YEAR 8 : 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

• Round to nearest 10,100, or 1000

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

• 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

• Recognise triangular and square numbers

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

• Use index notation for small positive integer powers

• Use fraction notation to describe parts of shapes

• Convert terminating decimals to fractions

• Know that a recurring decimal is 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

W time as fraction or decimal

• Begin to add and subtract simple fractions

• Add and subtract 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

• Calculate percentages

• Calculate percentages and % increase and decrease

• Use percentages to compare simple proportions

• 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

• Consolidate understanding of multiplication and division

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

• Know how to use the laws of arithmetic

• Know and use order of operations including brackets

• Use order of operations with more complex calculations

• 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

• Decimals, fractions and percentages

• Consolidate decimals, fractions and percentages

W Decimal division

W W W Percentages

• Consolidate squares and cubes and roots

• Solve simple word problems mentally

• Solve word problems mentally

• Make and justify estimates and approximations

• Make and justify estimates and approximations

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

• Standard column procedures for decimals up to 2 dp

• Column procedures for x and ÷ of integers/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 the sign change key

• Use the sign change key

• Use the square root key

• Use powers and roots

• Use the fraction keys

• 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

• 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

• 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

• Simplify linear expressions by collecting like terms

• Simplify/transform linear expressions by collecting terms

• Begin to multiply a single term over a bracket

• Multiply a single term over a bracket

• Construct and solve simple linear equations

• Construct and solve simple linear equations

• Begin to use graphs to set up equations

• Use simple 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

• Derive simple formulae

• Derive simple formulae

• 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 sequences from practical contexts

• Begin to use linear expression to describe the nth term

• Express simple functions in words, then symbols

• Express simple functions in symbols

• Represent simple functions in mappings

• Represent  mappings expressed algebraically

• 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)

• 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

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