NUMBER - LEVEL 3. Understand place value in numbers up to Round numbers up to Know where to put a decimal point

Transcription

1 NUMBER - LEVEL 3 Understand place value in numbers up to 1000 Round numbers up to 1000 Know where to put a decimal point Add numbers with two digits mentally Add numbers with three digits on paper Subtract numbers with two digits mentally Subtract numbers with three digits on paper

2 NUMBER - LEVEL 3 Recognise negative numbers Use negative numbers on a thermometer Recall (mentally) facts to 20 (addition and subtraction) to solve larger problems Know the 2, 3, 4, 5 and 10 times tables Use the knowledge of the 2, 3, 4, 5 and 10 times table when dividing Do whole number multiplication and division including remainders Use fractions such as ¾ Recognise when two simple fractions are equivalent

3 SHAPE - LEVEL 3 Classify 3-D and 2-D shapes in various ways using mathematical properties Reflective symmetry for 2-D shapes Use non-standard units Use standard metric units of length in a range of contexts Use standard metric units of capacity in a range of contexts Use standard metric units of mass in a range of contexts Use standard units of time, in a range of contexts

4 HANDLING DATA - LEVEL 3 Extract information presented in simple tables and list Interpret information presented in simple tables and lists Construct simple bar charts Interpret simple bar charts Gather information Construct pictograms, where the symbol represents a group of units Interpret pictograms, where the symbol represents a group of units

5 NUMBER - LEVEL 4 I can add decimals to three decimal places I can subtract decimals to three decimal places Know when answers are wrong because of the size of the answer Know what ½,1/10,1/4 etc. are Know what 10%,25%,50%,75% and 100% means

6 NUMBER - LEVEL 4 Know what a multiple is Know what a square number is Know what a triangle number is Know what a factor is Know what a prime number is Know what a prime factor is

7 NUMBER - LEVEL 4 Know the quick way of multiplying a number by 10 or 100 Know the times tables; 6 7, 8 and 9 Know how to divide using the times tables I can add and subtract in my head I can multiply and divide in my head I can add whole numbers on paper I can subtract whole numbers on paper

8 ALGEBRA - LEVEL 4 I can recognise a number sequence Use simple formulae expressed in words Plot co-ordinates in the first quadrant

9 SHAPE - LEVEL 4 Make 3-D mathematical models by linking given faces or edges Draw common 2-D shapes in different orientations on grids Reflect simple shapes in a mirror line Choose and use appropriate units and instruments Interpret accurately numbers on a range of measuring instruments Find perimeters of simple shapes Find areas by counting squares

10 HANDLING DATA - LEVEL 4 Collect discrete data and record them using a frequency table Understand and use the mode and range to describe sets of data Group data, where appropriate, in equal class intervals Represent collected data in frequency diagrams Interpret frequency diagrams Construct simple line graphs Interpret simple line graph

11 NUMBER - LEVEL 5 Multiply whole numbers by 10, 100 and 1000 Multiply decimals by 10, 100 and 1000 Divide whole numbers 10, 100 and 1000 Divide decimals by 10, 100 and 1000 Order negative numbers because I know the answer to "Which is colder 3 or 5?" Find the difference between negative numbers such as 6 and 10 Know what the temperature will be when it has risen or fallen

12 NUMBER - LEVEL 5 Divide my three-digit number by any two-digit number Solve simple problems involving direct proportion Multiply any three-digit number any two-digit number Check solutions by applying inverse operation Estimate using approximations

13 NUMBER - LEVEL 5 I can add decimals to two places I can subtract decimals to two places I can multiply decimals to two places I can divide decimals to two places Reduce fractions Calculate fractional parts of quantities and measurements Calculate percentage parts of quantities and measurements

14 ALGEBRA - LEVEL 5 Construct formulae using symbolic form with one operation Construct formulae using symbolic form with two operations Write formulae involving one operation using the laws of algebra Write formulae involving two operations using the laws of algebra Use simple formulae involving one operation Use simple formulae involving two operations Use brackets appropriately Plot co-ordinates in all four quadrants Read co-ordinates in all four quadrants

