Year 8 Maths - Learning Aims

Transcription

1 Year 8 Maths - Learning Aims 1 Use integer powers and associated real roots (square, cubeand higher), recognise powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their decimal approximations. 2 Learning Aim Use the concepts and vocabulary of prime numbers, factors, and highest common factor (HCF) 1 - Beginning Understand and know square numbers and cube numbers. 2 - Working towards You can square and cube large numbers and decimals. You can estabilish whether a You can find factor pairs. number up to 100 is prime and recall prime. 3 - Secure 4 - Mastered You can use square root and understand powers up to 5. You can explain primes and factors. You can find the highest common factors of two numbers. Perimeter, missing values etc. 'Highest common factors, what number am I? 3 Use the concepts and vocabulary of multiples and lowest common multiples (LCM). You can identify multiples of different numbers. You can find the lowest common multiple of two numbers. You can calculate the lowest common deminators of two fractions. 'real life situations - 2 buses, when is the next time they will meet, BBQ hotdogs and rolls ' 4 Add and Subtract fractions with the same denominator. You can draw diagrams to show add and subtract fractions with the same denominator. You can be fluent when add and subtract fractions with the same denominator. You can explain reasons for adding and subtracting fractions with the same denominator. Work out the value of missing numbers, and calculating perimeter. 5 Add and Subtract fractions with a denominator that is a multiple of other or both different. You can calculate common multiples for the denominators. You can calculate equvalient fractions in order to add and subtract fractions. You can calculate add and subtract fractions involving whole numbers. Missing numbers, >, <, = 6 Substitute numerical values into formulae and expressions, including scientific formulae. You can substitute numbers into basic formulae. You can substitute numbers You can substitute numbers that involve fractions, decimals using powers and roots. and negatives. Creating your own formulaes. Find missing numbers by using a formulae, working backwards when given a formulae.

2 7 Simplify and manipulate algebraic expressions to maintain equivalence by multiplying a single term over a bracket. You can multiply algebra to make a single term. You can multiply single brackets. You can multiply two+ single brackets and simplify. Perimeter, Proof 8 Simplify and manipulate algebraic expressions to maintain equivalence by taking out common factors. You can calculate common factors in an expression. You can factorise single expressions. You can develop factorise expressions involving powers, decimals and fractions. Matching expressions 9 Simplify and manipulate algebraic expressions to maintain equivalence by expanding products of two or more binomials. You can multiply algebra involving powers. You can expand quadratic brackets. You can expand quadratic brackets involving powers. area involving brackets, pattern spotting. 10 Simplify and manipulate algebraic expressions to maintain equivalence by simplifying expressions involving sums, products and powers, including the laws of indices. You can simplify expressions. You can simplify expressions involving fractions. You can simplify using powers, including laws of indices. magic square, sequence, pyramid. 11 Using alebraic methods to solve linear equations in one variable (including all forms that require rearrangement). You can solve one and two equations involving whole numbers. You can solve equations involving brackets and variables on both sides. You can solve equations involving fractional equations. Spot the mistake, perimeter, age 12 Understand and use the concepts and vocabulary of inequalities. You can compare numbers and sums using inequalities. You can represent the solution set to an inequality on an number line and vice versa. You can find the integer solutions of an inequality Who is correct, comparing from a table using inequalities. 13 Understand and use the concepts and vocabulary of inequalities. You can solve linear inequalities in one variable, also drawing these on a number line. You can solve linear inequalities in one variable on both sides. You can solve linear inequalities in one variable on both sides involving brackets and fractions. Money, What numbers fit the rule, coordinates. 14 Rearrange formulae to change the subject, where the subject appears once. You can rearrange a formulae involving addition and/or subtraction. You can rearrange formulae involving multiplication and/or division. You can rearrange formulae involving a mixture of the four operations. Also rearranging mathematical formulae. Rearrange a mathematical formulae to calculate the missing answers.

3 15 Recongnise arithmetic sequences and find the nth term. You can identify the pattern of a number and picture sequence. You can identify the multiples a sequence is increasing/decreasing in and the difference (addition or subtraction). You can identify and explain the nth term in a number and pattern sequence. Will a number appear in a sequence? How many tiles will you need in th pattern? 16 Draw and measure line segments and angles in geometric figures, including interpreting scale drawings and use of bearings You can draw and measure line segments and angles. You can construct triangles from given instructions/pictures. You can use bearings to find a location. constructing a shape from a circle, calculate height from a instruction, calulate bearings. 17 Understand and use alternate and corresponding angles on parallel lines. You can indentify alternate and corresponding angles on parallel lines. You can calculate missing angles on parallel lines involving alternate and corresponding angles. You can explain missing anlges on parallel lines using alternate algebra, missing angles within and corresponding angles. shapes. 18 Derive and use the sum of angles in triangle and a quadrilateral. You can explain what angles in a trianlge and quadrilateral add up to. You can calculate missing angles in a triangle and a quadrilateral. You can explain missing angles in triangles and quadrilaterals with special properities. Missing angles in a puzzle grid, missing angles from words, name the shape from the angles. 19 Derive and use the sum of angles in a trianlge and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons. You can indentify the interior angles sum of polygons. You can calculate missing angles in polygons. You can calculate missing exterior angles of a polygon, Algebra, missing angle with 2+ also be able to state how many polygons put together. sides a shape has when give the exterior angle. 20 Convert between cm 2 to m 2. You can convert cm to m lengths. You can Convert between cm 2 to m 2. You can calculate surface area and convert between cm 2 to m 2. What could the lengths be when givent the area, pattern tiles, fraction/percentage of amounts.

