# MATHS LEVEL DESCRIPTORS

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### Level 3

•• Understand the place value of numbers up to thousands. Order numbers up to 9999. • Round numbers to the nearest 10 or 100.

• Understand the number line below zero, and relate this to temperature. • Know the 2,3,4,5, and 10 times tables and the related division facts. • Divide numbers by 2,3,4,5 and 10 which give a remainder. • Recognise one half and one quarter of a diagram or number.

• Write amounts of money in £ using a decimal point and understand the value of each digit. • Use a calculator to solve simple problems involving money and real-life situations.

### Level 4

•• Read and write whole numbers in figures and in words and kn9ow what each digit represents, up to 1 million. Understand decimal notation for tenths and hundredths. • Order numbers less than 1 million and numbers with the same number of decimal places.

• Round integers to the nearest 10, 100 or 1000 and numbers with 1 or 2 decimal places to the nearest integer. • Know the multiplication tables to 10 x 10 and the related division facts.

• Multiply and divide whole numbers by 10 and 100.

• Begin to use brackets in calculations.

• Use fraction notation, including mixed numbers, and vocabulary numerator and denominator. • Order a set of fractions and position them on a number line.

• Change an improper fraction to a mixed number and recognize simple equivalent fractions, including tenths and hundredths. • Add and subtract simple fractions and those with the same denominator.

• Find one tenth and one hundredth of numbers and quantities.

• Begin to understand % as the number of parts in every 100.

• Add and subtract integers and decimals with the same number of decimal places. • Extend written methods to TU x TU and HTU divided by U.

### Level 5

•• Understand decimal notation for tenths, hundredths and thousandths. Order numbers and measurements with up to 3 decimal places. • Round a number with two decimal places to the nearest tenth or whole number. • Round up or down after division depending on the context.

• Order, add and subtract negative numbers.

• Multiply whole numbers and decimals by 10, 100 and 1000. • Use brackets in calculations.

• Order fractions by converting them to a common denominator and position them on a number line. • Change an improper fraction to a mixed number and vice-versa.

• Reduce a fraction to its simplest form.

• Calculate fractional or percentage parts of quantities and measurements, using a calculator where appropriate. • Use decimal notation for tenths, hundredths and thousandths.

• Multiply and divide a three-digit number by a two-digit number without using a calculator. • Add, subtract, multiply and divide decimal numbers with up to two decimal places. • Solve simple problems involving ratio and direct proportion.

### Level 6

•• Round numbers to any power of 10 and to two decimal places. Multiply and divide by powers of 10.

• Compare numbers and evaluate one number as a fraction or percentage of another. • Add and subtract fractions and different denominators.

• Divide a fraction by an integer.

• Order and approximate decimals when solving problems. • Calculate percentage increase and decrease.

• Understand and be able to use the equivalences between fractions, decimals and percentages.

• Multiply integers and decimals and understand where to position the decimal point. • Use ratios in appropriate situation.

### Level 7

•• Round numbers to one significant figure and multiply and divide mentally. Understand the affects of multiplying by a number between 0 and 1. • Multiply and divide decimals by writing as equivalent problems involving integers.

• Use percentages to solve problems.

• Solve numerical problems involving multiplication and division with numbers of any size. • Understand and use proportional changes.

• Use a calculator efficiently and appropriately.

### Level 8

• Use powers or roots, with numbers expressed in standard form, to solve problems, checking that the answers are of the correct order of magnitude.

• Choose fractions or percentages to solve problems involving repeated proportional changes or the calculation of the original

quantity given the result of a proportional change.

• Evaluate algebraic formulae, substituting fractions, decimals and negative numbers. • Calculate one variable, given the others in a formulae.

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### Level 3

•• Know the names of some 2D polygons, a circle, some 3D solids and a sphere. Know how many edges, faces and vertices (corners) there are on a cube. • Recognise reflective (line) symmetry in simple pictures.

• Recognise and describe simple translations and rotations of shapes.

