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Term
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What are we learning
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1
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Decimal Manipulation
Estimation and Limits of Accuracy
Related Calculations
HCF and LCM of Large Numbers
Fraction Calculations
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- Adding, subtracting, multiplying and dividing integers and decimals.
- Manipulation of Decimals e.g. 2.54 ÷ 4, using one calculation to perform another, ordering decimals (including use of inequality symbols).
- Calculations involving money and correct use of units.
- Order of operations (BIDMAS): use conventional notation for priority of operations, including brackets, powers, roots and reciprocals.
- Rounding number to the nearest 10, 100, 1000, and to a given number of decimal places
- Rounding to significant figures
- Estimate answers to one or two step calculations
- Apply sensible rounding depending on the calculation
- Recognise and use relationships between operations
- Prime numbers, prime factor decomposition, LCM, HCF (of large numbers)
- Add and subtract fractions and mixed numbers with different denominators
- Multiply and divide fractions and mixed numbers. Simplify calculations by cancelling first
- Fraction of an amount
- Identify and work with fractions in ratio problems
- Express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1
- Find the reciprocal of an integer, decimal or fraction
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2
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Algebraic Manipulation
Index Laws
Expanding and Factorising
Expression and Substitution
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- Collect like terms
- Multiply together two simple algebraic expressions, e.g. 2a × 3b
- Simplify expressions by cancelling, e.g. = 2x
- Add and subtract fractions with an algebraic numerator including with powers
- Multiply, divide and simplify algebraic fractions including with powers
- Simple laws of indices
- Use index notation when multiplying or dividing algebraic terms
- Use index notation for integer powers of 10, including negative powers
- Simplify and calculate the value of numerical expressions involving multiplication and division of integer powers, negative powers and powers of a power
- Understand the term reciprocal
- Expand single brackets
- Factorise - single brackets
- Expanding double brackets
- Factorising quadratics of the form x2 + bx + c
- Difference of two squares
- Use algebra to show expressions are equivalent
- Know the difference between an equation and an identity; argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments
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3
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Percentages with a Calculator
Proportion
Probability
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- Percentage of an amount (including of a measurement) with and without a calculator
- Percentage increase and decrease
- Finding the original amount (reverse percentage) with and without a calculator
- Work with percentages greater than 100%
- Compare two quantities using percentages
- Express one quantity as a percentage of another
- Use percentages in real-life situations e.g. price after VAT, value of profit or loss, simple interest, income tax
- Best buy
- Recipes
- Currency
- Unitary method
- Use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate
- Solve problems involving direct and inverse proportion, including graphical and algebraic representations
- Interpret equations and graphs that describe direct and inverse proportion
- Conversion graphs
- Apply systematic listing strategies
- Describe probability using the probability scale, tables and frequency trees
- Apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments
- Calculate expected outcomes
- Mutually exclusive events sum to one
- Experimental and theoretical probability
- Venn diagrams and appropriate notation
- Possibility spaces/sample spaces
- Find a missing probability from a list or table including algebraic terms
- Unbiased samples and effects of increasing sample size
- Sets and combinations of sets using Venn diagrams
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4
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Linear Equations
Linear Inequalities
Sequences
Pythagoras
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- Solve linear equations in one unknown algebraically, with unknowns on one side e.g. 5x - 7 = 18
- Solve linear equations which contain brackets, fractional coefficients, negative signs, negative solutions
- Substitute into a formula, and solve the resulting equation
- Solve linear equations in one unknown algebraically, with unknowns on both sides
- Form and solve algebraic equations and interpret the solution
- Solving linear equations that require algebraic fraction manipulation
- Solve linear inequalities in one variable e.g. 5x - 7 > 18
- Represent and interpret solution sets to inequalities on a number line
- Solve two inequalities in x, find the solution sets and compare them to see which value of x satisfies both
- Fibonacci sequences and simple geometric progressions (r^n where n is an integer, and r is a rational number > 0)
- Continue a geometric progression and find the term-to-term rule, including negatives, fraction and decimal terms
- Use finite/infinite and ascending/descending to describe sequences
- Recognise and use simple geometric progressions
- Calculate with roots, and with integer indices
- Pythagoras’ theorem
- Leave answers in surd form
- Given 3 sides of a triangle, justify if it is right-angled or not
- Apply Pythagoras’ Theorem with a triangle drawn on a coordinate grid
- Calculate the length of a line segment AB given pairs of points
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5
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Interior and Exterior Angles
Parallel Lines
Basic Vectors
Basic Transformations
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- Interior and exterior angles, angle sums
- Understand a proof that the exterior angle of a triangle is equal to the sum of the interior angles at the other two vertices
- Explain why some polygons fit together and others do not
- Alternate and corresponding angles on parallel lines
- Solve missing angle problems, giving reasons for answers
- Apply properties of angles in parallel lines to an algebraic context
- Describe translations as 2D vectors
- Translate a given shape by a vector
- Addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors
- Be able to represent information graphically given column vectors
- Identify two column vectors which are parallel
- Reflection and rotation symmetry
- Transformations - rotation, reflection, translation, enlargement (with a positive scale factor)
- Identify the equation of a line of symmetry
- Identify the scale factor of an enlargement of a shape as the ratio of the lengths of two corresponding sides, simple integer scale factors, or simple fractions
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6
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Plans and Elevations
Circles
Surface Area
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- Identify properties of the faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres
- Draw sketches of 3D solids
- Interpret Plans and elevations of 3D shapes
- Construct plans and elevations of 3D shapes
- Given the front and side elevations and the plan of a solid, draw a sketch of the 3D solid
- Circle definitions - centre, radius, chord, diameter, circumference
- Use Circumference of a circle = 2πr = πd and area of a circle = πr2
- Circle definitions including tangent, arc, sector and segment
- Arc lengths, angles and areas of sectors of circles
- Calculate exactly with multiples of π
- Use rearranging to calculate missing lengths given the area or circumference
- Estimate surface areas by rounding measurements to 1 significant figure
- Sketch nets of cuboids and prisms
- Surface area of spheres, pyramids, cones and composite solids (hemispheres, frustums)
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Links
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https://corbettmaths.com/contents/ https://www.mathsgenie.co.uk/
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