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 Key Stage 3 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.

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 algebraic fractions, looking at increasing their knowledge of fractions, but without being explicitly re-taught a skill. 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.

 

High-Level Plan

TermY7Y8Y9
1Numbers 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
2Checking, 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
3Algebraic 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
4Measuring 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
5Solving 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
6Presentation 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

 

Medium-Term Plans

Year 7

Numbers and the number system

Calculating

Checking, approximating and estimating

Counting and comparing

Visualising and constructing

Investigating properties of shape

Algebraic proficiency

Exploring fractions decimals and percentages

Proportional reasoning

Pattern sniffing

Measuring space

Investigating angles

Calculating with fractions, decimals and percentages

Solving equations and inequalities

Calculating space

Mathematical movement

Presentation of data

Measuring data

Year 8

Numbers and the number system

Calculating

Visualising & constructing

Understanding risk

Algebraic proficiency

Exploring fractions, decimals and percentages

Proportional reasoning

Pattern sniffing

Investigating angles

Calculating fractions, decimals and percentages

Solving inequalities and equations

Calculating space

Algebraic proficiency

Understanding risk

Presentation of data

Measuring data

Year 9

Calculating

Visualising and constructing

Algebraic proficiency tinkering

Proportional reasoning

Pattern sniffing

Solving equations and inequalities

Calculating space

Conjecturing

Algebraic proficiency

Solving equations and inequalities

Understanding risk

Presentation of data

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