Year Nine Scheme of Work. Overview

Transcription

1 Year Nine Scheme of Work Overview Unit Topic 1 Angles 2 Manipulating Algebra and Rules of Negatives 3 Place Value and Decimals 4 Sequences 5 Data 6 Fractions 7 Perimeter and Area of Polygons and Circles 8 Pythagoras and Trigonometry 9 Multiplying Numbers and Brackets 10 Number Properties and Indices 11 Probability 12 Formulae 13 Percentages 14 Using a Calculator 15 Volume and Surface Area 16 Algebraic Graphs 17 Reflection, Rotation, Translation 18 Equations and Inequalities 19 Mean, Median, Mode and Range Please note: Any topics highlighted are for no good reason (I cannot undo it!) Year Nine: Revision guide: Page 1

2 1 Topic: Angles 5,4 5,4,3 3,2,1 2,1 Recognise acute, obtuse and reflex angles Estimate angles Calculate angles around a point - Calculate angles on a straight line - Calculate angles in a triangle - Calculate exterior angles in a triangle Calculate angles in quadrilaterals and polygons + Calculate angles on parallel lines (vertically opposite, corresponding, alternate, interior angles) + Draw simple bearings diagrams - Complete more complex angles problems involving parallel lines + Complete more complex problems involving bearings - Recognise the arrow head theorem and find missing angles - Recognise the bow tie theorem and find missing angles - Label parts of a circle (tangent, segment etc.) + Recognise angles in a semi-circle and find missing angles - Recognise cyclic quadrilaterals and find missing angles - 2 Topic: Manipulating Algebra and Rules of Negatives 5,4 5,4,3 Negative numbers in the context of temperature and Adding with negative numbers Add and subtract, Multiply and divide Negatives Order negative numbers - Simplify basic expressions (one variable) + Simple substitution involving one variable + Simplify harder expressions by addition (two variables) - Simplify expressions by multiplication (2c x 4d) - Substitution involving two variables and involving negative values and powers Simplify expressions involving quadratic terms and mixed variable terms (e.g x 2 + 2xy 5x 2 + 3xy + y) + Simplify using indice rules (adding and subtracting powers, powers of powers) Substitution involving fractions, decimals and negatives of these 3,2,1 Understand and use negative indices + 2,1 Understand and use simple fractional indices - Understand and use more complex fractional indices + Year Nine: Revision guide: Page 2

3 3 Topic: Place Value and Decimals 5,4 5,4,3 Writing numbers in words and vice versa Adding and subtracting up to 3 digits and in context Place value to 1000 Decimal notation in the context of money Multiply and divide numbers by powers of 10 Order decimals to 3 decimal places Multiply decimals by whole numbers Multiply and divide decimals by powers of 10 Round numbers to decimal places Add and subtract decimals and Divide decimals by whole numbers Multiply and divide decimals Use known multiplication facts to carry out related decimal calculations Round to significant figures Estimate by rounding to one significant figure,2,1 Finding bounds of measurements - 1 Simple calculations involving bounds (addition and multiplication) 4 Topic: Sequences 5,4 5,4,3 Recognise a sequence Recognise and describe a number sequence Find the next term in a simple sequence Find a missing term in a simple sequence Continue simple sequences from pictures Describe a sequence using a term to term rule Generate sequences using a term to term rule - Generate and continue sequences using pictures and diagrams Generate sequences using position to term rule (nth term rules) Find position to term (nth term) rules for linear sequences + 3,2,1 Recognise and use quadratic sequences - Recognise and use Fibonacci type sequences + 2,1 Recognise and use simple geometric sequences - 1 Find position to term (nth term) rules for simple quadratic sequences (e.g. n 2 + 3) Year Nine: Revision guide: Page 3

4 5 Topic: Representing Data 5,4 5,4,3 3,2,1 2,1 Construct a pictogram Construct a bar chart Sort data in a venn diagram Interpret information in a table Interpret a pictogram Interpret a bar chart Construct line graphs Interpret line graphs Record discrete data in a suitable table Interpret pie charts Interpret a range of graphs Construct pie charts + Construct bar charts for continuous data Construct time series graphs Identify which graph to use in different situations Interpret and compare a wide range of graphs Construct scattergraphs - Identify types of data (categorical, discrete, continuous, secondary and primary) Understand correlation + Add lines of best fit to scattergraphs and use them to predict data + Construct and interpret line graphs for time series data Identify sources of bias in sampling Understand different sampling techniques Year Nine: Revision guide: Page 4

