# Key Stage 3

## Year 7

##### Intent

Building on the foundations of Key Stage 2, the Year 7 curriculum strengthens students’ mathematical fluency and logical problem solving whilst building vocabulary to accurately articulate their reasoning. We strategically interleave multiple mathematical concepts into all lessons to reinforce the connections between the different strands of number, algebra and geometry.

##### Learning Journey

##### Key Concepts and Themes

- Use of the number line for representing relationships, ordering and comparing to include integers, fractions and decimals both positive and negative.
- Familiarity with terminology and symbols used in algebra. Simplifying expressions by collecting like terms.

##### Vocabulary

- Place value
- Equivalent
- Numerator
- Denominator
- Proper/improper fraction
- Algebra
- Commutative
- Term
- Expression
- Simplify

##### Key Concepts and Themes

- Solving angle problems by using angle facts.
- Use of the probability scale and use of fractions to represent probabilities. Using the sum-to-one and calculating probabilities of events not occurring.
- Building on understanding of powers and roots to use laws of indices. Rounding to significant digits and estimating.

##### Vocabulary

- Intersect
- Parallel
- Perpendicular
- Vertically opposite
- Random
- Probability scale
- Equally likely
- Outcome
- Power
- Root
- Square
- Cube
- Significant digit

##### Key Concepts and Themes

- Substituting into formulae. Using growth patterns to understand number sequences and predict based on established patterns.
- Convert between standard metric units for mass/distance/capacity. Calculate perimeter/area/surface area/volume for 2D and 3D shapes including compound shapes.

##### Vocabulary

- Formula/formulae
- Substitute, Sequence
- nth term
- Common difference
- Predict
- Quadrilateral
- Parallelogram
- Rhombus
- Trapezium
- Compound
- Cuboid
- Surface area
- Volume

##### Key Concepts and Themes

- Use of tally/bar/pie charts and frequency tables including grouped data to display data and draw inferences and comparisons.
- Use inverse operations to work backwards including powers and roots and understanding the role of brackets to change the order of operations. Use of BIDMAS.
- Use of scientific calculators.

##### Vocabulary

- Frequency
- Discrete
- Continuous
- Data
- Interpret
- Inverse
- Order of operations (BIDMAS)
- Equals, Brackets

##### Key Concepts and Themes

- Representing and solving one-step and two-step (and more steps) linear equations.
- Illustrate 2D-shapes using accurate measurements and correct conventions for labelling.
- Use ratio notation and diagrams for comparing quantities.

##### Vocabulary

- Equation
- Solve
- Solution
- Unknown
- Radius
- Diameter
- Vertex
- Edge
- Face
- Ratio
- Simplest from

##### Key Concepts and Themes

- Plotting coordinates in all four quadrants establishing rules for horizontal, vertical and then diagonal lines. Calculating gradient.
- Accurately measuring lengths and angles. Using scale drawings. Establishing congruence in triangles.

##### Vocabulary

- Quadrant
- Gradient
- Origin
- Axis/Axes,
- X/Y-coordinates
- Similar (shapes)
- Congruent
- (Line) segment
- Scale
- Enlargement

##### Skill Development

- Learn to select the most appropriate methods for their calculations through reasoning about the structure of the numerical problems they face.
- Begin to look at both diagrammatic and algebraic representations to make sense of concrete and abstract problems and start to make connections between these representations and the number relationships they represent.
- Explore patterns and make conjectures, looking for proof or counter-examples to support their ideas
- Gain knowledge through their experience of multi-step problems including unfamiliar problems, relating their solutions to the context and evaluating different approaches

## Year 8

##### Intent

In Year 8, we continue on students’ understanding of linear algebra with a deeper look at solving equations and manipulating expressions. This year we look at fundamental geometry through angle reasoning, symmetry, transformations and construction. Students also meet sets and unions as well as averages and spread for the first time.

##### Learning Journey

##### Key Concepts and Themes

- Use conventional methods for multiplying and dividing including decimals and negatives
- Solve multi-step equations with unknown on both sides including brackets and fractions
- Use rules associated with parallel lines to solve for missing angles

##### Vocabulary

- Integer
- Decimal (place/number)
- Transform (both sides)
- Expand
- Equals
- Parallel
- Alternate (angle)
- Corresponding (angle)
- Co-interior (angle)
- Allied (angle)

##### Key Concepts and Themes

- Use Venn and Carroll diagrams to represent data
- Use fractions and percentages as operators. Calculate percentages with or without calculators. Define a quantity as a percentage of another including percentages greater than 100
- Establish nth term rules for linear sequences and use to generate sequences. Construct and interpret conversion graphs, representing relationship algebraically.

##### Vocabulary

- Venn diagram
- Carroll diagram
- Intersection
- Union
- Green
- Linear (sequence)
- Arithmetic (sequence)
- Conversion (graph)

##### Key Concepts and Themes

- Identify symmetries in polygons. Constructions with lines and angles using compasses.
- Use averages and range to describe data and make inferences and comparisons. Construct and interpret scatter diagrams.

