Foundation only

Foundation and Higher

Higher only

AQA specification

Learning objectives

Grade

Resources

recall all positive integer complements to 100  

Be able to 'make 100' from an integer

G

recall all multiplication facts to 10 x 10 and use them to derive quickly the corresponding division facts  

know all times tables up to 10 x 10

G

P  P  W  W  W  division as reverse multiplication

W  30 division questions

Use times tables to work out the answers to simple division problems

F

understand and use positive numbers and negative integers, both as positions and translations on a number line

Understand positive and negative integers

G

B  blank number lines from -9 to 9

P  negative number scales and temperature problems

W  temperature problems

order integers  

Be able to order a list of negative and positive integers

F

add, subtract, multiply and divide integers, and then any number

multiply and divide by a negative number  

Add and subtract negative integers

F

W  4 in a line - adding a multiple of 10 to a number

W  W  subtraction practice

W  addition and subtraction including negative numbers

W  Four rules 'Collect a letter'

W  calculating with negative numbers

Multiply and divide negative integers

E

use brackets and the hierarchy of operations

Understand and use BIDMAS

E

W  BIDMAS Collect a letter

H  insert brackets to make the calculations correct

understand ‘reciprocal’ as multiplicative inverse, knowing that any non-zero number multiplied by its reciprocal is 1 (and that zero has no reciprocal, because division by zero is not defined)  

Find the reciprocal of a number

C

know about prime numbers and find the prime factor decomposition of positive integers  

Recognise prime numbers

D

W  shade the prime numbers picture puzzle

Write a number as a product of prime factors

C

use the concepts and vocabulary of factor (divisor), multiple and common factor, highest common factor, least common multiple.  

Find the factors of a number

G

W  multiples on a hundred square

W  spider diagrams - fill in the factors

W  shade factors of 24 picture puzzle

W  Shade factors of 20 and 50 picture puzzle

W  factor grid - shade in the factors

W  primes, factors and multiplies

W  mixed questions  

Find the LCM of two simple numbers

C

Find the LCM of two or more numbers

B

Find the HCF of two simple numbers

C

Find the HCF of two or more numbers

B

AQA specification

Learning objectives

Grade

Resources

round to the nearest integer.

Round to the nearest integer

G

P  rounding to the nearest whole number

W  rounding to the nearest whole number or nearest ten

A  4 in a line - nearest 10 or 100

A  blockbusters - nearest 100 or 1000

use their previous understanding of integers and place value to deal with arbitrarily large positive numbers and round them to a given power of 10

Round numbers to given powers of 10.

F

round to a given number of decimal places.

round to one significant figure.

round to a given number of significant figures.

Round numbers to a given number of decimal places

F

O  examples of rounding to decimal places and significant figures

W rounding off - includes decimal places and significant figures

W  rounding and accuracy  

Round a number to one significant figure

D

Round to a given number of significant figures

B

estimate answers to problems involving decimals  

derive unknown facts from those they know

estimate answers to problems involving decimals

G

Estimate square roots

F

Estimate answers to calculations involving division

D

Estimate answers to calculations involving division by numbers less than one

C

W  estimating answers to complex calculations 

understand the calculator display, knowing when to interpret the display when it h as been rounded by a calculator and not to round during the intermediate steps of a calculation  

Know not to round a calculation until the last step.

C

recognise upper and lower bounds of a rounded value

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

Find minimum and maximum values

C

AQA specification

Learning objectives

Grade

Resources

use decimal notation and

order decimals

Use decimal notation for money

G

W  decimals and money

W  understanding place value and ordering decimals

W  ordering decimals

W  W  decimal pictures examples

P  Ordering decimals using decimal pictures

Write down the place value of a digit, e.g. what is the value of 4 in 0.24?

F

Order decimals, e.g. which is bigger 0.24 or 0.3?