5 6 Topic: Fractions 4 and 5 4 and 5 3,4 and 5 (1 and 2 assumed knowledge) Recognise simple fractions Recognise a range of fractions Order simple fractions - Find equivalent fractions - Simplify fractions Add and subtract fractions with the same denominator + Find simple fractions of quantities + Convert between mixed numbers and improper fractions - Add and subtract fractions with different denominators - Find fractions of amounts Add mixed numbers Multiply and divide fractions by whole numbers Multiply and divide fractions by fractions Subtract, multiply and divide mixed numbers 7 Topic: Perimeter and Area of Polygons and Circles Find the perimeter of basic shapes 4 and 5 Find the area of regular and irregular shapes by counting squares Use the formula for the area of a rectangle 4 and 5 Calculate the perimeter and area of compound shapes (made up from rectangles) Calculate missing lengths given the area of a rectangle Use the formula for the area of a parallelogram (including finding missing lengths from the area) Use the formula for the area of a triangle (including finding missing lengths from the area) Calculate compound area involving rectangles, parallelograms, triangles 3,4 and Discover and use the formula for the circumference of a circle 5 Discover and use the formula for the area of a circle Use the formula for the area of a trapezium Calculate the perimeter and area of semicircles Calculate compound area involving rectangles, parallelograms, triangles, trapezia and circles 2 and 1 Complete reverse calculations involving area and circumference of circles Year Nine: Revision guide: Page 5

6 8 Topic: Triangles and Quadrilaterals (Pythagoras & Trigonometry) 5,4,3 Tessellate basic shapes Tessellate more complex shapes Be able to identify congruent shapes Use Pythagoras Theorem to find a missing hypotenuse 3,2,1 Use Pythagoras Theorem to find missing sides Use Pythagoras Theorem in other shapes (rectangles and isosceles triangles) Use Pythagoras Theorem in word problems Use trigonometry to find missing sides 2,1 Use trigonometry to find missing angles Use trigonometry in word problems 9 Topic: Multiplying Numbers and Brackets 5,4 5,4,3 3,2,1 2,1 1 Know Times Tables Multiply and divide two digit numbers by 2,3,4, 5,10 Divide by 2,3,4,5,10 with remainders Use efficient written methods to multiply two digit numbers by single digits Use efficient written methods to divide two digit numbers by single digits including decimal answers Multiply 3 digit numbers by 2 digit numbers Divide 3 digit numbers by 2 digit numbers Multiply a single number over a bracket Multiply brackets with coefficients (e.g: 2(3x+ 3) Multiply a letter over a bracket Simple factorisation (involving the factorising out of a number) Multiply two brackets of the form (x + a) or (x a) Simple factorisation (involving the factorising out of a letter, or number and letter) Multiply two brackets of the form (ax +b) or (ax b) Factorisation of quadratics Difference of two squares Solving quadratics by factorisation of the form x 2 ± bx ± c Solving quadratics by factorisation of the form ax 2 ± bx ± c Year Nine: Revision guide: Page 6

7 10 Topic: Number Properties and Indices 5,4 5,4,3 3,2,1 Know what a reciprocal is Recognise multiples Recognise primes Recognise factors Recognise square numbers and cube numbers Write numbers using indices Finding square roots Find products of primes Find HCF and LCM from listing numbers Find HCF and LCM using prime factorisation Converting numbers between ordinary and standard form Calculating with numbers in standard form Calculating with numbers in standard form (using a calculator) Power of zero Working with negative and fractional indices 11 Topic: Probability 3,4 and 5 3,4 1 and 2 Use the probability scale from 0-1 Basic experimental probability Finding the probability of an event happening Find the probability of an event not happening Design and use two way tables Find and record all mutually exclusive outcomes Know the sum of mutually exclusive outcomes in 1 and use this to solve problems Construct and use sample space diagrams Know when to add and when to multiply probabilities Use tree diagrams for independent events Year Nine: Revision guide: Page 7

