# Key Stage 3

## Year 7

##### Intent

In year 7 we extend our students’ knowledge from key stage two by developing their fluency, reasoning and problem solving in the different strands of mathematics. We interleave topics already covered and introduce the more formal notation for algebra.

##### Learning Journey

**Reasoning with Number**

• Comparing numbers and identifying missing numbers in a sequence.

• Inequalities on number lines

• Rounding numbers and decimals

**Addition and Subtraction**

• Add and subtract decimals and negatives

• Bank account statements

• Working with time

• Create and interpret frequency trees

• Perimeter

**Multiplication and Division**

• Multiply by powers of 10

• Multiply and divide decimals

• Multiply and divide negative numbers

**Application of Multiplication and Division**

• Recognise triangular, square, cube, odd, even and prime

• Powers and roots of numbers

• Law of indices (adding and subtracting)

• Product of prime and HCF, LCM

• Order of operations with roots and indices.

• Approximation

• Mean of date and reverse mean

**Understanding Fractions**

• One quantity as a fraction of another

• Equivalent fractions and simplifying

• Conversion between mixed numbers and improper fraction

• Fraction of amounts using improper fractions or mixed numbers

• Fractional increase and decrease

• Fractional change

**Fractional Operations**

• Add and subtract fractions and mixed numbers

• Multiply fractions and mixed numbers

• Divide fractions and mixed numbers

**Percentages**

• Convert between fraction, decimal and percentages

• Write an amount as a percentage of another

• Percentage of amounts

• Percentage increase and decrease

• Reverse percentages

• Percentage change

**Algebraic Expressions **

• Equation, Expression, identity

• Form expressions, simplify expressions

• Substitute into formulae

• Expand and simplify single brackets

• Expand double brackets with coefficient of 1

**Algebraic Equations**

• Form and solve equations and inequalities

**Geometric Multiplication and Division**

• Finding missing lengths in area

• Area of a trapezium

• Area of compound shapes

• Surface area of 3D shapes

**Shape Properties**

• Language of congruency and similarity

• Classify triangles and reason

• Quadrilaterals

• Coordinates

• Parallel and perpendicular lines with notation

• Lines of symmetry

• Rotational symmetry

**Working with Angles**

• Draw and measure angles and angle notation

• Construct shapes

• Missing angle around a point and on a line

• Vertically opposite angles

• Missing angles in triangles and quadrilaterals

**Representing Data**

• Mean, median, mode and range

• Justify use of average

• Compare data sets

• Create pie charts

• Mean median mode and rage from diagrams

• Find probability

• Sample space diagrams

• Venn diagrams

## Year 8

##### Intent

Into year 8 we develop our students’ knowledge of algebra, geometry and statistics gained from year 7 to allow them to tackle more sophisticated problem solving. We introduce and build students’ ratio and proportion knowledge and explore constructions and loci for the first time.

##### Learning Journey

**Algebraic Manipulation**

• Rearrange formulae which have roots and powers

• Substitute into formulae including powers and roots

• Expand any pair of double brackets

• Factorise into a single bracket

• Factorise a quadratic expression with coefficient of x^2 is 1

• Expand three binomials with coefficient of 1

**Sequences and Order**

• Find the term to term rule

• Continue arithmetic sequences

• Different types of sequences

• Nth term for arithmetic sequence

**Working in the Cartesian Plane**

• Problems with coordinates and area

• Linear graphs

• Quadratic Graphs

• Cubic Graphs

• Equation of a line from graph

• Equation of line given two points

• Equations of parallel and perpendicular lines

**Algebra**

• Simultaneous equations graphically

• Simultaneous equations pictorially

• Solve linear simultaneous equations

**Angle Reasoning**

• Scale Drawings

• Angles in parallel lines

• Bearings

• Interior and Exterior Angles

**2D Shape Application**

• Circumference and area of a circle

• Perimeter and area of arcs and sectors

• Area of compound shapes containing trapezia, circles and sectors

• Similar shapes

**Reasoning in 3D and Understanding Capacity**

• Nets

• Plans and elevations

• Volume of cubes, cuboids, prisms and cylinder

**Constructions**

• Perpendicular bisectors

• Angle bisectors

• Construct triangles

• Loci

**Working with Data**

• Listing possible outcomes and combinations

• Averages and Range from ungrouped and grouped data

• Frequency polygons

• Equal width histograms

• Scatter diagrams

**Ratio**

• Simplify ratios

• Divide into a given ratio

• Ratios with three quantities

**Compound Units**

• Use and apply speed distance time

• Speed, distance, time graphs

• Density, mass and volume

• Population density

**Direct and Inverse Proportion**

• Conversion graphs

• Direct proportion problems

• Best buy

• Algebraic direct proportion

• Conversion graphs

## Year 9

##### Intent

Students’ knowledge continues to be extended into year 9 and 10 over all of the strands of mathematics; content they have met previously is extended and some new concepts are introduced. Students will use the skills they have learnt to reason and articulate their thinking and attempt problems involving many different skills.