F

use standard column procedures for addition and subtraction of integers and decimals  

Add and subtract whole numbers using standard column procedures

G

O  3 addition methods

H  addition questions

O  3 subtraction methods  

H  subtraction questions

W 999 problem

W  worded four rules problems

Add and subtract decimals using standard column procedures

E

add and subtract mentally numbers with up to two decimal places  

Add and subtract decimals using mental procedures

E

W  adding and subtracting decimals with 1 dp

A  A  4 in a line activities - adding decimals

develop a range of strategies for mental calculation  

W  basic arithmetic

derive unknown facts from those they know  

W  W  use known facts for decimal calculations

use inverse operations  

use standard column procedures for multiplication and division of integers and decimals, understanding where to position the decimal point by considering what happens if they multiply equivalent fractions.

multiply and divide numbers with no more than one decimal digit, using the commutative, associative, and distributive laws and factorisation where possible, or place value adjustments  

solve a problem involving division by a decimal (up to 2dp) by transforming it to a problem involving division by an integer.

Multiply and divide whole numbers using standard column procedures

E

O  4 multiplication methods

O  3 division methods 

W  2 by 1 multiplication grids

W  2 by 2 multiplication grids

W  3 by 1 multiplication grids

W  3 by 2 multiplication grids

W  2 by 1 Italian grids

W  2 by 1 & 2 by 2  Italian questions  

W  2 by 1 & 3 by 1  Italian questions

W  H  3 by 2 Italian questions

A  4 in a line game - two digit by 1 digit multiplication   

W  worded four rules problems

Multiply two decimals, such as 2.4 x 0.7

D

W  decimal multiplication (up to 3 decimal places)

W  multiplying decimals using a grid method

W  Decimal fun multiplication

W  four rules calculations with decimals

Divide a number by a decimal, such as 1 ÷ 0.2 and 2.8 ÷ 0.07

C

W  decimal division  

W  decimal calculations derived from known calculations

AQA specification

Learning objectives

Grade

Resources

recall the fraction-to-decimal conversion of familiar simple fractions

Recall fraction to decimal conversions for simple fractions such as 1/4, 1/2, 3/4, 1/3, and 2/3

F

P  W  comparing decimals, fractions and percentages

P  W  unscrambles (choose the biggest)

recognise that each terminating decimal is a fraction  

recognise that recurring decimals are exact fractions, and that some exact fractions are recurring decimals  

perform short division to convert a simple fraction to a decimal  

Convert decimals to fractions

D

W  converting decimals to fractions

Convert fractions to decimals

D

W  Collect a letter

convert a recurring decimal to a fraction  

Convert recurring decimals to fractions

B

Convert fractions to recurring decimals

B/A

distinguish between fractions with denominators that have only prime factors of 2 and 5 (which are represented by terminating decimals), and other fractions (which are represented by recurring decimals)

know that fractions with prime denominators (other than 2 or 5) are recurring decimals 

B

AQA specification

Learning objectives

Grade

Resources

understand equivalent fractions

Find equivalent fractions

G

simplify a fraction by cancelling all common factors 

Simplify fractions

F

order fractions by rewriting them with a common denominator  

Arrange fractions in order of size

F

W  Ordering fractions

calculate a given fraction of a given quantity, expressing the answer as a fraction  

Work out fractions of quantities.

E

P  finding fractions of pictures

P   fractions of amounts examples

P   fractions of amounts spider diagrams

P  fractions of amounts using division

W  fractions of amounts using pictures

W  4 in a line activity

W  W  shade fractions of diagrams

W  T  fractions of amounts

W  W  H fractions of amounts

W  W  Puzzle  shade in the answers picture puzzle

express a given number as a fraction of another  

Find one number as a fraction of another

E

add and subtract fractions by writing them with a common denominator  

Do calculations with simple fractions involving addition

E

W  4 in a line activity - adding two fractions

Do calculations with simple fractions involving subtraction

D

use efficient methods to calculate with fractions, including cancelling common factors before carrying out the calculation, recognising that, in many cases, only a fraction can express the exact answer  

Do calculations with mixed numbers

C

W  H  higher arithmetic

W  mixture of fraction questions  

Be able to cancel down a calculation in order to work out the answer.

