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Introduction
# has studied counting, partitioning and calculating, securing number facts, understanding shape, handling data and measures, and number relationships.
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Applying
Year 5 Using and applying mathematics objectives
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^ can solve one-step and two-step problems involving whole numbers and decimals and all four operations, choosing and using appropriate calculation strategies, including calculator use.
^ is able to represent a puzzle or problem by identifying and recording the information or calculations needed to solve it.
^ has been able to find possible solutions to a problem and confirmed them in the context of the problem
^ is able to plan and pursue an enquiry. ^ is able to present evidence by collecting, organising and interpreting ~ information. ^ can suggest extensions to ~ enquiry to increase its scope.
^ is able to explore patterns, properties and relationships and propose a general statement involving numbers or shapes. ^ is then able to identify examples for which the statement is true or false.
^ can explain ~ reasoning by using diagrams, graphs and text. ^ has been successful in refining ~ ways of recording using images and symbols.
Year 6 Using and applying mathematics objectives
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^ is able to solve multi-step problems, and problems involving fractions, decimals and percentages. ^ choose and use the appropriate calculation strategies at each stage, including calculator ~ use.
^ has tabulated systematically the information in a problem or puzzle.^ has then identified and recorded the steps or calculations needed to solve it, using symbols where appropriate. When complete, ^ interpreted ~ solutions in the original context and checkd ~ accuracy.
^ is able to suggest, plan and develop lines of enquiry.
^ knows how to collect, organise and represent information, interpret results and review ~ methods.
^ is able to identify and answer related questions.
^ has represented and and interpreted sequences, patterns and relationships involving numbers and shapes.
^ has suggested and tested hypotheses related to ~ ideas.
^ is able to 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).
^ is able to explain ~ reasoning and conclusions, using words, symbols or diagrams as appropriate.
Progression Year 6/7 Using and applying mathematics objectives
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^ is able to solve problems by breaking down complex calculations into simpler steps.
^ could choose and use operations and calculation strategies appropriate to the numbers and context.
^ has tried alternative approaches to overcome difficulties.
^ is able to present, interpret and compare ~ solutions.
^ knows how to represent ~ information or unknown numbers in a problem, for example in a table, formula or equation. In addition, ^ was able to ~ explain solutions in the context of the problem.
^ knows how to develop and evaluate ~ lines of enquiry. ^ also has shown that he is able to identify, collect, organise and analyse relevant information. ^ could then decide how best to represent ~ conclusions and what further questions ^ needed to ask.
^ is able to generate sequences and describe the general term.
^ can use letters and symbols to represent unknown numbers or variables.
^ knows how to represent simple relationships as graphs.
^ was able to explain and justify ~ reasoning and conclusions, using notation, symbols and diagrams.
^ can find a counter-example to disprove a conjecture.
^ knows how to use step-by-step deductions to solve problems involving shapes.
"
Counting
Year 5 Counting and understanding number objectives
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^ can count from any given number in whole-number and decimal steps, extending beyond zero when counting backwards.
^ can relate numbers to their positions on a number line.
^ has explained what each digit represents in whole numbers and decimals with up to two places, and knows how to partition, round and order these numbers.
^ is able to express a smaller whole number as a fraction of a larger one (e.g. recognise that 5 out of 8 is five eighths).
^ can find equivalent fractions (e.g. seven tenths = fourteen twentieths, or nineteen tenths = 1nine tenths).
^ has correctly related fractions to their decimal representations.
^ understands percentages as the number of parts in every 100 and ^ has expressed tenths and hundredths as percentages.
^ can use sequences to scale numbers up or down.
^ is capabable of solving problems involving proportions of quantities (e.g. decrease quantities in a recipe designed to feed six people).
Year 6 Counting and understanding number objectives
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^ could find the difference between a positive and a negative integer, or two negative integers, in context.
^ has used decimal notation for tenths, hundredths and thousandths.
# can partition, round and order decimals with up to three places, and position them on a number line.
^ is able to express a larger whole number as a fraction of a smaller one (e.g. recognise that 8 slices of a 5-slice pizza represents eight fifths or 1three fifths pizzas).
^ has simplified fractions by cancelling common factors.
^ can order a set of fractions by converting them to fractions with a common denominator.
^ can express one quantity as a percentage of another (e.g. express 400 as a percentage of 1000).
^ is able to find equivalent percentages, decimals and fractions.
^ can solve simple problems involving direct proportion by scaling quantities up or down.
Progression Year 6/7 Counting and understanding number objectives
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^ is able to compare and order integers and decimals in different contexts.