15 SHAPE - LEVEL 5 When constructing models, measure and draw angles to the nearest degree When drawing or using shapes, measure and draw angles to the nearest degree Use language associated with angle Know the angle sum of a triangle and that of angles at a point Know the angle sum of angles at a point

16 SHAPE - LEVEL 5 Identify all the symmetries of 2-D shapes Know the rough metric equivalent of imperial units still in daily use Convert one metric unit to another Make sensible estimates of a range of measures in relation to everyday situations Understand and use the formula for the area of a rectangle

17 DATA HANDLING - LEVEL 5 Understand and use the mean of discrete data Compare two simple distributions, using the range and mode, mean Compare two simple distributions, using the range and the median Interpret graphs and diagrams, including pie charts, and draw conclusions Understand and use the probability scale from 0 to 1 Use equally likely outcomes to calculate probability Understand that different outcomes may result from repeating an experiment

18 NUMBER - LEVEL 6 Order and approximate decimals when solving numerical problems and equations (for example x - x = 20) Use trial and improvement methods Find one number as a fraction of another Find one number as a percentage of another Find the equivalence between fractions and decimals Find the equivalence between fractions and percentages Find the equivalence between decimals and percentages Calculate using ratios Add and subtract fractions by writing them with a common denominator

19 ALGEBRA - LEVEL 6 Find and describe in words the rule for the next term of a sequence where the rule is linear Find and describe in words the rule for the nth term of a sequence where the rule is linear Formulate and solve linear equations with whole number coefficients Represent mappings expressed algebraically Use co-ordinates for graphical representation Interpret general features of graph drawn from equations

20 SHAPE - LEVEL 6 Know the properties of quadrilaterals in classifying types of quadrilaterals Recognise and use common 2-D representations of 3-D objects Use the properties of quadrilaterals to classifying different types of quadrilaterals Solve problems using angle properties of polygons and explain these properties Solve problems using symmetry properties of polygons and explain these properties Solve problem angle properties of parallel lines and explain these properties Devise instructions for a computer to generate and transform shapes and paths when solving problems

21 SHAPE - LEVEL 6 Understand formulae for finding circumference of a circle. Use appropriate formulae for finding circumferences of circles when solving problems Understand and use appropriate formulae for areas of circles when solving problems Understand and use appropriate formulae for finding areas of squares, rectangles, trapezium and parallelograms. Understand and use appropriate formulae for finding volumes of cuboids when solving problems Enlarge shapes by a positive whole-number scale factor

22 HANDLING DATA - LEVEL 6 Collect and record continuous data choosing appropriate equal class intervals over a sensible range to create frequency tables Construct frequency diagrams Interpret frequency diagrams Construct pie charts Draw conclusions from scatter diagrams, having a basic understanding of correlation Identify all the outcomes when dealing with a combination of two experiments In solving problems, use knowledge that the total probability of all the mutually exclusive outcomes of an experiment is 1

23 NUMBER - LEVEL 7 In making estimates, round to one significant figure and multiply In making estimates, round to one significant figure and divide mentally Understand the effects of multiplying by numbers between 0 and 1 Understand the effects of dividing by numbers between 0 and 1

24 NUMBER - LEVEL 7 Solve numerical problems involving multiplication using a calculator with numbers of any size efficiently and appropriately Solve numerical problems involving division using a calculator with numbers of any size efficiently and appropriately Understand and use proportional changes Calculate the result of any proportional change using only multiplicative methods

25 ALGEBRA - LEVEL 7 Find the next term of a sequence where the rule is quadratic Find and describe in symbols the next term of a sequence where the rule is quadratic Find and describe in symbols the nth term of a sequence where the rule is quadratic Multiply out and simplify two brackets such as (x + a)( x + b) Use graphical methods to solve simultaneous linear equations in two variables Use algebraic methods to solve simultaneous linear equations in two variables Solve simple inequalities

26 SHAPE - LEVEL 7 Understand and apply Pythagoras' theorem when solving problems in two dimensions Calculate lengths in plane shapes and right prisms Calculate areas in plane shapes and right prisms Calculate volumes in plane shapes and right prisms Understand and use compound measures, such as speed

