Download Grades C-E - The John Warner School

Number
A grade E student can …
Multiply & divide a 2 digit by 2 digit number, including knowing when to round up or down.
Round a number to one significant figure
Add, subtract, multiply and divide negative integers
Add and subtract decimals up to 4 decimal places
Find one number as a fraction or a percentage of another
Do calculations with simple fractions involving addition & subtraction like 1/5 + 3/10
Find a fraction of a quantity
Order fractions and decimals
Calculate cubes and cube roots up to 5 cubed (with and without the use of a calculator)
Compare simple percentages, fractions and decimals
Simplify ratios – when given in same unit
Solve equations such as
x
 9 or 4x – 2 = 22
2
Geometry and Measures
Read from a conversion graphs
Write an expression from a problem
Substitute negative numbers into a simple formula
Use formulae from mathematics and other subjects
Plot the graphs of straight lines such as x = 3 and y = 4
Complete a table of values for equations such as y = 3x + 3 and draw the graph
Show that the angles of a triangle add up to 180° and use this to find angles
Show that an exterior angle of a triangle is equal to the sum of the interior opposite angles
Use angle properties of isosceles, equilateral and right-angled triangles
Find the area and perimeter of compound shapes made up of rectangles
Calculate interior and exterior angles of a quadrilateral
Investigate tessellations
Find the volume of a cube or cuboid
Find the height of a cuboid, given volume, length and breadth
Reflect shapes in the axes of a graph
Enlarge a shape by a positive scale factor (Not from centre of enlargement)
Find the measurements of the dimensions of an enlarged shape
Use map scales to find distance
Draw a triangle given three sides, or two angles and a side, or two sides and the included angle
Draw a cuboid on an isometric grid and mark its dimensions
Statistics
Algebra
Find a particular term in a sequence
Write the term-to-term rule in a sequence
Simplify expressions with more than one variable such as 2a + 5b + a – 2b
Draw lines such as x = 3 and y = x + 2
Compare the mean and range of two distributions
Calculate the ‘fx’ column for a frequency distribution
Construct and interpret a pie chart
Interpret a stem-and-leaf diagram
Complete and use two-way tables for discrete and grouped data
Understand the difference between experimental and theoretical probabilities
Understand and use simple relative frequency
Decide with a reason whether a simple statement is true or false
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Multiply and divide a 3 digit by 2 digit number
Estimate answers to calculations involving division by rounding
Use the terms square, positive and negative square root, cube and cube root
Recall integer squares from 2×2 to 15×15 and the corresponding square roots
Recall the cubes of 2, 3, 4, 5 and 10
Multiply and divide two decimals such as 2·4 × 0·7
Convert decimals to fractions and fractions to decimals
Do calculations with simple fractions involving addition and subtraction
Increase or decrease a quantity by a given percentage
Simplify ratios when given in different units and calculate with ratios - recipes
Multiply out expressions with brackets such as 5(3x – 2)
Factorise expressions such as 5x - 15
Write the terms of a sequence or a series of diagrams given the nth term
Draw lines such as y = 2x + 3
Solve linear equations with unknowns on each side such as 3x – 4 = 5 + x
Solve linear equations with brackets such as 2(5x + 1) = 28
Geometry & measures
Substitute numbers into more complicated formulae such as C  ( A  1)D
9
Solve problems involving graphs, such as finding where the line y = x + 5 crosses the line y = 1
Draw graphs of simple quadratic functions such as y = 2x2 and y = x2 + 2
Find the area of a triangle, parallelogram, kite and trapezium
Find the area and perimeter of compound shapes
Calculate the circumference & area of a circle including in terms of pi
Reflect shapes in lines such as x = 2 or y = –1
Rotate shapes about the origin
Describe fully reflections and rotations about the origin
Identify reflection symmetry in 3-D solids
Translate a shape using a description such as 4 units right and 3 units down
Enlarge a shape by a positive scale factor from a given centre
Draw and interpret distance time graphs
Calculate simple average speeds from distance–time graphs
Draw a quadrilateral such as a kite or a parallelogram with given measurements
Construct and recognise the nets of 3-D solids such as pyramids and triangular prisms
Draw plans and elevations of 3-D solids
Understand the idea of a locus
Measure and draw bearings
Statistics
Algebra
Number
A grade D student can …
Calculate the mean and the median for a frequency table
Construct a stem-and-leaf diagram (ordered)
Construct a frequency polygon
Draw a scatter graph by plotting points on a graph and describe the correlation
Classify and know the difference between various types of data
Design and use data collection sheets and questionnaires
Use a two-way table to find a probability
Understand mutually exclusive events
Use the fact that the probabilities of mutually exclusive events add up to 1
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Number
Find the least common multiple (LCM) and highest common factor (HCF) of two simple numbers
Write a number as a product of prime factors
Find the reciprocal of a number
Estimate answers to calculations by rounding to 1 significant figure
Understand the effects of multiplying by numbers between 0 and 1
Divide a number by a decimal such as 2·8 divided by 0·07
Work out any percentage increase or decrease
Add, subtract, multiply & divide fractions including mixed fractions
Solve ratio and proportion problems, such as Share a quantity in a given ratio
Solve ratio and proportion problems using the unitary method; best buys.
Algebra
Multiply out expressions with brackets such as y(3y – 8)
Factorise an expression into a single bracket such as 12a2 + 24a
Expand and simplify two expressions of the form (x + a)(x – b)
Use index notation and index laws for positive and negative powers
Write the nth term of a sequence or a series of diagrams
Solve linear equations, unknown both sides and with brackets and fractions
Find a solution to a problem by forming an equation and solving it (Usually related to geometry)
Solve equations such as x3 + x = 12 using trial and improvement methods to 1 d.p.
Rearrange linear formulae such as s = 4q - 7
Draw & interpret straight line graphs and recognise the equations of straight-line graphs
Draw graphs of harder quadratic functions such as y = x2 + 3x -5
Use graphs to find the approximate solutions of quadratic equations
Solve inequalities such as 3x < 9, 4x – 3 < 10 and 4x < 2x + 7 and 12 ≤ 3n < 20
Represent sets of solutions on the number line
Geometry & Measures
Solve problems involving circles by finding the area & perimeter of a semicircle, quarter circle
Solve problems involving surface area and volume of prisms and cylinders
Convert between measures of area and volume
Classify a quadrilateral by geometric properties
Solve problems using angle properties of polygons and properties of parallel lines
Calculate exterior and interior angles of a regular polygon
Find the midpoint of a line segment
Use and understand coordinates in three dimensions
Reflect shapes in the lines y = x, y = –x, y = a and x = k and fully describe a reflection
Rotate shapes about any point and fully describe a rotation
Translate a shape by a vector such as  4  and fully describe a translation
  3


Enlarge a shape by a positive scale factor and describe fully an enlargement.
Transform shapes by a combination of translation, reflection and rotation
Understand and use compound measures such as speed and density
Recognise accuracy in measurements given to the nearest whole unit
Calculate complex average speeds from distance–time graphs
Construct perpendicular and angle bisector, solve loci problems.
Use Pythagoras’ theorem to solve problems involving right angled triangles.
Statistics
A grade C student can …
Find the mean for grouped data
Find the modal and median class for grouped data
Use measures of average and range to compare distributions and make inferences
Draw a line of best fit on the scatter graph by inspection and use it to make prediction
Identify possible sources of bias in the design and use of questionnaires; write questionnaires
Understand and use relative frequency as an estimate of probability and to compare outcomes
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