8 12 Topic: Formulae 5,4,3 Use formulae expressed in words Change from words to simple algebraic expressions Construct simple formula using algebra (e.g: with single operations) Use simple algebraic formula (e.g: with single variable substitution) Use more complex algebraic formulae (e.g: with multiple operations or variables) 3,2,1 Construct more complex formula using algebra (e.g: with two operations or variables) 2,1 Simple changing the subject of the formula (letter one side) Construct more complex formula using algebra (e.g: with multiple operations or variables) 1 More complex changing the subject of the formula (letter on one side, multiple stages) 13 Topic: Percentages 5,4 Find simple percentages of amounts (50%, 25%, 10%) Find percentages of amounts with a calculator 5,4,3 Find percentages of amounts (percentages are multiples of 10) Calculate percentage change Finding more difficult percentages of amounts Percentage increase (non-calculator methods) Percentage decrease (non-calculator methods) 3,2,1 Percentage increase with multipliers Percentage decrease with multipliers 2,1 Compound percentage problems 1 Reverse percentage problems Year Nine: Revision guide: Page 8

9 14 Topic: Using a Calculator All sets Use a calculator to solve simple problems Interpret calculator displays in the context of money BODMAS Harder BODMAS Using the square, square root, cube and cube root buttons on the calculator Using the power buttons on the calculator Entering complex calculations into a calculator Using the fraction button on a calculator Using the ANS button a calculator 15 Topic: 3D Shapes, Volume and Surface Area 5,4 5,4,3 3,2,1 2,1 Identify nets of 3D shapes Make 3D shapes from their nets Complete isometric drawings of 3D shapes Calculate the volume of a cuboid Draw accurate nets of cuboids Draw plans and elevations of 3D shapes (made from cubes) Draw plans and elevations of 3D shapes (not made from cubes) Sketch 3D shapes from their plans and elevations Calculate the surface area of a cuboid Calculate the volume of a prism (including cylinders) Calculate the surface area of a prism (including cylinders) Harder volume and surface area problems Year Nine: Revision guide: Page 9

10 16 Topic: Algebraic Graphs 5,4 5,4,3 3,2,1 1 Use coordinates in the first quadrant Use coordinates in all four quadrants Plot simple graphs of the form y = mx or y = x + c Plot graphs of the forma y = mx + c Plot graphs of quadratic functions Draw graphs from real life situations (e.g. conversion graphs) Draw speed, distance, time graphs Interpret speed, distance and time graphs Understand the gradient and y intercept of a graph and how it relates to the equation Plot graphs of cubic functions Solve equations using quadratic and cubic graphs 17 Topic: Reflection, Rotation, Translation 5,4 5,4,3 Identify lines of symmetry Reflect shapes in horizontal and vertical lines Describe a translation without using vectors Reflect shapes in mirror lines (including diagonals) Translate a shape (without using vectors) Rotate a shape around a point Understand column vectors Identify if a shape has rotational symmetry and describe its order Translate a shape using vectors Describe a translation using vectors Rotate a shape on a coordinate grid around a centre of rotation Describe a rotation using an angle, direction and centre of rotation Reflect a shape on a coordinate grid Describe a reflection using a line of reflection 3,2,1 Combinations of transformations Year Nine: Revision guide: Page 10

11 18 Topic: Equations and Inequalities 5,4 5,4,3 3,2,1 2,1 1 Use function machines to find missing output and inputs Use function machines to find missing operations Use multi-step function machines Solve simple (single step) equations with integer solutions Solve two-step equations with integer solutions Solve equations with x on one side but involving brackets Solve linear equations with x on both sides (where all x terms are positive) Solve linear equations with x on both sides (where x terms are negative) Solve linear equations with x on both sides, involving brackets Represent inequalities on a number line Solve simple inequalities Solve inequalities with x on both sides Solve harder equations with fractional and negative solutions Solve harder inequalities with fractional and negative solutions Use trial and improvement to solve simple equations 19 Topic: Mean, Median, Mode and Range 5,4 5,4,3 3,2,1 1 Calculate the mode Calculate the range Calculate the median Calculate the mean Use the mean, median, mode and range to compare data Find the mean, median, mode and range from an ungrouped frequency table Draw stem and leaf diagrams Find the median and range from a stem and leaf diagram Find the mean and median from a grouped frequency table Compare data using the mean and median from frequency tables Draw cumulative frequency curves Calculate the median and IQR from cumulative frequency curves Compare data using the median and IQR Year Nine: Revision guide: Page 11