• Recognise the 4 compass directions, right angles and clockwise and anticlockwise turns. • Read scales where divisions are 1,2,5,10, 100 or one half.

• Draw and measure lines in whole cm accurately.

• Know commonly used units for money, time, length, mass and capacity.

### Level 4

•• Classify triangles. Identify and recognize the properties of rectangles.

• Recognise a 3D shape from a 2D drawing and identify linking edges and vertices. • Identify nets of a cube.

• Recognise reflective (line) symmetry, especially in regular polygons. • Reflect shapes in a mirror line parallel to one side.

• Make patters from rotating shapes.

• Recognise where a shape will be after a translation.

• Find the perimeter of simple shapes, areas by counting squares and volumes by counting cubes. • Use the formula in words for the area of a rectangle.

• Recognise directions and parallel perpendicular lines.

• Identify and estimate acute and obtuse angles.

• Understand degrees and measure acute and obtuse angles to the nearest five degrees. • Calculate missing angles on a straight line.

• Choose appropriate measuring instruments and units and measure accurately from a variety of scales. • Convert larger to smaller units of length, mass and capacity.

• Read the time on a 24 hour digital clock.

### Level 5

•• Classify quadrilaterals. Draw 3D shapes on an isometric grid. • Draw nets for 3D shapes.

• Construct triangles from given information.

• Recognise reflective and rotational symmetry in 2D shapes.

• Recognise where a shape will be after reflection in a line not parallel to a side, or in two mirrors at right angles to each other. • Recognise where a shape will be after a 90 degree rotation about a vertex (corner).

• Calculate the perimeter of rectangles and simple compound shapes. • Understand and be able to use the formula for the area of a rectangle. • Calculate the area of a shape formed from rectangles.

• Calculate the volume of a cuboid.

• Measure acute and obtuse angles to the nearest degree and know the language associated with angle. • Calculate missing angles in a triangle and around a point.

• Make a sensible estimate of a range of measures in relation to everyday situations.

• Convert between metric units of length, mass and capacity.

• Know the rough metric equivalents of imperial units in common use.

### Level 6

•• Know the properties of quadrilaterals and be able to recognize quadrilaterals from their properties. Recognise common 2D representations of 3D objects.

• Draw constructions using a ruler and pair of compasses. (Eg. Mid-point and perpendicular bisector of a straight line and the

bisector of an angle).

• Draw plans and elevations.

• Enlarge 2D shapes by a positive whole-number scale factor.

• Transform 2D shapes by a combination of reflection, rotations or translations.

• Use angle and symmetry properties of polygons and properties of intersecting and parallel lines to solve problems. • Calculate the area of a triangle, parallelogram and trapezium using appropriate formulae.

• Calculate the surface area of cuboids.

• Understand and use the formulae for finding the circumference and area of circles. • Calculate three-figure bearings.

### Level 7

•• Recognise planes of symmetry in 3D shapes. Find the scale factor that produces an enlargement that is smaller than the original shape. • Enlarge a shape by a scale factor between 0 and 1 or by a negative scale factor.

• Calculate lengths, areas and volumes in plane shapes. • Calculate the surface area and volume of a prism.

• Understand and be able to apply Pythagoras’ theorem when solving problems in two dimensions. • Determine the locus of an object moving according to some rule.

• Know that measurements is continuous and that measures given to the nearest whole number can be in error by up to one half a

unit.

• Use compound measures such as speed.

### Level 8

•• Understand congruence. Understand and use mathematical similarity.

• Distinguish between formulae for perimeter, area and volume by considering dimensions. • Use sine, cosine and tangent in right-angled triangles when solving problems in two dimensions.

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### Level 3

• Interpret simple bar charts and pictographs.

• Read information from a Venn diagram and a Carroll diagram.

• Carry out a survey and collect data in a tally chart.

### Level 4

• Present and interpret data on a bar chart, bar line graph and line graph. • Construct simple line graphs.

• Group data and represent this in a frequency diagram. • Collect discrete data and record it in a table.

• Find the mode of a set of data.

• Use the mode and median of a set of data. • Know what the range of a set of data is.