^ knows how to order a set of fractions by converting them into decimals.
^ can use ratio notation, reduce a ratio to its simplest form and divide a quantity into two parts in a given ratio.
^ is able to 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).
^ recognises approximate proportions of a whole and ^ is able to use fractions and percentages to describe and compare them, for example when interpreting pie charts.
"
Number facts
Year 5 Knowing and using number facts objectives
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^ is able to use ~ knowledge of place value and addition and subtraction of two-digit numbers to derive the sums, differences, doubles and halves of decimals.
^ can quickly recall multiplication facts up to 10 × 10 and then use them to multiply pairs of multiples of 10 and 100.
^ can use ~ knowledge of multiplication to derive quickly corresponding division facts.
^ has identified pairs of factors of two-digit whole numbers and found common multiples (e.g. for 6 and 9).
^ is able to use ~ knowledge of rounding, place value, number facts and inverse operations to estimate and check calculations.
Year 6 Knowing and using number facts objectives
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^ can 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).
^ knows how to use ~ knowledge of multiplication facts to derive quickly squares of numbers to 12 × 12 and the corresponding squares of multiples of 10.
^ has recognised that prime numbers have only two factors and identify prime numbers less than 100.
^ recognises the prime factors of two-digit numbers.
^ is able to use approximations, inverse operations and tests of divisibility to estimate and check ~ results.
Progression Year 6/7 Knowing and using number facts objectives
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^ has consolidated ~ rapid recall of number facts, including multiplication facts to 10 × 10 and the associated division facts.
^ recognise the square roots of perfect squares to 12 × 12.
^ can recognise and use multiples, factors, divisors, common factors, highest common factors and lowest common multiples in simple cases.
^ is able to make and justify ~ estimates and approximations to calculations.
"
Calculating
Year 5 Calculating objectives
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^ can extend ~ mental-methods for whole-number calculations to subtract one near-multiple of 1000 from another (e.g. 6070 - 4097).
^ has used efficient written methods to add and subtract whole numbers and decimals with up to two places.
^ can use ~ understanding of place value to multiply and divide whole numbers and decimals by 10, 100 or 1000.
^ has refined and used efficient written methods to multiply and divide HTU × U, TU × TU, U.t × U and HTU ÷ U.
^ is able to find fractions using division (e.g. one hundredth of 5 kg), and percentages of numbers and quantities (e.g. 10%, 5% and 15% of ?80).
^ can use a calculator to solve problems, including those involving decimals or fractions (e.g. find three quarters of 150 g).
^ is able to interpret the display correctly in the context of measurements.
Year 6 Calculating objectives
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^ is able to calculate mentally with integers and decimals: U.t ± U.t, TU × U, TU ÷ U, U.t × U, U.t ÷ U.
^ uses 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.
^ is able to relate fractions to multiplication and division (e.g. 6 ÷ 2 = one half of 6 = 6 × one half ).
^ can express a quotient as a fraction or decimal (e.g. 67 ÷ 5 = 13.4 or 13two fifths ).
^ knows how to find fractions and percentages of whole-number quantities (e.g. five eighths of 96, 65% of 260).
^ has used a calculator to solve ~ problems involving multi-step calculations correctly.
Progression Year 6/7 Calculating objectives
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^ understand how the commutative, associative and distributive laws, and the relationships between operations, including inverse operations, can be used to calculate more efficiently.
^ knows how to use the order of operations, including brackets.
^ has consolidated and extended ~ mental methods of calculation to include decimals, fractions and percentages.
^ is able to 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.
^ knows how to extend division to dividing three-digit integers by a two-digit integer.
^ can calculate percentage increases or decreases and fractions of quantities and measurements which give integer answers.
^ knows how to use bracket keys and the memory of a calculator to carry out calculations with more than one step. In addition, ^ recognised when to use the square root key.
"
Shapes
Year 5 Understanding shape objectives
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^ can identify, visualise and describe properties of rectangles, triangles, regular polygons and 3-D solids.
^ has used ~ knowledge of properties to draw 2-D shapes, and to identify and draw nets of 3-D shapes.
^ is able to read and plot coordinates in the first quadrant.
^ can recognise parallel and perpendicular lines in grids and shapes.
^ has successfully used a set-square and ruler to draw shapes with perpendicular or parallel sides.
^ is able to complete patterns with up to two lines of symmetry.
^ knows how to draw the position of a shape after a reflection or translation.
^ estimates, draws and measures acute and obtuse angles with an angle measurer or protractor to a suitable degree of accuracy.