##### Vocabulary

- Reflective symmetry
- Rotational symmetry
- Polygon
- Construct
- Bisect
- Average
- Spread
- Mean
- Median
- Mode
- Range
- Correlation

##### Key Concepts and Themes

- List factors and multiples and identify HCF and LCM. Identify prime numbers. Decompose composite numbers into prime factor products.
- Complete tables of values to represent linear equations and plot graphs moving on to use of gradient intercept for plotting and using y=mx+c

##### Vocabulary

- Factor (HCF)
- Multiple (LCM)
- Prime
- Composite
- Prime factor product
- Linear graph
- Gradient
- Intercept

#### Key Concepts and Themes

- Use inequality notation to represent error intervals. Pupils build on their mensuration including rounding to appropriate levels of accuracy when solving problems and moving onto more complex shapes.
- Use ratios to share quantities and solve problems with missing quantities. Use ratios 1:n and n:1 for comparison
- Use common factors to factorise algebraic expressions with numbers and letters as common factors. Factorise an expression into the difference of two squares.

##### Vocabulary

- Inequality
- Significant figures
- Estimate
- Prism
- Cylinder
- Unitary method
- Factorise expressions

##### Key Concepts and Themes

- Translate, reflect and rotate shapes in the plane.
- Use scale factors with similar shapes and to construct enlargements.

##### Vocabulary

- Translate
- Vector
- Reflect
- Rotate
- Enlargement
- Scale factor

##### Skill Development

- Select appropriate methods for their calculations based upon their own evaluation of their solutions
- Explore patterns and make conjectures, increasingly looking to generalise from particular problems
- Use diagrammatic and algebraic representations based upon the context of a problem and compare different approaches
- Gain knowledge through their evaluation of approaches to multi-step problems including unfamiliar problems

## Year 9

##### Intent

In Year 9, students develop their geometric reasoning looking at polygons before being introduced to Pythagoras’ theorem and then trigonometry. In algebra students begin to form links between topics looking at using formulae for different types of problem and then working with graphs. Students develop their understanding of probability.

##### Learning Journey

##### Key Concepts and Themes

- Use conventional methods for operating with fractions including converting between improper fraction and mixed numbers
- Expand the product of two binomials to form a quadratic expression. Rearrange formulae to change the subject.
- Recognise and calculate interior and exterior angle sums for polygons

##### Vocabulary

- Mixed number
- Improper fraction
- Binomial
- Quadratic
- Subject (of a formula)
- Interior angle
- Exterior angle
- Tessellation

##### Key Concepts and Themes

- Represent outcomes using a sample space diagram and calculate theoretical probabilities and recognise the effect of adding conditions
- Calculate the result of a percentage change both with and without calculator including the inverse. Calculate interest both simple and compound
- Set up and solve increasingly complex linear equations including brackets and fractional coefficients using formal methods. Add/subtract and simplify algebraic fractions.

##### Vocabulary

- Sample space
- Theoretical probability
- Conditional probability
- Mutually exclusive
- Independent
- Simple interest
- Compound interest
- Coefficient
- Algebraic fraction

##### Key Concepts and Themes

- Use known geometrical facts and formulae to solve problems including multi-step problems. Use Pythagoras theorem and properties of similar and congruent shapes.
- Use grouped data, both discrete and continuous and estimate the mean. Create and interpret stem-and-leaf plots, box-plots and frequency polygons.

##### Vocabulary

- Similar
- Congruent
- Pythagoras’ theorem
- Frequency polygon
- Box and whisker plot
- Stem and leaf plot
- Estimated mean

##### Key Concepts and Themes

- Model real-life situations with expressions, formulae and graphs making links between these representations. Solve direct and inverse proportion problems informally and algebraically.
- Identify the key points of a parabola. Construct a parabola using a table of values or given roots and vertex. Use graphs to find solutions for quadratic equations. Use graphs to estimate solutions for simultaneous equations including quadratics.

##### Vocabulary

Direct proportion, Inverse proportion, Constant of proportionality, Parabola, Roots, Vertex, Quadratic equation, Simultaneous equations

##### Key Concepts and Themes

- Use Pythagoras’ theorem to solve problems of lengths in 2D and 3D shapes. Use trig ratios to find missing side lengths as well as missing angles in right-angled and non-right-angled triangles.
- Express numbers in standard form and use standard form to calculate. Classify and represent different types of number (real, rational/irrational).
- Generate terms and use nth term rule to describe geometric sequences.

##### Vocabulary

- Pythagoras’ theorem
- Hypotenuse
- Trigonometry
- Sine ratio
- Cosine ratio
- Tangent ratio
- SOHCAHTOA
- Standard form
- Scientific notation
- Rational number
- Irrational number
- Real number
- Geometric sequence
- Common ratio

##### Key Concepts and Themes

- Use compound units for speed and density including both metric and Imperial equivalents. Calculate best value.
- Model situations graphically and algebraically expressing quadratic relationships. Construct and interpret graphs of cubic, reciprocal and exponential functions.

##### Vocabulary

- Compound units
- Density
- Displacement
- Value
- Quadratic
- Linear
- Cubic
- Reciprocal
- Exponential

##### Skill Development

- Select and use appropriate calculation strategies to solve increasingly complex problems
- Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships
- Reason deductively in geometry, number and algebra, including using geometrical constructions
- Move freely between different numerical, algebraic, graphical and diagrammatic representations
- Model situations mathematically and express the results using a range of formal mathematical representations

## Mathematics News

- Return of UKMT Maths Challenge

Senior challenge on Wednesday 10th November 2021 (15/10/2021)