• Understand the use simple words associated with probability, such as “fair”, “certain” and “likely”.

### Level 5

• Interpret graphs and diagrams, including pie charts. • Present and interpret grouped discrete data on a bar chart.

• Find the mean, median, mode and range of a set of data.

• Use the range and one of the averages to compare two sets of data. • Understand and be able to use the probability scale from 0 to 1.

• Know the different outcomes may result from repeating the same experiment.

• Find and justify probabilities using either experimental evidence or theoretical probabilities.

### Level 6

• Construct pie charts.

• Draw scatter diagrams and understand correlation.

• Collect and record continuous data, choosing appropriate class intervals, and create frequency diagrams. • Calculate the mean for a set of data using an assumed mean.

• When dealing with two experiments, identify all the outcomes and show them in diagrammatic or tabular form. • Know that the total probability of all the mutually exclusive events of an experiment is 1 and use this to solve problems.

### Level 7

• Draw a line of best fit on a scatter diagram by eye.

• Specify a hypothesis and test it by designing an appropriate survey sheet or experiment that takes bias into account.

• Select the most6 appropriate statistic for your line of enquiry.

• Find the model class and estimate the mean, median and range of sets of grouped data.

• Compare two distributions using the measures of average and range and draw the associated polygons. • Understand relative frequency as an estimate of probability and use it to compare the outcomes of experiments.

### Level 8

• Interpret and construct cumulative frequency tables and diagrams, using the upper boundary of the class interval. Be able to

estimate the median and inter-quartile range and use these to compare distributions and make inferences.

• Understand when to apply the methods for calculating the probability of a compound event, given the probabilities of either

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### Level 3

• Recognise patterns of numbers, eg. 14, 24, 34, 44. • Recognise odd and even numbers.

### Level 4

• Explore and describe number patterns.

• Recognise multiples, factors and square numbers.

• Know and apply tests of divisibility for dividing by 2, 4, 5, 10 and 100. • Use co-ordinates in the first quadrant.

• Solve simple equations involving one stage. • Use simple formulae expressed in words.

### Level 5

• Recognise prime numbers to at least 20 and find common multiples. • Factorise numbers to 100 into prime numbers.

• Know and apply tests of divisibility for dividing by 2, 3, 4, 5, 6, 8, 9, 10 and 100. • Read and plot co-ordinates in all four quadrants.

• Generate co-ordinates from a simple linear rule and plot the graphs of simple functions, where y is given in terms of x.

• Simplify expressions and expand brackets. • Solve simple equations involving two stages.

• Use mathematical symbols to write down a formula or rule. • Check your answers by working backwards and by approximating.

### Level 6

• Find the LCM and HCF of two or more numbers. • Find the prime factor decomposition of any number.

• Give a rule for the term of a number pattern where the pattern increases by a fixed amount each term. • Express a mapping algebraically and interpret the general features of linear graphs.

• Sketch graphs of real-life situations.

• Expand and simplify brackets with variables on the outside.

• Substitute into formulae involving squares and square roots, or more than one variable. • Solve equations where the solution is not a whole number or where the variable is on both sides.

• Set up and solve linear equations, and use algebra in problems.

### Level 7

• Use prime factors to find the LCM and HCF of two numbers. • Use the rules of indices for powers.

• Find the inverse of a function.

• Be able to give a rule for the next term or the term of a number pattern where the rule is quadratic. • Represent average speed on a distance-time graph.

• Expand an expression such as (x 2) (x3) abd factorise simple expressions.

• Use a calculator to estimate square roots and cube roots and to solve equations by trial and improvement. • Solve simple inequalities and linear equations with negative signs anywhere in the equation.

• Solve simult6aneous equations algebraically and graphically.

### Level 8

• Sketch and interpret graphs of linear, quadratic, cubic and reciprocal functions, and graphs that model real situations. • Manipulate algebraic formulae, equations and expressions, finding common factors and multiplying twp linear expressions. • Solve inequalities in two variables.

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## References

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Related subjects : Level Descriptors