KEY STAGE THREE MATHEMATICS
LEVEL 3
USING AND APPLYING
Tries different approaches to solving problems as difficulties arise.
Begins to organise work and check results.
Discusses work and begins to explain their thinking.
Uses and interprets mathematical symbols and diagrams.
Can show understanding of a general statement by finding particular examples that match.
NUMBER AND ALGEBRA
Understands place value up to 1 000.
Can use decimal notation for money and tenths.
Recognises and uses negative numbers in context of temperature.
Can add and subtract, two digit numbers, mentally.
Can add/subtract three digit numbers on paper.
Mentally recalls 2, 3, 4, 5, & 10 times table and can use these to derive answers to divisions.
Solves whole number problems involving multiplication and division, including remainders.
Uses fractions as parts of a whole.
Recognises equivalent fractions.
SHAPE AND SPACE
Classifies and knows the names of two and three dimensional shapes.
Can identify reflection symmetry in shapes.
Can use standard metric units in context and convert between them.
Can use units of time to solve problems.
HANDLING DATA
Can extract and interpret information from lists and tables.
Can draw bar charts and pictograms (including when a symbol represents a group).
Can draw up lists and tables and simple graphs from their own gathered data
KEY STAGE THREE MATHEMATICS
LEVEL 4
USING AND APPLYING
Begins to use own strategies to solve problems.
Uses strategies to solve problems in mathematics and in application to practical contexts.
Presents information in a clear and organised way.
Use own ideas in searching for solutions to problems.
NUMBER AND ALGEBRA
Can multiply and divide whole numbers by 10 and 100.
Can mentally recall multiplication/division facts up to 10 by 10.
Can add /subtract any values efficiently without a calculator.
Can multiply/divide by a single digit efficiently without a calculator.
Can add/subtract decimals up to two decimal places.
Can put three decimal place numbers in order of size.
Can check the reasonableness of their answers.
Uses simple fractions or percentages to estimate or accurately describe proportional diagrams.
Recognises and describes simple number patterns.
Knows and understands the terms factor, multiple and square.
Can use formulae expressed in words and diagrams.
Can plot and label co-ordinates in the first quadrant.
SHAPE AND SPACE
Can make models from multi-link etc.
Can draw squares, rectangles, triangles, etc.
Can reflect shapes in mirror lines.
Chooses appropriate instruments to draw and measure approximating appropriately.
Can find perimeters.
Can find areas of rectangles and squares by counting.
HANDLING DATA
Can collect data by counting (discrete) and enter it into a frequency table.
Can find the mode and the range.
Can group data together into equal class intervals.
Can draw and interpret line graphs and frequency diagrams.
KEY STAGE THREE MATHEMATICS
LEVEL 5
USING AND APPLYING
Identifies and gathers necessary information to carry through tasks and solve problems.
Checks results and whether the results make sense.
Shows understanding of mathematical situations by representing/describing them with words, symbols and
diagrams.
Draws simple conclusions with simple explanations of their reasoning.
NUMBER AND ALGEBRA
Can divide and multiply whole numbers and decimals by 10, 100, 1 000.
Can order, add and subtract negative numbers.
Can multiply, divide, add and subtract numbers with up to two places of decimals.
Can cancel fractions into their simplest form.
Can calculate fractions and percentages of amounts.
Can solve simple ratio and direct proportion problems.
Can multiply and divide any three digit number by a two digit number.
Can check solutions using inverse operations and approximations.
Can construct and use simple formulae and equations/flow diagrams with one or two operations.
Uses brackets appropriately.
Plots, interprets, and writes co-ordinates with negative values.
SHAPE AND SPACE
Can measure and draw angles to the nearest degree.
Knows acute, reflex, obtuse & right angle.
Knows angles in a triangle add up to 180 degrees.
Knows angles around a point sum to 360 degrees.
Can find line and rotation symmetry in 2D shapes.
Knows roughly how many kilometres in a mile, cm in an inch/foot, kilograms in a pound, litres in a
pint/gallon.
Can change: km into m and cm and mm; kilograms into grams; cc's into litres.
Can estimate: lengths and weights; volumes and areas.
Can use the an area formulae for a rectangle.
HANDLING DATA
Can calculate and understand the use of the mean of a set of numbers.
Can compare sets of data using range and one measure of average - mean, median or mode.
Can read bar charts, graphs & pie charts and draw conclusions.
Can understand and use the probability scale from 0 to 1.
Can write probabilities as fractions using equally likely outcomes/lists.
Understands different outcomes will happen when you repeat the same experiment.
KEY STAGE THREE MATHEMATICS
LEVEL 6
USING AND APPLYING
Carries through substantial tasks involving complex problems by independently breaking them down into smaller
manageable tasks.
Interprets discuss and synthesises information presented in a variety of mathematical forms.
Explains and informs through writing, their use of symbols and diagrams.
Begins to give mathematical justifications in and for solutions.
