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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 4 Using and applying mathematics objectives
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^ was able to solve one-step and two-step problems involving numbers, money or measures, including time.
^ can choose and carry out appropriate calculations, using calculator methods where appropriate
^ is able to represent a puzzle or problem using number sentences, statements or diagrams.
^ can use a wide range of informal skills to solve problems. When ^ was solved a problem, ^ can present and interpret the solution in the context of the problem.
^ has suggested a line of enquiry and the strategy needed to follow it. ^ was successful in collecting, organising and interpreting ~ selected information to ~ bid to find the answers.
^ can identify and use patterns, relationships and properties of numbers or shapes.
^ has investigated a statement involving numbers and tested it with examples.
^ is able to report solutions to puzzles and problems, giving ~ own explanations and reasoning orally and in writing, using both diagrams and symbols.
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.
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Counting
Year 4 Counting and understanding number objectives
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^ recognise and continues number sequences formed by counting on or back in steps of constant size.
^ can partition, round and order four-digit whole numbers.
^ has used positive and negative numbers in context and position them on a number line.
^ can state inequalities using the symbols < and > (e.g. -3 > -5, -1 < plus1).
^ can use decimal notation for tenths and hundredths and partition decimals.
^ has related the notation of decimals to money and measurement.
^ was successful in positioning one-place and two-place decimals on a number line.
^ can recognise the equivalence between decimal and fraction forms of one half, quarters, tenths and hundredths.
^ is able to use diagrams to identify equivalent fractions (e.g. six eighths and three quarters, or seventy hundredths and seven tenths).
^ has interpreted mixed numbers and positioned them on a number line (e.g. 3 one half)
^ can use the vocabulary of ratio and proportion to describe the relationship between two quantities (e.g. 'There are 2 red beads to every 3 blue beads, or 2 beads in every 5 beads are red').
^ has experienced estimating a proportion (e.g. 'About one quarter of the apples in the box are green').
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.
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Number facts
Year 4 Knowing and using number facts objectives
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^ can use ~ knowledge of addition and subtraction facts and place value to derive sums and differences of pairs of multiples of 10, 100 or 1000.
^ has identified the doubles of two-digit numbers. ^ can use this knowledge to calculate doubles of multiples of 10 and 100 and derive their corresponding halves.
^ has derived and recalled multiplication facts up to 10 × 10, the corresponding division facts and multiples of numbers to 10 up to the tenth multiple.
# can identify pairs of fractions that total 1.
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.
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Calculating
Year 4 Calculating objectives
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^ is able to add or subtract mentally pairs of two-digit whole numbers (e.g. 47 + 58, 91 - 35).
^ has refined and used efficient written methods to add and subtract two-digit and three-digit whole numbers and with money.
^ can multiply and divide numbers to 1000 by 10 and then 100 (whole-number answers), understanding the effect.
^ can relate to scaling up or down a number.
^ has developed and used written methods to record, support and explain multiplication and division of two-digit numbers by a one-digit number, including division with remainders (e.g. 15 × 9, 98 ÷ 6).
^ is able to find fractions of numbers, quantities or shapes (e.g. one fifth of 30 plums, three eighths of a 6 by 4 rectangle).
^ is able to use a calculator to carry out one-step and two-step calculations involving all four operations. In addition, ^ can recognise negative numbers in the display, correct ~ mistaken entries and interpret the display correctly in the context of money.
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.
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Shapes
Year 4 Understanding shape objectives
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^ was able to draw polygons and classify them by identifying their properties, including their line symmetry.
^ can visualise 3-D objects from 2-D drawings.
^ has made nets of common solids.
^ recognise horizontal and vertical lines.
^ can use the eight compass points to describe direction.
^ is able to describe and identify the position of a square on a grid of squares.
^ know that angles are measured in degrees and that one whole turn is 360°.
^ has compared and ordered angles less than 180°
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.
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Measuring
Year 4 Measuring objectives
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^ can choose and use standard metric units and their abbreviations when estimating, measuring and recording length, weight and capacity.
^ knows the meaning of 'kilo', 'centi' and 'milli' and, where appropriate, ^ has use decimal notation to record measurements (e.g. 1.3 m or 0.6 kg).
^ is able to interpret intervals and divisions on partially numbered scales and record readings accurately, where appropriate to the nearest tenth of a unit.
^ has draw rectangles and measured and calculated their perimeters. During these activities, ^ also found the area of rectilinear shapes drawn on a square grid by counting the internal number of squares.
^ is able to read time to the nearest minute.
^ can use am, pm and 12-hour clock notation.
^ knows the appropriate units of time to measure time intervals.
^ has calculated time intervals from clocks and timetables.
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.
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Handling Data
Year 4 Handling data objectives
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# can answer a question by identifying what data ^ needs to collect.
^ has organised, presented, analysed and interpreted ~ data in tables, diagrams, tally charts, pictograms and bar charts, using ICT where appropriate.
^ is able to compare the impact of representations where the scales have intervals of differing step sizes.
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.
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