MATHS LEVEL DESCRIPTORS
Number
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.
Shape, Space and Measures
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.
Handling Data
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
Algebra
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.