NUMBER AND ALGEBRA
Can approximate decimals and put decimals in order of size.
Can solve numerical problems with decimal answers by trial and improvement.
Can compare one number as a fraction or percentage of another number.
Understands the relationship between fractions, decimals and percentages.
Can solve problems by calculating numbers in the correct ratio.
Can add and subtract fractions by writing them with the same denominator.
Can find rules for number patterns, to find next and nth term.
Can write and solve linear equations with whole number coefficients.
Can draw lines to represent linear equations, by finding pairs of co-ordinates.
Can draw graphs to represent situations and interpret general features.
SHAPE AND SPACE
Can recognise solid shapes by their pictures (3D shapes recognised in 2D pictures).
Knows all the four-sided shapes and their properties.
Solves problems using, symmetry and angles from intersecting/parallel lines.
Can devise instructions to change shapes and journeys.
Knows and uses circle formulae for area and circumference.
Can find areas of compound shapes made up of triangles and rectangles.
Can find volumes of cuboids.
Can enlarge shapes by positive, whole number, scale factors.
HANDLING DATA
Can collect and record heights/weights etc., (continuous data) choosing correct class intervals.
Can construct and interpret frequency tables and diagrams.
Can calculate angles from data to construct pie charts.
Can interpret pie charts.
Can draw scatter diagrams and interpret in terms of correlation.
Can find all outcomes of two combined events and record them using co-ordinate /tree diagrams.
Understands and uses the knowledge of combined probabilities equalling 1, to solve problems.
KEY STAGE THREE MATHEMATICS
LEVEL 7
USING AND APPLYING
Begins to refine and extend work to generate fuller solutions.
Gives reasons for choice of mathematical presentations and explains selected features.
Shows some insight into the mathematical structure of problems, through justifying their arguments and
generalisations.
Appreciates the difference between mathematical explanation (proof) and experimental evidence
(examples that show a rule works).
NUMBER AND ALGEBRA
Can make estimates by rounding to significant figures.
Can multiply and divide mentally, three-figure numbers by one digit numbers.
Understands the effect of multiplying/dividing by numbers between zero and one.
Can use a calculator effectively and efficiently, to solve problems with numbers of any size.
Can solve complicated equations/problems.
Understands and uses multiplicative methods in solving proportional problems.
Can find and describe the next term or nth term of a quadratic sequence.
Can expand brackets like (a + n) (a – t) and simplify the quadratic result
Can solve simultaneous equations in two unknowns, using algebraic and graphical methods.
Can understand, draw and solve simple inequalities (< , >)
SHAPE AND SPACE
Can understand apply Pythagoras' theorem in 2D problems.
Can calculate lengths, areas, volumes with/without formulae.
Can enlarge shapes by fractional scale factors.
Understands similarity and congruence.
Can find the locus of a point according to a rule.
Appreciates the imprecision of measurement.
Can round values to decimal places/significant figures and understands boundaries.
Can use and understand compound measures like speed and density.
HANDLING DATA
Can write hypotheses and test them by designing appropriate experiments/questionnaires that take
account of variability and bias.
Can determine the modal class, and estimate the median, mean and range of a set of grouped data.
Can select the most appropriate values to use to compare; frequency polygons; tables; distributions.
Can draw a line of best fit on a scatter diagram.
Understands relative frequency from an experiment as an estimate of probability, and can use it to
compare outcomes of experiments.
KEY STAGE THREE MATHEMATICS
LEVEL 8
USING AND APPLYING
Develops and follows alternative approaches to problem solving.
Reflects on their own lines of enquiry, bringing into play a range of mathematical techniques.
Conveys mathematical or statistical meaning, through precise and consistent use of symbols.
Examines generalisations and comments on the logic or processes, involved in arriving at a solution/generalisation
- using this to develop an enquiry or solution further.
NUMBER AND ALGEBRA
Can solve problems involving calculations with powers, square roots, and standard form.
Can check for the correct order of magnitude of large and small numbers in standard form.
Can use fractions and percentages to make repeated proportional changes, in one calculation.
Can find an original amount after a described, proportional change has been made.
Can evaluate algebraic expressions, including the substitution of fractions negative numbers and decimals.
Can calculate the value of one variable in a formula given the others e.g. V = ∏r2 h
Can rearrange formulae with squares and square roots.
Can multiply out double brackets and factorise.
Can use and recognise the difference of two squares.
Can solve inequalities in two variables.
Can sketch graphs of quadratic, cubic, and reciprocal functions and graphs modelling real life situations.
SHAPE AND SPACE
Can understand and use mathematical congruence and similarity.
Can use sine, cosine and tangent in right-angled triangles and in solving 2D problems.
Can distinguish between formulae for length, area and volume, by considering dimensions.
HANDLING DATA
Can draw cumulative frequency diagrams for grouped data.
Can estimate median and inter-quartile range and use them to compare and describe distributions.
Can make inferences from data.
Can calculate probabilities of compound events, using tree diagrams.