find areas and perimeters of rectangles, recalling the formula, understanding the connection to counting squares and how it extends this approach

G

W  area and perimeter investigation

W  counting squares

W  W  Area and perimeter of rectangles

A  who wants to be a millionaire

G

recall and use the formulae for the area of a parallelogram and a triangle

use their knowledge of rectangles, parallelograms and triangles to deduce formulae for the area of a parallelogram, and a triangle, from the formula for the area of a rectangle

W  triangles for measuring area

O  W  parallelogram and trapezium

W  area and volume worksheet

P  missing lengths

calculate perimeters and areas of shapes made from triangles and rectangles

O  rectangle and triangle

W  W  W  Compound shapes 

calculate the area of a triangle using ½ ab sin C

A

find circumferences of circles and areas enclosed by circles, recalling relevant formulae

P  W  circles

W  circles - shaded area

T  circles test  

W  Circles

W  Circumference

find volumes of cuboids, recalling the formula and understanding the connection to counting cubes and how it extends this approach

P  P  volume by counting cubes

find the surface area of simple shapes using the area formulae for triangles and rectangles

calculate volumes of right prisms and of shapes made from cubes and cuboids

solve problems involving surface areas and volumes of prisms, cylinders, pyramids, cones and spheres

W  cylinders  

W  cone composites

solve problems involving more complex shapes and solids, including segments of circles and frustums of cones.

calculate the lengths of arcs and the areas of sectors of circles

T  perimeter and area problems involving semi-circles

H  complex circle problems

convert between area measures, including square centimetres and square metres, and volume measures, including cubic centimetres and cubic metres.

W  converting area and volume measures

distinguish in meaning between the words 'equation', 'formula', 'identity' and 'expression'.

manipulate algebraic expressions by collecting like terms, by multiplying a single term over a bracket, and by taking out common factors

W  simplifying expressions

A  simplifying blockbusters

W  factorising  

W  simplifying collect a joke

H  simplifying

C

generate terms of a sequence using term-to-term and position-to-term definitions of the sequence.

P  W  number patterns

O  W  B  number sequences  

generate common integer sequences (including sequences of odd or even integers, squared integers, powers of 2, powers of 10, triangular numbers)

P  Sequence envelope

use linear expressions to describe the nth term of an arithmetic sequence, justifying its form by reference to the activity or context from which it was generated

W  W  sequences and formulae

W  W  number patterns

O&W  Sequences based on patterns

H  nth term

use the conventions for coordinates in the plane

plot points in all four quadrants and use axes and coordinates to specify points in all four quadrants

locate points with given coordinates

find the coordinates of points identified by geometrical information

Solve geometrical problems using coordinates such as finding the 4th corner of a parallelogram given the other 3

Find the midpoint of a line segment

understand that the form y = mx + c represents a straight line and that m is the gradient of the line, and c is the value of the y-intercept

set up simple equations

solve simple equations by using inverse operations or by transforming both sides in the same way

solve linear equations, with integer  or fractional coefficients, in which the unknown appears on either side or on both sides of the equation

solve linear equations that require prior simplification of brackets, including those that have negative signs occurring anywhere in the equation, and those with a negative solution

F

W  forming equations

W  W  making equations

W  word equations

E

recognise and visualise rotations including rotational symmetry of 2-D shapes

Give the order of rotation symmetry of a 2D shape

P  rotational symmetry

P  example

P  W  rotations  

measure the angle of rotation using right angles, simple fractions of a turn or degrees.

understand that rotations are specified by a centre and an (anticlockwise) angle

rotate a shape about the origin or any other point.

D

C

C

C

recognise and visualise reflections including reflection symmetry of 2-D and 3-D shapes.

