# Maths

**Intent Statement**

Mathematics is a highly interconnected discipline that have provided the solution to some of the most intriguing problems in history and is also essential to everyday life and plays a critical part in science, technology, and engineering. With maths being a highly disciplined and interconnected subject, the Parker Maths curriculum aims to develop student’s ability to be fluent, mathematically reason and problem solve in the domains of number, algebra, geometry and measure, statistics and probability and ratio. It fully fosters a mastery approach to learning, to which knowledge is challenged, developed and secured by providing pupils with tasks that allow depth rather than breadth. To do this our lessons are structured in three parts, fluency, reasoning and problem solving, where not all students will experience all sections of this, so only when students feel confident and fluent with a skill, do they then move onto reasoning and finally problem solving with each skill. We encourage students to use models and manipulatives to support the development of the mathematical components, such as fractions which enable students to go from the concrete, to visual and then through to conceptual.

As we adopt a mastery approach to the learning, we also look at a spiralling curriculum so the domains are revisited multiple times a year as well as through the year groups. Topics are not meant to be retaught during the key stage, however prior knowledge will be retrieved, activated and built upon. The sequencing of tasks have been designed to maximise interleaving strategies, especially in the problem solving section of the lessons, by encouraging cross topics links and application.

Students study more number topics in Year 7 and these gradually become fewer as over the terms and years as the students master this substantive knowledge and then apply these in the other units, such as algebra and shape, due to the disciplinary demands of Mathematics itself. For example, you cannot look at index laws in algebra, or the area of shapes, if you have not understood the concept of multiplication first. We also use more time in year 7 looking at the number topics at the beginning of year 7, to ensure that students who are not secondary ready to build up the basics they require to be able to access the other topics of maths, which do generally have a basis from the number skills. To allow for this we do not start looking at probability until year 8, to really ensure the number skills are mastered, to maximise the mastery of all topics going forward. We also keep the conjecturing and proof elements of the curriculum, which cross the domains of shape and algebra, until the middle of year 9, due to the complexity of the topic, ensuring students have fully mastered the required knowledge, such as similarity, Pythagoras’ Theorem, and secure algebraic manipulation, before deepening their learning by taking it more into the most abstract learning met in key stage 3. This knowledge is then looked at in KS4 by combining more complex algebra with shape and the students learning to argue mathematically using algebra, and other areas of maths, to look at proving statements algebraically.

We also look at deepening learning across the years, for example, in year 7 we will look at using the four operations with proper fractions in number, and then in year 8 students will then move to master the four operations with mixed numbers and negative fractions, and then in year 9 moving onto the four operations with fractions that include unknowns and solving equations involving fractions, which looking at increasing their knowledge of fractions, but without being explicitly re-taught a skill. We then continue this further into KS4 by looking at rationalising the denominator in year 10 and moving to solving algebraic fractions in year 11. Across all of the domains we also have the following key concepts: BIDMAS (including 4 operations), ratio and proportion, percentages, decimals, substitution, index laws and factors and Multiples (including times tables), which we aim to bring elements of into all of our lessons, helping build on student’s knowledge and develop their long term memory of these key concepts and help them to access and deeper understand the connectivity of the subject.

**KS3 High-Level Plan**

Term | Y7 | Y8 | Y9 |
---|---|---|---|

1 | Numbers and the number system • Solve problems using common factors and highest common factors • Exploring prime numbers • Solve problems using common multiples and lowest common multiples • Explore powers and roots Calculating • Exploring place value • Exploring written methods of calculation • Calculating with decimals • Know and apply the correct order of operations | Numbers and the number system • Identify and use the prime factorisation of a number • Understand and use standard form Calculating • Calculate with negative numbers • Apply the correct order of operations Visualising and constructing • Explore enlargement of 2D shapes • Use and interpret scale drawings • Use and interpret bearings • Explore ways of representing 3D shapes Understanding risk I • Understand the meaning of probability • Explore experiments and outcomes • Develop understanding of probability | Calculating • Calculate with powers and roots • Explore the use of standard form • Explore the effects of rounding |

2 | Checking, approximating and estimating • Approximate any number by rounding to the nearest 10, 100 or 1000, 10 000, 100 000 or 1 000 000 • Approximate any number with one or two decimal places by rounding to the nearest whole number • Approximate any number with two decimal places by rounding to the one decimal place • Simplify a fraction by cancelling common factors Counting and comparing • Comparing numbers • Ordering integers and decimals • Ordering fractions • Ordering integers, decimals and fractions (including mixed numbers) • Using comparison symbols in algebraic contexts Visualising and constructing • Investigate the properties of 3D shapes • Explore quadrilaterals • Explore triangles Investigating properties of shape • Interpret geometrical conventions and notation • Apply geometrical conventions and notation | Algebraic proficiency: Tinkering • Understand the concept of a factor • Understand the notation of algebra • Manipulate algebraic expressions • Evaluate algebraic statements Exploring Fractions, decimals and percentages • Explore links between fractions, decimals and percentages Proportional reasoning • Explore the uses of ratio • Investigate the connection between ratio and proportion • Solve problems involving proportional reasoning • Solve problems involving compound units | Algebraic proficiency: Tinkering • Know standard mathematical constructions • Apply standard mathematical constructions • Explore ways of representing 3D shapes • Proportional reasoning • Solve problems involving different types of proportion • Investigate ways of representing proportion • Understand and solve problems involving congruence • Understand and solve problems involving similarity • Know and use compound units in a range of situations Pattern sniffing • Investigate Fibonacci numbers • Investigate Fibonacci type sequences • Explore quadratic sequences |

