YEAR 9 : number and algebra

• Decimal notation and place value
• Compare and order decimals in context

• Order decimals

S Builder Ted (BBC Maths file)

B graph paper

• Multiply and divide by powers of 10

• Multiply and divide integers and decimals by 0.1, 0.01

• Multiply and divide any integer by any power of 10

W  Multiplying and dividing by powers of 10

A 4 in a line

• Understand upper and lower bounds

• Begin to write numbers in standard index form

• Round to nearest 10,100, or 1000

• Round to any given power of 10
• Round decimals to 0, 1, or 2 decimal places

• Round numbers to 3dp's and a given number of sig. figs.

• Understand negative numbers on a no. line

• Order, add and subtract -ve no.s in context

• Add, subtract, multiply and divide integers

• Recognise and use multiples and factors

• Recognise and use multiples, factors and common factors

• LCM and HCF

• LCM and HCF

• Recognise and use prime numbers < 100

• Recognise and use prime numbers
• Find the prime factor decomposition of a number

• Use the prime decomposition of a number

• Recognise triangular and square numbers

• Use squares and square roots (-ve and +ve)
• Use cubes and cube roots

• Use ICT to estimate square roots and cube roots

• Use index notation for small positive integer powers

• Use index notation for integer powers
• Use simple instances of the index laws
• Know/use the index laws for x and ÷ of +ve integer powers

• Use fraction notation to describe parts of shapes

• Convert terminating decimals to fractions

• Know that a recurring decimal is a fraction

• Know that a recurring decimal is an exact fraction
• Use methods to convert a recurring decimal to a fraction

• Express a smaller number as a fraction of another

• Express a number as a percentage of another

• Simplify fractions
• Use a diagram to compare simple fractions

• Use division to convert a fraction to a decimal
• Order fractions using common denominators or decimals

• Begin to add and subtract simple fractions

• Add and subtract fractions

• Add, subtract, multiply and divide fractions
• Cancel common factors before x or ÷ fractions

• Multiply a fraction by an integer

• Multiply and divide an integer by a fraction

• Calculate simple fractions of quantities

• Calculate fractions of quantities

• Understand percentage as the 'number of parts per 100'

• Interpret percentage as the 'so many 100ths of'

• Recognise equivalence of %'s, fractions and decimals

• Use equivalence of fractions, decimals and percentages

H higher questions

O bingo numbers

• Calculate percentages

• Calculate percentages and % increase and decrease

• Solve problems involving percentage changes
• Calculate the result of a proportional change using only x

• Use percentages to compare simple proportions

• Use fractions or percentages to compare proportions
• Use proportional reasoning to solve a problem

• Understand the relationship between ratio and proportion

• Consolidate understanding of ratio and proportion
• Recognise the links between fraction notation and ratio

• Reduce a ratio to its simplest form

• Reduce a ratio to its simplest form (inc. different units)

• Divide a quantity by a given ratio

• Divide a quantity by a given ratio

• Solve simple problems about ratio and proportion informally

• Solve simple problems about ratio and proportion formally

• Interpret and use ratio in a range of contexts

• Consolidate understanding of multiplication and division

• Understand operations of + and - of fractions and integers
• Understand the operations of x and ÷ of integers

• Understand effects of x and ÷ by numbers between 0 and 1

• Know how to use the laws of arithmetic

• Use laws of arithmetic and inverse operations

• Recognise and use reciprocals

• Know and use order of operations including brackets

• Use order of operations with more complex calculations

• Understand the order of precedence and effect of powers

• Positive integer complements of 100

• Recall fraction to decimal conversions

• Multiplication facts up to 10x10 and related division facts

• Use known facts to derive unknown facts

• Use known facts to derive unknown facts

• Extend decimals, fractions and percentages

• Consolidate squares and cubes and roots

• Extend factors, powers and roots

• Decimals, fractions and percentages

• Consolidate decimals, fractions and percentages

• Solve simple word problems mentally

• Solve word problems mentally

• Solve word problems mentally

• Make and justify estimates and approximations

• Make and justify estimates and approximations

• Make and justify estimates and approximations
• Estimate calculations by rounding to 1 significant figure

• Standard column procedures for whole numbers
• Standard column procedures for decimals up to 2 dp