C

multiply and divide a fraction by an integer, by a unit fraction and by a general fraction  

Do calculations with simple fractions involving multiplication

E

Do calculations with simple fractions involving division

C

understand and use unit fractions as multiplicative inverses  

AQA specification

Learning objectives

Grade

Resources

use the terms square, positive and negative square root, cube and cube root

Calculate squares and square roots (with and without the use of a calculator)

F

A  4 in a line activity - square, cube, factor and multiples  

W  square numbers from pictures

W  square numbers and cube numbers

W  cube numbers from pictures

W  W  shade the square numbers picture puzzle

W  shade the square  and cube numbers picture puzzles

Calculate cubes and cube roots (with and without the use of a calculator)

E

use the terms square, positive and negative square root, cube and cube root  

D

use calculators effectively and efficiently: know how to enter complex calculations use function keys for reciprocals, squares and powers.  

Use function keys on a calculator for powers and roots

E

W  using a calculator - notes on functions followed by questions

recall integer squares from 2x2 to 11x11 (15x15) and the corresponding square roots.

recall integer squares from 2x2 to 15x15 and the corresponding square roots.

D

P  squares and cubes

recall the cubes of 2, 3, 4, 5 and 10

recall the cubes of 2, 3, 4, 5 and 10  

D

use index notation for squares, cubes and powers of 10  

use index laws to simplify and calculate the value of numerical expressions involving multiplication and division of integer, fractional and negative powers  

Use index notation and index laws for positive and negative powers

C

W  introducing powers of 10 including negative powers

N  some notes on index laws

W  powers and indices including fractional and negative powers and use of index laws

W  index laws and standard form

H  index laws

W  indices and index laws

Use index notation and index laws for fractional  powers where the power is a unit fraction

A

Use index notation and index laws for fractional  powers where the power is not a unit fraction

A*

understand that the inverse operation of raising a positive number to power n is raising the result of this operation to power 1/n  

recall the facts that n^0= 1 and n^-1 = 1/n for positive integers n, the corresponding rule for negative numbers, n^1/2 and n^1/3 for any positive number n

Interpret fractional and negative powers

A*

W  blank table for investigating indices

N  notes on indices - fractional and negative powers

H  indices including fractional and negative powers

W  mixed questions on indices and decimals

W  negative and fractional indices

use surds in exact calculations without a calculator.

Simplify surds

A*

H  recurring decimals, surds and irrational numbers

rationalise a denominator

Rationalise a denominator.

A

P  explaining the concept of irrational numbers

AQA specification

Learning objectives

Grade

Resources

multiply or divide any number by powers of 10, and any positive number by a number between 0 and 1

Know how to multiply a number by a power of 10 such as 10, 100, 100

F

W  multiplying by powers of 10  

W  multiplying and dividing by powers of 10  

Know how to divide a number by a power of 10 such as 10, 100, 100

F

Know how to multiply a number by a power of 10 such as 0.1, or 0.01

D

W  dividing by numbers between 0 and 1

express standard index form both in conventional notation and on a calculator display

enter a range of calculations onto a calculator, including those involving standard index form.

use standard index form display and how to enter into a calculator numbers in standard index form  

calculate with standard index form

Use standard index form both with and without a calculator

C

W  W  standard form  

W  index laws and standard form

W  standard form questions

A  millionaire cards including standard index form

convert between ordinary and standard index form representations, converting to standard index form to make sensible estimates for calculations involving multiplication and/or division

Convert between ordinary and standard index form notation

B

W  converting between ordinary and standard index form

W  questions in standard index form

AQA specification

Learning objectives

Grade

Resources

understand that ‘percentage’ means ‘number of parts per 100’ and use this to compare proportions

Understand that percentage means 'out of 100'

F

interpret percentage as the operator ‘so many hundredths of’  

convert simple fractions of a whole or decimals to percentages of the whole and vice versa

Change a percentage to a fraction and vice versa

F

W  changing a out of b to a percentage

W  match cards

W  W  mixed percenatge, fraction and decimal questions

W  Fractions, decimals and percentages conversion

Change a percentage to a decimal and vice versa

F

Compare percentages, fractions and decimals

E

use percentage in real-life situations  

solve simple percentage problems, including percentage increase and decrease  

Work out a percentage of a given quantity without a calculator

E

O  W  blank percentage spider diagram

O    blank percentage spider diagram (reversed for printing on OHT)