3 | Algebraic Proficiency: Tinkering • Understand the vocabulary and notation of algebra • Manipulate algebraic expressions • Explore functions • Evaluate algebraic statements Exploring fractions decimals and percentages • Understand and use top-heavy fractions • Understand the meaning of ‘percentage’ • Explore links between fractions and percentages Proportional reasoning • Understand and use ratio notation • Solve problems that involve dividing in a ratio Pattern sniffing • Investigate number patterns • Explore number sequences • Explore sequences | Pattern Sniffing • Explore sequences Investigating Angles • Develop knowledge of angles • Explore geometrical situations involving parallel lines Calculating fractions, decimals and percentages • Calculate with fractions • Calculate with percentages | Solving equations and inequalities I • Explore the meaning of an inequality • Solve linear inequalities Calculating space • Solve problems involving arcs and sectors • Solve problems involving prisms • Investigate right-angled triangles • Solve problems involving Pythagoras’ theorem |

4 | Measuring space • Measure accurately • Convert between measures • Solve problems involving measurement Investigating angles • Identify angles that meet at a point • Identify angles that meet at a point on a line • Identify vertically opposite angles • Know that vertically opposite angles are equal Calculating fractions, decimals and percentages • Calculate with fractions • Calculate with percentages | Solving inequalities • Solve linear equations with the unknown on one side • Solve linear equations with the unknown on both sides • Explore connections between graphs and equations Calculating space • Investigate circles • Discover pi • Solve problems involving circles • Explore prisms and cylinders Algebraic proficiency: visualising • Plot and interpret linear graphs • Plot and quadratic graphs • Model real situations using linear graphs | Conjecturing • Explore the congruence of triangles • Investigate geometrical situations • Form conjectures • Create a mathematical proof Algebraic proficiency: Visualising • Investigate features of straight line graphs • Explore graphs of quadratic functions • Explore graphs of other standard non-linear functions • Create and use graphs of non-standard functions • Solve kinematic problems |

5 | Solving equations and inequalities • Explore way of solving equations • Solve two-step equations • Solve three-step equations Calculating space • Develop knowledge of area • Investigate surface area • Explore volume Mathematical movement • Explore lines on the coordinate grid • Use transformations to move shapes • Describe transformations | Understanding risk II • Explore experiments and outcomes • Develop understanding of probability • Use probability to make predictions | Solving equations and inequalities II • Solve simultaneous equations • Use graphs to solve equations • Solve problems involving simultaneous equations Understanding risk • Understand and use tree diagrams • Develop understanding of probability in situations involving combined events • Use probability to make predictions |

6 | Presentation of data • Construct and interpret • Construct and interpret graphs • Select appropriate graphs and charts Measuring Data • Investigate averages • Explore ways of summarising data • Analyse and compare sets of data | Presentation of data • Explore types of data • Construct and interpret graphs • Select appropriate graphs and charts Measuring data • Investigate averages • Explore ways of summarising data • Analyse and compare sets of data | Presentation of Data • Construct and interpret graphs of time series • Interpret a range of charts and graphs • Interpret scatter diagrams • Explore correlation |

**KS3 Medium-Term Plans**

**Year 7**

Checking, approximating and estimating

Investigating properties of shape

Exploring fractions decimals and percentages

Calculating with fractions, decimals and percentages

Solving equations and inequalities

**Year 8**

Exploring fractions, decimals and percentages

Calculating fractions, decimals and percentages

Solving inequalities and equations

**Year 9**

Algebraic proficiency tinkering

Solving equations and inequalities

Solving equations and inequalities

**KS4**

**Year 10 Foundation**

Parker MTP Year 10F Unit 01 – Integers and place value

Parker MTP Year 10F Unit 02 – Decimals

Parker MTP Year 10F Unit 03 – Indices, powers and roots

Parker MTP Year 10F Unit 04 – Factors multiples and primes

Parker MTP Year 10F Unit 05 – Algebra the basics

Parker MTP Year 10F Unit 06 – Expressions and formulae

Parker MTP Year 10F Unit 07 – Tables, charts and graphs

Parker MTP Year 10F Unit 08 – Pie Charts

Parker MTP Year 10F Unit 09 – Scatter graphs

**Year 10 Higher**

Parker MTP Year 10H Unit 01 – Calculating checking and rounding

Parker MTP Year 10H Unit 02 – Indices, roots and reciprocals

Parker MTP Year 10H Unit 03 – Factors, multiples,primes, standard form and surds

Parker MTP Year 10H Unit 04 – Setting up, rearranging and solving equations

Parker MTP Year 10H Unit 05 – Sequences

Parker MTP Year 10H Unit 06 -Averages and range

Parker MTP Year 10H Unit 07 -Representing and interpreting data

Parker MTP Year 10H Unit 08 -Fractions and percentages

**Year 11 Foundation**

Parker MTP Year 11f Unit 25- multiplicative reasoning

Parker MTP Year 11f Unit 26- Plans and elevations

Parker MTP Year 11f Unit 27- Constructions, loci and bearings

Parker MTP Year 11f Unit 28-Quadratics- expanding and factorising

Parker MTP Year 11f Unit 29-Quadratics- graphing

Parker MTP Year 11f Unit 30-Circles, cylinders, cones and spheres

Parker MTP Year 11f Unit 31-Fractions and reciprocals

Parker MTP Year 11f Unit 32-Indices and standard form

**Year 11 Higher**

Parker MTP Year 11H Unit 24 – Similarity and congruence

Parker MTP Year 11H Unit 25 -Graphs of trigonometric functions

Parker MTP Year 11H Unit 26 -Further trigonometry

Parker MTP Year 11H Unit 28-Cumulative frequency, box plots and histograms

Parker MTP Year 11H Unit 29-Algebraic proficiency visualising

Parker MTP Year 11H Unit 30-Circle Theorems