##### Learning Journey - Pathway 1

**Basic Number**

- Solving real life problems
- Multiplication and division with decimals
- Approximation of calculations
- Multiples, primes, powers and roots
- Prime factors, LCM and HCF
- Negative numbers

**Fractions, Ratio and Proportion **

- One quantity as a fraction of another
- Adding, subtracting and calculating with fractions
- Fractions on a calculator
- Increasing and decreasing quantities by a percentage
- Expressing one quantity as a percentage of another

**Number and Sequences**

- Patterns in number
- Number sequences
- Finding the nth term of a linear sequence
- Special sequences
- General rules for given patterns
- The nth term of a quadratic sequence
- Finding the nth term for quadratic sequences

**Algebraic manipulation**

- Basic algebra
- Factorisation
- Quadratic expansion
- Expanding squares
- More then two binomials
- Quadratic factorisation
- Factorising ax2+bx+c
- Changing the subject of a formula
- Identities
- Proof with identities

**Linear Graphs **

- Drawing linear graphs from points
- Gradient of line
- Drawing graphs by gradient-intercept and cover-up methods
- Finding the equation of a line from its graphs
- Solving simultaneous equations using a graphs

**Equations and Inequalities**

- Linear equations
- Simultaneous equations: all methods
- Using simultaneous equations to solve problems
- Linear and graphical inequalities
- Trial and Improvement

**Angles **

- Angle facts
- Triangles
- Angles in a polygon
- Regular polygons
- Angles in parallel lines
- Special quadrilaterals
- Scale drawings and bearings

**Transformations, constructions and loci**

- Congruent triangles
- Rotational symmetry
- Transformations
- Combinations of transformations
- Invariance in transformations
- Bisectors
- Defining a locus
- Loci problems
- Plans and elevations

**Length, area and volume**

- Circles
- Parallelograms
- Trapezium
- Sectors
- Volume of prism
- Cylinders
- Volume of pyramids, cones and spheres

**Right angled triangles**

- Pythagoras theorem
- Calculating the length of a shorter side
- Pythagoras in real life
- Isosceles triangles
- Pythagoras theorem in 3d
- Trigonometric ratios
- Calculating angles
- Using the sine and cosine functions
- Using the tangent function
- Which ratio to use
- Solving problems using trigonometry
- Trigonometry and bearings
- Trigonometry and isosceles triangles

**Similarity**

- Similar triangles
- Areas and volume of similar shapes
- Similar triangles
- Areas and volume of similar shapes

**Statistical Reasoning**

- Statistical diagrams and averages
- Statistical representation
- Statistical measures
- Scatter diagrams

**Ratio and Proportion**

- Ratio
- Direct proportion problems
- Best buys
- Compound measures
- Compound interest and repeated percentage change
- Reverse percentage

**Exploring and applying probability **

- Experimental probability
- Mutually exclusive and exhaustive outcomes

##### Learning Journey - Pathway 2

**Basic number**

- Place value and ordering numbers
- Order of operations and BIDMAS
- The four rules

**Number Properties **

- Multiples of whole numbers
- Factors of whole numbers
- Prime numbers
- Prime factors, LCM and HCF
- Square numbers
- Square roots
- Basic calculations on a calculator

**Approximations**

- Rounding whole numbers
- Rounding decimals
- Approximating calculations

**Decimals and Fractions**

- Calculating with decimals
- Fractions and reciprocals
- Fractions of quantities
- Adding and subtracting fractions
- Multiplying and dividing fractions
- Fractions on a calculator

**Linear graphs**

- Graphs and equations
- Drawing linear graphs by finding points
- Gradient of a line
- Y=mx+c
- Finding the equation of a line from its graph
- The equation of a parallel line
- Real life uses of graphs
- Solving simultaneous equations using a graph

**Expressions and formulae**

- Basic Algebra
- Substitution
- Expanding brackets
- Factorisation
- Quadratic expansion
- Quadratic factorisation
- Changing the subject of a formulae

**Measures and scale drawings**

- Systems of measurement
- Conversion factors
- Scale drawings
- Nets
- Using an isometric grid

**Angles **

- Angle facts
- Triangles
- Angles in a polygon
- Regular polygons
- Angles in parallel lines
- Special quadrilaterals
- Bearings

**Perimeter and Area**

- Rectangles
- Compound shapes
- Area of a triangle
- Area of a parallelogram
- Area of a trapezium
- Circles
- The area of a circle
- Answers in terms of pi

**Transformations and vectors**

- Rotational symmetry
- Translation
- Reflection
- Rotation
- Enlargement
- Using more then one translation
- Vectors

**Charts, tables and averages**

- Frequency tables
- Statistical diagrams
- Line graphs
- Statistical averages

**Ratio, speed and proportion**

- Ratio
- Speed, distance and time
- Direct proportion problems
- Best buys

## Mathematics News

- Reading in Maths

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UK Mathematical Trust Girlâ€™s Mathematical Olympiad and Senior Mathematics Challenges (18/11/2019) - NFS and UKMT

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