O   W  using 10% and 50% to work out other percenatges    

A  find the reward - simple percentages

W  blanks for working out mental pecentages

W  Collect a letter - includes percentages of amounts and four rules questions

P  P   spider diagrams for explaining mental percentages

W  blank spider diagrams for students

W  W  H  H  working out percentage mentally

W  W  W  4 in a line activities - 4 in a line

W  millionaire cards  

W  percentages unscramble puzzle  

W  W  Puzzle  shade in the answers picture puzzle

W  collect a joke

W  W  W  calculator percentages  

W  worded percentage questions

Calculate simple interest

E

Increase or decrease a given quantity by a percentage

D

W  percentage increase and decrease

W  percentages including increase and decrease

Work out percentage increase or decrease

C

express one quantity as a percentage of another

D

Understand how to use successive percentages (compound)

B

Solve problems to do with compound percentage such as compound interest.

B

calculate an original amount when given the transformed amount after a percentage change  

(reverse percentages problems)

use calculators for reverse percentage calculations by doing an appropriate division.  

Work out reverse percentage problems

B

use calculators to explore exponential growth and decay, using a multiplier and the power key.

Work out compound percentage problems using a multiplier and the power key

A

AQA specification

Learning objectives

Grade

Resources

use ratio notation, including reduction to its simplest form and its various links to fraction notation

Solve problems to do with 'best value'

E

P  W  W  W  W  Best value

W  identify ratio from pictures and simplify

divide a quantity in a given ratio  

solve word problems about ratio and proportion, including using informal strategies and the unitary method of solution  

represent repeated proportional change using a multiplier raised to a power

Solve more complex ratio and proportion problems such as sharing out money between two groups in the ratio of their numbers

C

O  sharing £240 into given ratios

W  using fractions to share into a ratio

W mixed ration questions

W  understanding map scales

W  W  map problems (questions and maps)  

Solve ratio and proportion problems using the unitary method

C

Calculate proportional changes using a multiplier

B

calculate an unknown quantity from quantities that vary in direct or inverse proportion 

Solve direct and inverse proportion problems

A

set up and use equations to solve word and other problems involving direct proportion or inverse proportion and relate algebraic solutions to graphical representation of the equations

Interpret the graphs of direct and inverse proportion relationships

A

P  explaining direct and inverse proportion

W  questions on direct and inverse proportion

AQA specification

Learning objectives

Grade

Resources

know the meaning of and use 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

Be able to collect like terms

E

A   blockbusters activity

Factorise simple expressions requiring one bracket.

D

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

expand and simplify harder expressions

C

W  expanding and simplifying collect a joke

H  expanding and simplifying

W  factorising including quadratics

Factorise quadratic expressions where the coefficient of x² is 1

B

Factorise quadratic expressions where the coefficient of x² is greater than 1

A

Simplify rational expressions

B

Simplify harder rational expressions

A*

expand the product of two linear expressions  

Expand and simplify quadratic expressions where the coefficient of x² is 1

B

W  W  expanding and simplifying expressions including two brackets

Expand and simplify quadratic expressions where the coefficient of x² is greater than 1

A

AQA specification

Learning objectives

Grade

Resources

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  

Draw graphs of simple quadratic functions such as y=3x² and y=x²+4

D

P  explaining plotting curved graphs

W  quadratic graphs  

Draw graphs of harder quadratic functions such as y=x²-2x+1

C

find the intersection points of the graphs of a linear and quadratic function, knowing that these are the approximate solutions of the corresponding simultaneous equations representing the linear and quadratic functions

Find the points of intersection of quadratic graphs with lines

C

P  explaining intersection points for solving equations

W  W    graphical solutions of equations  

Use graphs to find the approximate solutions of quadratic equations

C

Use points of intersection of a quadratic graph such as y=x²-2x-4 with lines such as y=2x+1 to solve equations like x²-2x-4=2x+1 and simplify this to x²-4x-5

A

Solve equations using two graphs where the equation needs manipulating to match the graphs

A