Year 8 Summer Term Learning Objectives
Number 17
Algebra 9
All should be able to
Consolidate and extend mental methods of calculation to include decimals, fractions and percentages, accompanied where appropriate by suitable jottings.
Multiply and divide three-digit by two-digit whole numbers; extend to multiplying and dividing decimals with one or two places by single-digit whole numbers. Convert one metric unit to another (e.g. grams to kilograms).
Most should be able to
Understand addition and subtraction of fractions and integers, and multiplication and division of integers; use the laws of arithmetic and inverse operations.
Use the order of operations, including brackets, with more complex calculations.
Consolidate and extend mental methods of calculation, working with decimals, fractions and percentages, squares and square roots, cubes and cube roots; solve word problems mentally. Make and justify estimates and approximations of calculations. Consolidate standard column procedures for addition and subtraction of integers and decimals with up to two places. Use standard column procedures for multiplication and division of integers and decimals, including by decimals such as 0.6 or 0.06; understand where to position the decimal point by considering equivalent calculations. Check a result by considering whether it is of the right order of magnitude and by working the problem backwards. Use units of measurement to estimate, calculate and solve problems in everyday contexts.
Some should be able to
Understand the effects of multiplying and dividing by numbers between 0 and 1.
Understand the order of precedence and effect of powers.
Extend mental methods of calculation, working with decimals, fractions, percentages, factors, powers and roots. Use standard column procedures to add and subtract integers and decimals of any size. Multiply and divide by decimals, dividing by transforming to division by an integer.
Simplify linear algebraic expressions by collecting like terms.
Construct and solve simple linear equations with integer coefficients (unknown on one side only) using an appropriate method (e.g. inverse operations).
Generate coordinate pairs that satisfy a simple linear rule; recognise straight-line graphs parallel to the x-axis or y-axis. Break a complex calculation into simpler steps, choosing and using appropriate and efficient operations, methods and resources, including ICT.
Simplify or transform linear expressions by collecting like terms; multiply a single term over a bracket. Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets) using appropriate methods (e.g. inverse operations, transforming both sides in the same way). Begin to use graphs and set up equations to solve simple problems involving direct proportion. Plot the graphs of linear functions, where y is given explicitly in terms of x, on paper and using ICT. Construct linear functions arising from real-life problems and plot their corresponding graphs; discuss and interpret graphs arising from real situations. Solve more demanding problems and investigate in a range of contexts: algebra. Solve more complex problems by breaking them into smaller steps or tasks, choosing and using efficient techniques for algebraic manipulation.
Simplify or transform algebraic expressions by taking out single term common factors. Construct and solve linear equations with integer coefficients (with and without brackets, negative signs anywhere in the equation, positive or negative solution), using an appropriate method. Use systematic trial and improvement methods and ICT tools to find approximate solutions of equations such as x3 + x = 20. Solve problems involving direct proportion using algebraic methods, relating algebraic solutions to graphical representations of the equations; use ICT as appropriate. Plot graphs of linear functions (y given implicitly in terms (f x), e.g. ay + bx = 0, y + bx + c = 0, on paper and using ICT. Use trial and improvement methods where a more efficient method is not obvious.