27 SHAPE - LEVEL 7 Enlarge shapes by a fractional scale factor Appreciate the similarity of enlarged shapes Determine the locus of an object moving according to a rule Appreciate the imprecision of measurement Recognise that a measurement given to the nearest whole number may be inaccurate by up to one half in either direction

28 HANDLING DATA - LEVEL 7 Specify hypotheses and test them by designing and using appropriate methods that take account of variability or bias Draw a line of best fit on a scatter diagram, by inspection Understand relative frequency as an estimate of probability Use relative frequency to compare outcomes of experiments

29 HANDLING DATA - LEVEL 7 Determine the modal class of grouped data Estimate the mean of sets of grouped data Estimate the median of sets of grouped data Estimate the range of sets of grouped data Use the measures of average and range to compare distributions and make inferences

30 NUMBER - LEVEL 8 Solve problems involving calculating with powers Solve problems involving calculating roots Solve problems involving numbers expressed in standard form checking for correct order of magnitude Choose to use fractions or percentages to solve problems involving repeated proportional changes Calculate the original quantity given the result of a proportional change

31 ALGEBRA - LEVEL 8 Evaluate algebraic formulae Evaluate algebraic formulae substituting fractions Evaluate algebraic formulae substituting decimals Evaluate algebraic formulae substituting negative numbers Calculate one variable, given the others, in formulae such as V = πr 2

32 ALGEBRA - LEVEL 8 Manipulate algebraic formulae, equations and expressions. Find common factors Multiply two linear expressions Know that a 2 b 2 = (a + b) (a b) Solve inequalities in two variables

33 ALGEBRA - LEVEL 8 Sketch and interpret graphs of linear functions Sketch graphs of quadratic functions Interpret graphs of quadratic functions Sketch graphs of cubic functions Interpret graphs of cubic functions Sketch graphs of reciprocal functions Interpret graphs of reciprocal functions Sketch graphs that model real situations Interpret graphs that model real situations

34 SHAPE - LEVEL 8 Understand and use congruence and mathematical similarity Use sine, cosine and tangent in right-angled triangles when solving problems in two dimensions Distinguish between formulae for perimeter, area and volume, by considering dimensions

35 HANDLING DATA - LEVEL 8 Interpret cumulative frequency tables and diagrams, using the upper boundary of the class interval Construct cumulative frequency tables using the upper boundary of the class interval Construct cumulative frequency diagrams, using the upper boundary of the class interval Estimate the median from cumulative frequency diagrams Use median / interquartile range to compare distributions and make inferences Understand how to calculate the probability of a compound event and use this in solving problems

36 NUMBER - EXTENDING LEVEL 8 Understand and use rational numbers Understand and use irrational numbers Determine the bounds of intervals Understand and use direct proportion Understand and use inverse proportion

37 ALGEBRA - EXTENDING LEVEL 8 In simplifying algebraic expressions, use rules of indices for negative values In simplifying algebraic expressions, use rules of indices for fractional values In finding formulae that approximately connect data, express general laws in symbolic form Solve simultaneous equations in two variables where one equation is linear and the other is quadratic Solve problems using intersections of graphs Solve problems using gradients of graphs

38 SHAPE - EXTENDING LEVEL 8 Sketch the graph of the sine function for any angle Generate and interpret graphs based on sine function Sketch the graph of the cosine function for any angle Generate and interpret graphs based on cosine function Sketch the graph of the tangent function for any angle Generate and interpret graphs based on the tangent function

39 SHAPE - EXTENDING LEVEL 8 Use sine, cosine and tangent of angles of any size when solving problems in two and three dimensions Use Pythagoras' theorem when solving problems in 2-D and 3-D Use the conditions for the congruent triangles in formal geometric proofs Calculate lengths of circular arcs and areas of sectors Calculate the surface area of cylinders Calculate volumes of cones and spheres Appreciate the continuous nature of scales that are used to make measurements

40 HANDLING DATA - EXTENDING LEVEL 8 Interpret histograms Construct histograms Understand how different methods of sampling and different sample sizes may affect the reliability of conclusions drawn Select and justify a sample and method to investigate a population Recognise when and how to work with probabilities associated with independent mutually exclusive events