4 21 Derive and apply formulae to calculate and solve problems involving area of circle, compound shapes and trapeziums. You can calculate the area of a circle. You can calculate the area of a trapezium. You can calculate the area of a compound shape that can also involve parts of a circle and/or trapeziums Working back when given the answer, missing lengths, money, is the area big enough. 22 Calculate and solve problems involving perimeters of 2D shapes (including circles). You can calculate the circumference of a circle. You can calculate the perimeter of regular/irregular polygons. You can calculate the perimeter of nets of shapes, semi-circles and compound shapes. Draw shapes when given instructions, calculate the perimeter when given the area. 23 Use ratio notation, including reduction to simplest form. You can identify a ratio from pictures and words. You can identify what ratios numbers can be places in, eg 100 (75:25, 60:40). You can simplify any given ratio, eg 12:9 = 4:3. increase/decrease ratio to calculate an answer, calculate missing ratios 24 Divide a given quantity into two or more parts. You can divide a number in to equal parts. Working Towards: You can divide an amount into a ratio of two. Secure: You can divide an amount into a ratio of 3+ parts. Mastering: calculate the largest part, Why is somebody correct, working backwards, twice as much. 25 Given information abot one part, find the whole of other part(s). You can divide ratio in to parts. You can calculate the whole ratio when given part of the ratio. You can calculate the whole ratio when part of the ratio is more/less another ratio, eg Ratio 3:5 James and Sam, Sam has 12 more than James. Worded, Area, Not given any amount (use 100), calculate the percentage. 26 Change freely between related standard units (for example time, length, area. Volume/capacity, mass). You can convert between metric units. You can convert between metric units involving fractions and decimals. You can order metric units. Develop reasoning comparing units and stating what's incorrect. Calculate area/volume but you need to convert units, map reading scales, time.

5 27 Understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction. You can express pictures as fractions and ratios. You can draw shapes when a give ratio or fraction. State the ratio when given the fraction and vice versa. You can develop reasoning skills when explain why Fractions aren't with the same somebody is correct/incorrect. denominator calculating ratio, percentage, 2+ times as many of an amount whats the fraction. 28 Use compound units such as speed, unit pricing and density to solve problems. You can calculate basic best buy and speed distance time. You can calculate best buy, speed distance time and density. You can reason what is faster, best buy over a period of time and what has the greater density. Converting units, Time (ontime/late) and weight (float/sink) 29 Solve problems involving direct and inverse proportion, including graphical and algebraic representations. You can calculate amounts needed from a recipe. You can calculate exchange rates. You can explain why someone doesn't have enough ingredients, comparing exchange rates of an item which country is it cheaper. Comparing graphs are they direct/inversely proportional, using algrbra. 30 Beginning:ou can identify faces, edges and vertices on 3D shapes. Use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3D. You can explain and calculate how many faces, edges and vertices 3D shapes have.. You can give reasons when given the properties of a 3D shape, why it is/isn't that called a specific 3D shape. Also given statements are they Always, Sometimes, Never True? placing two 3D shapes together what happens to the F,E,V. What happens to the F,E,V when a 3D shape increase/decreases in size. 31 Convert between cm 3 and m 3. Know and use the fact that 1 litre = 1000cm 3 You can calculate the volume of a cube. You can convert between cm 3 and m 3. You can explain the difference to cm 3 and m 3. Have the understanding that 1 litre = 1000cm 3 Using powers of 10, calculating the length of the cube when given the volume, placing volumes into litre bottles. 32 Derive and apply formulae to calculate and solve problems involving volume and surface area of cuboids (including cubes) and other prisms (including cylinders). You can calculate the volume of a 3D shapes. You can calculate surface area of 3D shapes. You can explain/compare what shapes give you a greater volume or surface area. Agree/Disagree with a statement reguarding volume or surface area. Which tank will fill first, calculate missing lengths, how many 3D shapes can fit in to a larger 3D shape.

6 33 Construct and interpret plans and elevations of 3D shapes. You can draw the plans and elevations of regular 3D shapes and vice versa. You can draw the plans and elevations of compound shapes and vice versa. You can identify what plans and elevations match a 3D shape with reasons. State whether a statement is true or false. When given a plan, you can state what the elevation could be. Real-life examples. 34 For non-grouped data given in the form of a table, find the mean, median, mode and range. You can draw and interpret non-grouped data in a table. You can calculate the mean, median, mode and range from non-grouped table. You can compare two nongrouped tables relating to the mean, median, mode and range. Complete a non-grouped table when given the averages. Increase data how have these changed the averages? 35 Use and interpret scatter graphs of bivariate data and recognise correlation. You can indentify correlations from a scatter graph. You can draw a scatter graph or draw extra points on to a scatter graphs and draw a line of best fit. You can link scatter graphs to statements, use the line of best fit to find answers andor compare data eg results. Using a trend and estimate amounts 36 Draw and analyse frequency polygons. You can draw a frequency polygon from a ungrouped table. You can draw a frequency polygon from a grouped table/continuous data. You can compare frequency polygons, place a reasonable scale on a graph. calculate the estimated mean, calculate an amount from to points example how many people spent 2-5 hours doing homework. 37 For continuous data given in the form of a table find an estimate of the mean, modal class interval and class interval that contains the median. You can calculate the median from continuous data. You can calculate estimated mean. You can explain whether statements are correct by using the estimated mean and/or median. calculate missing values when give the estimated mean or median, the the amounts change will these affect the averages.