Draw a line of symmetry on a 2D shape

Draw all the lines of symmetry on a 2D shape

understand that reflections are specified by a mirror line, (only using a line parallel to an axis or in a given mirror line such as y=x or y=-x)

G

P  example 

O  examples

F

E

D

C

D

D

transform triangles and other 2-D shapes by rotation, reflection and combinations of these transformations, recognising that these transformations preserve length and angle, so that any figure is congruent to its image under any of these transformations

use congruence to show that rotations and reflections preserve length and angle.

distinguish properties that are preserved under particular transformations

F

C

recall the definition of a circle and the meaning of related terms, including centre, radius, chord, diameter, circumference, tangent and arc, sector and segment

G

P  N  words and formulae  

W  diameter and radius

W  Circumference and diameter

understand that the tangent at any point on a circle is perpendicular to the radius at that point

understand and use the fact that tangents from an external point are equal in length

explain why the perpendicular from the centre to a chord bisects the chord

B

prove and use the facts that the angle subtended by an arc at the centre of a circle is twice the angle subtended at any point on the circumference, the angle subtended at the circumference by a semi-circle is a right angle, that angles in the same segment are equal and that opposite angles of a cyclic quadrilateral sum to 180 degrees

A

prove and use the alternate segment theorem

A

recognise translations

understand that translations are specified by a distance and direction and understand vector notation in this context

P  translations

W  translations

understand enlargements are specified  by a centre and positive scale factor

identify the scale factor of an enlargement as the ratio of the lengths of any two corresponding line segments and apply this (to triangles only)

F

E

P  enlargements

P  W  shapes to enlarge

P  examples

W  enlargements  

W  enlargement questions

W  scale factors

E

transform triangles and other 2-D shapes by rotation, reflection, translation and combinations of these transformations

P  W  tessellations

distinguish properties that are preserved under particular transformations, recognise that enlargements preserve angle but not length, understand the implications of enlargement for perimeter, understand and use the implications of enlargement for area and volume, understand and use simple examples of the relationship between / the effect of enlargement on areas and volumes of shapes and solids.

use congruence to show that translations preserve length and angle.

Distinguish between formulae for perimeter, area and volume by considering dimensions

P  enlargements and area

make sensible estimates of a range of measures in everyday settings

P   P  units of measure

W  units of length

P  W  litres and millilitres

P  the weight is right

interpret scales on a range of measuring instruments, including those for time and mass

W  measures questions

know rough metric equivalents of pounds, feet, miles, pints and gallons

convert measurements from one unit to another

know that measurements using real numbers depend on the choice of unit

A   Who wants to be a millionaire

N  W  W metric and imperial units

understand and use compound measures, including speed and density

P  P  understanding speed

W  W  Speed

W  Speed, Distance, Time

A  A  Millionaire cards

recognise that measurements given to the nearest whole unit may be inaccurate by up to one half in either direction

P  minimum and maximum values

W  measure is approximate

use calculators, or written methods, to calculate the upper and lower bounds of calculations, particularly when working with measurements 

interpret information presented in a range of linear and non-linear graphs

W  P  Conversion graphs without questions

W  conversion graphs questions

W  drawing conversion graphs

use formulae from mathematics and other subjects expressed initially in words and then using letters and symbols

W  number machines

substitute numbers into a formula

substitute positive and negative numbers into expressions with indices.

W  W  4 in a line

W  W  W  substitution

W  substitution

calculate, and represent graphically the sum of two vectors, the difference of two vectors and a scalar multiple of a vector

understand and use the commutative  and associative properties of vector addition

solve simple geometrical problems in 2-D using vector methods.

W  vector problems  

calculate the resultant of two vectors

factorise quadratic expressions including the difference of two squares and cancel common factors in rational expressions  

N  notes

solve simple linear inequalities in one variable, and represent the solution set on a number line

N  W  inequalities

solve several linear inequalities in two variables and find the solution set

find the exact solution of two simultaneous equations in two unknowns by eliminating a variable, and interpret the equations as lines and their common solution as the point of intersection

W  W  W  T  simultaneous equations

P  W  W  W  graphical solutions of equations  

W  Graphical method

solve exactly, by elimination of an unknown, two simultaneous equations in two unknowns, one of which is linear in each unknown, and the other is linear in one unknown and quadratic in the other, or where the second is of the form x² + y² = r²

plot graphs of functions in which y is given explicitly in terms of x, or implicitly; no table or axes given 

generate points and plot graphs of simple quadratic functions, then more general quadratic functions and find approximate solutions of a quadratic equation from the graph of the corresponding quadratic function

W  understanding equations

W  quadratic graphs

plot graphs of simple cubic functions, the reciprocal function y=1/x (with x not zero), the exponential function y=k^x for integer values of k and positive values of x.

recognise the characteristic shapes of all the above functions

 W  investigating graphs