programming a robot

Spring Term 1

Volume & Surface Area, 3D Shapes

Grammar

Students will build on their area and volume knowledge and learn how to find the surface area and volume of more complicated 3D shapes.
Students will learn Pythagoras Theorem and trigonometry as applied to right angles triangles

Dialectic

Students will investigate to find the formulae for volume of different shapes and solve problems involving them.
Once the knowledge of the basic techniques are understood ,students will apply Pythagoras’s Theorem and trigonometry to more complex problems developing their confidence in applying these techniques in more complex 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 & Surface Area

Volume and surface area of cubes, cuboids, triangular prisms, cylinders, pyramids, cones and spheres.

Pythagoras and trigonometry

How to find missing sides and angles on right-angled triangles

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

Deciding how much liquid can fill a container or how much paint is needed to paint a house

Finding the height of roof trusses when building a house. Calculating the height of a tree.

Spring Term 2 and Summer Term

Revision for GCSE Exams

Grammar

Students are re-taught anything they have not fully grasped.

Dialectic

Students will apply all previously taught knowledge to exam questions and then work on the gaps in their knowledge and be re-taught anything they still can’t do.

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...

Revision for GCSE Exams

Students will study any topic they have not previously grasped fully. These topics will be identified using mocks and past papers.

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

Applying everything they have learned in maths to different situations.

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