• Standard column procedures for decimals up to 2 dp

• Standard column procedures for any numbers

• Column procedures for x and ÷ of integers/decimals

• Multiply and divide by decimals

• Multiply and divide 3 digit by 2 digit whole numbers

• Understand where to position the point

• Use brackets and memory for multi step calculations

• Use brackets and memory for multi step calculations

• Use brackets and memory
• Use calculator efficiently - not rounding intermediate steps

• Use pi

• Use the sign change key

• Use the sign change key

• Use the sign change keys

• Use the square root key

• Use powers and roots

• Use powers and roots keys

• Use the fraction keys

• Use the fraction keys

• Use the reciprocal key

• Enter no.s and interpret the display in different contexts

• Enter no.s and interpret the display in different contexts

• Enter no.s and interpret the display in different contexts

• Check results by working the problem backwards

• Check results by working the problem backwards

• Check results by working the problem backwards

• Consider whether the result is the right order of magnitude

• Consider whether the result is the right order of magnitude

• Consider whether the result is the right order of magnitude

• Use letter symbols to represent unknowns

• Distinguish role of letters in equations, formulae, functions

• Distinguish role of letters in equations, formulae, functions

• Know the meanings of term, expression and equation

• Know the meanings of formula and function

• Know algebraic operations follow the rules of arithmetic

• Know algebraic operations follow the rules of arithmetic

• Use index notation for small positive integer powers

• Use index notation for integer powers - index laws
• Know use index laws in generalised form for x and ÷

• Simplify linear expressions by collecting like terms

• Simplify/transform linear expressions by collecting terms

• Simplify by taking out single term common factors

W W the dots game

O algebra shapes

• Begin to multiply a single term over a bracket

• Multiply a single term over a bracket

• Square a linear expression or expand (x ± n)(x ± m)
• Establish difference of two squares

• Construct and solve simple linear equations

• Construct and solve simple linear equations

• Construct/solve linear equations with integer coefficients

W W W W  Pyramid rules

M missing numbers

S Equation match (BBC Maths file)

• Begin to use graphs to set up equations

• Solve an equation graphically
• Solve simultaneous equations algebraically or graphically

• Solve inequalities in one variable and represent on no. line
• Begin to solve inequalities in two variables

• Use systematic trial and improvement methods (ICT)

• Solve problems involving direct proportion (ICT)

• Use simple formulae from mathematics and other subjects

• Use formulae from mathematics and other subjects

• Use formulae from mathematics and other subjects

• Substitute integers in simple linear expressions

• Substitute integers in simple formulae
• Substitute +ve integers into expressions with small powers

• Substitute numbers in expressions and formulae

W W the dots game

W W 4 in a line

H fahrenheit to celcius

• Derive simple formulae

• Derive simple formulae

• Derive and use more complex formulae

• Change the subject of a formula

• Generate and describe simple integer sequences
• Generate terms of a simple sequence, given a rule

• Generate and describe simple integer sequences
• Generate terms of a linear sequence (paper or ICT)

• Generate terms of a sequence (paper or ICT)

• Generate sequences from practical contexts

• Generate sequences from practical contexts

• Begin to use linear expression to describe the nth term

• Write the nth term of an arithmetic sequence
• Find the next term and nth term of quadratic sequences

• Express simple functions in words, then symbols

• Express simple functions in symbols

• Represent simple functions in mappings

• Represent  mappings expressed algebraically

• Deduce properties of sequences from spatial patterns

• Generate co-ordinate pairs that satisfy a simple rule

• Generate points in all four quadrants

• Plot graphs of simple linear functions (paper or ICT)

• Plot the graphs of linear functions (y in terms of x)  (ICT)

• Plot graphs of linear functions
• Find the inverse of a linear function - plot its graph

• Recognise straight line graphs parallel to x or y axis
• Begin to plot and interpret graphs of simple linear functions

• Recognise equations of the form y = mx + c

• Find the gradient of lines of the form y = mx + c
• Investigate the gradients of parallel and perpendicular lines

• Construct/plot linear functions from real-life problems
• Interpret graphs arising from real-life situations

• Construct linear functions & graphs from real life problems
• Discuss/interpret graphs arising from real life situations

• Discuss/interpret distance-time graphs

• Plot graphs of simple quadratic and cubic functions
• Know simple properties of quadratic functions