# Maths at Michaela

**Year 7 Mathematics**

The year 7 curriculum provides a solid foundational pre-algebra curriculum which becomes the basis upon which all subsequent work is built. The focus is entirely on number. Pupils are assessed on entry and those who struggle with abstract thinking follow an intensive Direct Instruction programme to close the gap. Rolling numbers and Times Tables Rockstars feature heavily and are well-loved by pupils.

**Unit 1: Place value and number**

- Place value, reading and writing numbers
- Comparing and ordering numbers
- Base 10 tricks
- Rounding

**Unit 2: Addition and subtraction**

- Addition
- Subtraction
- Perimeters
- Angle rules

**Unit 3: Multiplication and division**

- Multiplication
- Area
- Division
- Multiplication and division in context

**Unit 4: Indices**

- Squares, powers and roots
- Index rules

**Unit 5: Order of operations**

- Calculating with GEMS
- Applications of the order of operations: the mean average, midpoints and compound shapes

**Unit 6: Negatives**

- Understanding negative numbers
- Addition and subtraction with negatives
- Adding and subtracting efficiently
- Multiplication, division, indices and GEMS with negatives

**Unit 7: Number theory**

- Factors
- Primes and prime factors
- Multiples
- HCF and LCM

**Unit 8: Fractions**

- Fractions conceptually
- Equivalent fractions
- Adding and subtracting fractions
- Fractions of amounts
- Multiplying and dividing with fractions
- GEMS with fractions and worded contexts

**Year 8 Mathematics**

In year 8, pupils tackle algebra in earnest. This strong base allows all subsequent work in Y9-11 to quickly move to algebraic forms (e.g. forming equations to find angles in a polygon).

**Unit 1: Manipulating terms**

- Collecting like terms
- Multiplying and dividing terms

**Unit 2: Simplifying expressions**

- Substitution
- Expanding single brackets
- Factorisation
- Double and triple brackets

**Unit 3: Algebraic fractions**

- Multiplying and dividing
- Adding algebraic fractions
- GEMS and solving problems with algebraic fractions

**Unit 4: Forming expressions and proofs**

- Forming expressions from worded and geometry contexts
- Proof

**Unit 5: Solving equations**

- Principles of solving equations
- Solving one and two step equations
- Solving complex equations
- Applied equation solving

**Unit 6: Formulae**

- Forming equations
- Rearranging formulae
- Using formulae
- Formulae to learn by heart

**Unit 7: Inequalities**

- Plotting inequalities
- Solving inequalities

**Unit 8: Sequences**

- Understanding sequences
- Linear sequences
- Patterns and problem solving

**Unit 9: Graphs**

- The Cartesian plane
- Plotting linear graphs
- Finding the equations of linear graphs
- Graphing linear inequations

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**Year 9 Mathematics**

Once pupils have mastered number and linear algebra, pupils are ready to tackle geometry. In year 9, we look at Euclidean geometry and angle rules including circle theorems. Similarity feeds into work on Pythagoras’ theorem and trigonometry. Finally we look at area, surface area and volume of shapes.

**Unit 1: Percentages **

- Expressing values as percentages
- Percentage change
- Original amounts
- Simple and compound interest

**Unit 2: Angles**

- Angles on lines
- Angles in polygons
- Circle theorems
- Circle theorems and tangents
- Proofs

**Unit 1: Euclidean geometry**

- Principles and vocabulary
- Properties of shapes
- Measuring angles
- Construction with a protractor
- Bearings

**Unit 3: Similarity and congruence **

- Congruence
- Reflection and rotation
- Similarity
- Enlargement

**Unit 4: Triangles**

- Pythagoras’ theorem
- Pythagoras’ theorem in context
- Trigonometry and ratios
- Trigonometry: solving problems
- Non-right angle triangles
- Trigonometric graphs

**Unit 5: Area**

- Area conceptually and simple shapes
- Areas of circles
- Areas of compound shapes

**Unit 6: Surface area and volume**

- Nets, plans and elevations
- Surface area of prisms and cylinders
- Surface area of complex shapes
- Volume of prisms and cylinders
- Volumes of other solids

**Year 10**

In Year 10, pupils build on their foundations in algebra and geometry, learning alternative representations (such as surds) and applying them to more complex contexts (such as simultaneous equations and manipulations with quadratics). The pupils also begin formal study of statistics and probability, focusing on deep understanding and reasoning.

**Unit 1: ratio**

- sharing parts and wholes in a ratio
- comparing ratios
- relating ratios and fractions

**Unit 2: alternative representations of values**

- Surds
- Standard index form
- Recurring decimals and fractions

**Unit 3: probability**

- Counting rules
- Relative frequency
- Independent events
- Conditional probability
- Venn diagrams and set notation

**Unit 4: 3D solids**

- Plans and elevations
- Nets and surface area
- Volume of prisms and of curved objects
- Scale factors in different dimensions

**Unit 5: quadratics**

- Factorising
- Sketching quadratics
- The quadratic formula
- Advanced manipulation to solve equations

**Unit 6: simultaneous equations**

- Solving simultaneous equations
- Modelling situations to form equations
- Solving graphically

**Unit 7: statistics**

- Types of data
- Reading and constructing charts and diagrams
- Processing data
- Interpreting graphs and results

**Year 11**

In Year 11, pupils will study the final set of topics essential to aim for Grade 8 and above. A small number of pupils will use Y11 primarily to consolidate their learning from Y7-10, replacing some of the topics listed below. Those marked with an asterisk will be studied by all pupils.

**Unit 1: accuracy**

- *Estimation
- *Bounds
- Limits of accuracy

**Unit 2: vectors**

- Vectors as movement
- Interpreting diagrams of vectors
- Forming proofs

**Unit 3: graphs**

- *Compound measures
- *Linear graphs: interpretation
- Modelling situations using graphs

**Unit 4: roots**

- Completing the square
- Sketching turning points
- Interpreting the roots of an equation or graph

**Unit 5: curves and circles**

- Equation of a tangent to a curve
- Area under a curve
- *Equation of a circle

**Unit 6: algebra – advanced applications**

- Graphical inequalities
- Quadratic simultaneous equations (including as graphs)
- Nth term of a quadratic sequence

**Unit 7: functions**

- Interpreting functions
- Sketching
- Transforming

**Unit 8: advanced proof**

- *Geometric proof
- Circle theorems
- *Algebraic manipulations