^ has calculated the angles in a straight line.
Year 6 Understanding shape objectives
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^ has described, identified and visualised parallel and perpendicular edges or faces. In addition, ^ has used these properties to classify 2-D shapes and 3-D solids.
^ is able to make and draw shapes with an increasing accuracy and ^ can apply ~ knowledge of their properties.
^ is able to 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.
^ has used coordinates in the first quadrant to draw, locate and complete shapes that meet given properties.
^ is able to estimate angles, and use a protractor to measure and draw them, on their own and in shapes.
^ is able to calculate angles in a triangle or around a point.
Progression Year 6/7 Understanding shape objectives
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^ can use correctly the vocabulary, notation and labelling conventions for lines, angles and shapes.
^ knows how to extend knowledge of properties of triangles and quadrilaterals and use these to visualise and solve ~ problems, explaining ~ reasoning with diagrams.
^ knows the sum of angles on a straight line, in a triangle and at a point, and ^ recognises vertically opposite angles.
^ is able to use all four quadrants to find coordinates of points determined by geometric information.
^ has identified all the symmetries of 2-D shapes.
^ knows how to transform images using ICT.
^ is able to construct a triangle given two sides and the included angle.
"
Measuring
Year 5 Measuring objectives
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^ was able to read, choose, use and record standard metric units to estimate and measure length, weight and capacity to a suitable degree of accuracy (e.g. the nearest centimetre) and convert larger to smaller units using decimals to one place (e.g. change 2.6 kg to 2600 g).
^ has interpreted a reading that lies between two unnumbered divisions on a scale.
^ is able to draw and measure lines to the nearest millimetre.
^ has measured and calculated the perimeter of regular and irregular polygons.
^ has used the formula for the area of a rectangle to calculate the rectangle's area.
^ knows how to read timetables and time using 24-hour clock notation.
^ has used a calendar to calculate time intervals
Year 6 Measuring objectives
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^ is able to select and use standard metric units of measure and convert between different units using decimals to two places (e.g. change 2.75 litres to 2750 ml, or vice versa).
^ can read and interpret scales on a range of measuring instruments, and ^ recognises that the measurement made is approximate and that ^ needs to record ~ results to a required degree of accuracy.
^ is able to compare readings on different scales, for example when using different instruments.
^ can calculate the perimeter and area of rectilinear shapes.
^ knows how to estimate the area of an irregular shape by counting squares.
Progression Year 6/7 Measuring objectives
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^ is able to convert between related metric units using decimals to three places (e.g. convert 1375 mm to 1.375 m, or vice versa).
^ knows how to solve problems by measuring, estimating and calculating.
^ can measure and calculate using imperial units still in everyday use
^ know the approximate metric values of common imperial units.
^ can 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.
"
Handling Data
Year 5 Handling data objectives
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# has described the occurrence of familiar events using the language of chance or likelihood.
^ is able to answer a set of related questions by collecting, selecting and organising relevant data.
^ has drawn conclusions, used ICT to present some features of ~ investigation, and identified further questions ^ could ask to extend the scope of ~ work.
^ has constructed frequency tables, pictograms and bar and line graphs to represent the frequencies of events and changes over time.
^ is able to find and interpret the mode of a data set.
Year 6 Handling data objectives
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# can describe and predict outcomes from ~ data using the language of chance or likelihood.
^ is able to solve problems by collecting, selecting, processing, presenting and interpreting data, using ICT where appropriate.
^ has drawn ~ own conclusions and ^ has been able to identify further questions ^ could ask about ~ investigation.
^ has been able to construct and interpret frequency tables, bar charts with grouped discrete data, and line graphs.
# knows how to interpret pie charts.
^ is able to describe and interpret ~ results and ~ solutions to problems using the mode, range, median and mean.
Progression Year 6/7 Handling data objectives
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# understands and uses the probability scale from 0 to 1.
^ can find and justify probabilities based on equally likely outcomes in simple contexts.
# has explored hypotheses by planning surveys or experiments to collect small sets of discrete or continuous data. ^ then selected, processed, presented and interpreted ~ data, using ICT where appropriate and identified ways to extend the ~ survey or experiment.
^ is able to construct, interpret and compare graphs and diagrams that represent data, for example compare proportions in two pie charts that represent different totals.
^ has written a short report of a statistical enquiry and illustrated it with the appropriate diagrams, graphs and charts, using ICT as appropriate. ^ was able to successfully justify ~ choice of what ^ had decided to present.
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