1 Using and applying mathematics |
| Solve multi-step problems, and problems involving fractions, decimals and percentages; choose and use appropriate calculation strategies at each stage, including calculator use
| Solve problems by breaking down complex calculations into simpler steps; choose and use operations and calculation strategies appropriate to the numbers and context; try alternative approaches to overcome difficulties; present, interpret and compare solutions
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| Tabulate systematically the information in a problem or puzzle; identify and record the steps or calculations needed to solve it, using symbols where appropriate; interpret solutions in the original context and check their accuracy
| Represent information or unknown numbers in a problem, for example in a table, formula or equation; explain solutions in the context of the problem
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| Suggest, plan and develop lines of enquiry; collect, organise and represent information, interpret results and review methods; identify and answer related questions
| Develop and evaluate lines of enquiry; identify, collect, organise and analyse relevant information; decide how best to represent conclusions and what further questions to ask
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| Represent and interpret sequences, patterns and relationships involving numbers and shapes; suggest and test hypotheses; construct and use simple expressions and formulae in words then symbols (e.g. the cost of c pens at 15 pence each is 15c pence)
| Generate sequences and describe the general term; use letters and symbols to represent unknown numbers or variables; represent simple relationships as graphs
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| Explain reasoning and conclusions, using words, symbols or diagrams as appropriate
| Explain and justify reasoning and conclusions, using notation, symbols and diagrams; find a counter-example to disprove a conjecture; use step-by-step deductions to solve problems involving shapes
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2 Counting and understanding number |
| Find the difference between a positive and a negative integer, or two negative integers, in context | Compare and order integers and decimals in different contexts
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| Use decimal notation for tenths, hundredths and thousandths; partition, round and order decimals with up to three places, and position them on the number line | Order a set of fractions by converting them to decimals
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Express a larger whole number as a fraction of a smaller one (e.g. recognise that 8 slices of a 5-slice pizza represents  or 1 pizzas); simplify fractions by cancelling common factors; order a set of fractions by converting them to fractions with a common denominator
| Use ratio notation, reduce a ratio to its simplest form and divide a quantity into two parts in a given ratio; solve simple problems involving ratio and direct proportion (e.g. identify the quantities needed to make a fruit drink by mixing water and juice in a given ratio) (EOY)
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| Express one quantity as a percentage of another (e.g. express £400 as a
percentage of £1000); find equivalent percentages, decimals and
fractions
| Recognise approximate proportions of a whole and use fractions and percentages to describe and compare them, for example when interpreting pie charts | |
| Solve simple problems involving direct proportion by scaling quantities up or down
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3 Knowing and using number facts |
| Use knowledge of place value and multiplication facts to 10 × 10 to derive related multiplication and division facts involving decimals (e.g. 0.8 × 7, 4.8 ÷ 6)
| Consolidate rapid recall of number facts, including multiplication facts to 10 × 10 and the associated division facts | |
| Use knowledge of multiplication facts to derive quickly squares of numbers to 12 × 12 and the corresponding squares of multiples of 10
| Recognise the square roots of perfect squares to 12 × 12 | |
| Recognise that prime numbers have only two factors and identify prime numbers less than 100; find the prime factors of two-digit numbers | Recognise and use multiples, factors, divisors, common factors, highest common factors and lowest common multiples in simple cases | |
| Use approximations, inverse operations and tests of divisibility to estimate and check results | Make and justify estimates and approximations to calculations
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4 Calculating |
| Calculate mentally with integers and decimals: U.t ± U.t, TU × U, TU ÷ U, U.t × U, U.t ÷ U
| Understand how the commutative, associative and distributive laws, and the relationships between operations, including inverse operations, can be used to calculate more efficiently; use the order of operations, including brackets | |
| Use efficient written methods to add and subtract integers and decimals, to multiply and divide integers and decimals by a one-digit integer, and to multiply two-digit and three-digit integers by a two-digit integer (EOY)
| Consolidate and extend mental methods of calculation to include decimals, fractions and percentages | |
Relate fractions to multiplication and division (e.g. 6 ÷ 2 =  of 6 = 6 × ); express a quotient as a fraction or decimal (e.g. 67 ÷ 5 = 13.4 or 13 ); find fractions and percentages of whole-number quantities (e.g.  of 96, 65% of £260)
| Use standard column procedures to add and subtract integers and decimals, and to multiply two-digit and three-digit integers by a one-digit or two-digit integer; extend division to dividing three-digit integers by a two-digit integer | |
| Use a calculator to solve problems involving multi-step calculations
| Calculate percentage increases or decreases and fractions of quantities and measurements (integer answers) | |
| | Use bracket keys and the memory of a calculator to carry out calculations with more than one step; use the square root key
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5 Understanding shape |
| Describe, identify and visualise parallel and perpendicular edges or faces; use these properties to classify 2-D shapes and 3-D solids
| Use correctly the vocabulary, notation and labelling conventions for lines, angles and shapes
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| Make and draw shapes with increasing accuracy and apply knowledge of their properties | Extend knowledge of properties of triangles and quadrilaterals and use these to visualise and solve problems, explaining reasoning with diagrams | |
| Visualise and draw on grids of different types where a shape will be after reflection, after translations, or after rotation through 90° or 180° about its centre or one of its vertices
| Know the sum of angles on a straight line, in a triangle and at a point, and recognise vertically opposite angles
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| Use coordinates in the first quadrant to draw, locate and complete shapes that meet given properties | Use all four quadrants to find coordinates of points determined by geometric information | |
| Estimate angles, and use a protractor to measure and draw them, on their own and in shapes; calculate angles in a triangle or around a point | Identify all the symmetries of 2-D shapes; transform images using ICT
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| | Construct a triangle given two sides and the included angle
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6 Measuring |
| Select and use standard metric units of measure and convert between
units using decimals to two places (e.g. change 2.75 litres to 2750 ml,
or vice versa)
| Convert between related metric units using decimals to three places (e.g. convert 1375 mm to 1.375 m, or vice versa)
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| Read and interpret scales on a range of measuring instruments, recognising that the measurement made is approximate and recording results to a required degree of accuracy; compare readings on different scales, for example when using different instruments | Solve problems by measuring, estimating and calculating; measure and calculate using imperial units still in everyday use; know their approximate metric values
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| Calculate the perimeter and area of rectilinear shapes; estimate the area of an irregular shape by counting squares | Calculate the area of right-angled triangles given the lengths of the two perpendicular sides, and the volume and surface area of cubes and cuboids | |
7 Handling data |
| Describe and predict outcomes from data using the language of chance or likelihood | Understand and use the probability scale from 0 to 1; find and justify probabilities based on equally likely outcomes in simple contexts
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| Solve problems by collecting, selecting, processing, presenting and interpreting data, using ICT where appropriate; draw conclusions and identify further questions to ask
| Explore hypotheses by planning surveys or experiments to collect small sets of discrete or continuous data; select, process, present and interpret the data, using ICT where appropriate; identify ways to extend the survey or experiment | |
| Construct and interpret frequency tables, bar charts with grouped discrete data, and line graphs; interpret pie charts
| Construct, interpret and compare graphs and diagrams that represent data, for example compare proportions in two pie charts that represent different totals | |
| Describe and interpret results and solutions to problems using the mode, range, median and mean
| Write a short report of a statistical enquiry and illustrate with appropriate diagrams, graphs and charts, using ICT as appropriate; justify the choice of what is presented | |
