- Numbers and the Number System:
- Use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor and lowest common multiple
- Use positive integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5
- Recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions
- Calculating:
- Understand and use place value (e.g. when working with very large or very small numbers, and when calculating with decimals)
- Apply the four operations, including formal written methods, to integers and decimals
- Use conventional notation for priority of operations, including brackets
- Recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions)
- Checking, Approximating and Estimating:
- Round numbers and measures to an appropriate degree of accuracy (e.g. To a specified number of decimal places or significant figures)
- Estimate answers; check calculations using approximation and estimation, including answers obtained using technology
- Recognise and use relationships between operations, including inverse operations (e.g. Cancellation to simplify calculations and expressions)
- Counting and Comparing:
- Order positive and negative integers, decimals and fractions
- Use the symbols =, ≠, , ≤, ≥
- Visualising and Constructing:
- Use conventional terms and notations: points, lines, vertices, edges, planes, parallel lines, perpendicular lines, right angles, polygons, regular polygons and polygons with reflection and/or rotation symmetries
- Use the standard conventions for labelling and referring to the sides and angles of triangles
- Draw diagrams from written description
- Investigating Properties and shapes:
- Identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres
- Derive and apply the properties and definitions of: special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus; And triangles and other plane figures using appropriate language
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- Algebraic Proficiency: Tinkering:
- Understand and use the concepts and vocabulary of expressions, equations, formulae and terms
- Use and interpret algebraic notation, including: ab in place of a × b, 3y in place of y + y + y and 3 × y, a² in place of a × a, a³ in place of a × a × a, a/b in place of a ÷ b, brackets
- Simplify and manipulate algebraic expressions by collecting like terms and multiplying a single term over a bracket
- Where appropriate, interpret simple expressions as functions with inputs and outputs
- Substitute numerical values into formulae and expressions
- Use conventional notation for priority of operations, including brackets
- Exploring Fractions, Decimals and Percentages:
- Express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1
- Define percentage as ‘number of parts per hundred’
- Express one quantity as a percentage of another
- Proportional Reasoning:
- Use ratio notation, including reduction to simplest form
- Divide a given quantity into two parts in a given part:part or part:whole ratio
- Pattern Sniffing:
- Generate terms of a sequence from a term-to-term rule
- Measuring Space:
- Use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money, etc.) • Use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate
- Change freely between related standard units (e.g. Time, length, area, volume/capacity, mass) in numerical contexts
- Measure line segments and angles in geometric figures
- Investigating Angles:
- Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles
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- Calculating Fractions, Decimals and Percentages:
- Apply the four operations, including formal written methods, to simple fractions (proper and improper), and mixed numbers
- Interpret percentages and percentage changes as a fraction or a decimal, and interpret these multiplicatively
- Compare two quantities using percentages
- Solve problems involving percentage change, including percentage increase/decrease
- Solving Equations and Inequalities:
- Recognise and use relationships between operations, including inverse operations (e.g. Cancellation to simplify calculations and expressions)
- Solve linear equations in one unknown algebraically
- Calculating Space:
- Use standard units of measure and related concepts (length, area, volume/capacity)
- Calculate perimeters of 2d shapes
- Know and apply formulae to calculate area of triangles, parallelograms, trapezia
- Calculate surface area of cuboids
- Know and apply formulae to calculate volume of cuboids
- Mathematical Movement:
- Work with coordinates in all four quadrants
- Understand and use lines parallel to the axes, y = x and y = -x
- Solve geometrical problems on coordinate axes
- Identify, describe and construct congruent shapes including on coordinate axes, by considering rotation, reflection and translation
- Describe translations as 2d vectors
- Presentation of Data:
- Interpret and construct tables, charts and diagrams, including frequency tables, bar charts, pie charts and pictograms for categorical data, vertical line charts for ungrouped discrete numerical data
- Measuring Data:
- Interpret, analyse and compare the distributions of data sets from univariate empirical distributions through appropriate measures of central tendency (median, mean and mode) and spread (range)
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