Number Pyramids Guidance These activities should be completed before beginning the rest of Module 1 (Not in place of it!).

Transcription

1 Number Pyramids Guidance These activities should be completed before beginning the rest of Module 1 (Not in place of it!). Click here for Resources: Provide resource sheet per student Number Pyramids resource sheet (at the end of this document) Questions you may use to use for students to access the problem Why did they write 7 on the second row? Does this work for writing 11 & 18? Can you re-arrange the 3 numbers on the bottom row? Will your answer on the top row be the same? What do you notice? Could you explain why? Try this with 3 other numbers eg 2, 5 & 3 Try this using letters eg a, b & a or x + 1, x & x + 2 Page 1

2 MODULE 1 Number & Algebra 1 DURATION: 6 Lessons Know what a factor and multiple is How to use order of operations (BIDMAS) How to add and subtract negative integers Understand number properties e.g. factors, multiples, primes, squares Understand and use HCF and LCM Understand what prime numbers are Find out the prime factors of an integer Use simple divisibility tests Multiply and divide negative numbers Understand and use powers and roots Understand and use BIDMAS New Collins Frameworking Yr 8 2:2 Ex 1A, B, C, D, E & challenge activity AQA F Tier Ex 1 B, C, 4A - D Collins F TierEx 4a We teach maths My maths Mathswatch 28, 79, 80, 78, 68 Corbett maths KEYWORDS For the More able EXAM STYLE QUESTIONS Venn diagrams Negative, positive Number line Factor, multiple Common factor/multiple PS Pg 15 Challenge Question LCM & HCF Square (root) Problem solving PS Pg 23 Q7 Squares Power tasks involving PS Pg 23 Q8 LCM & HCF HCF, LCM HCF & LCM PS Pg 10 Q 8 & 10 Integer Prime numbers/factors Factor Tree Cube number (root) Index form Page 2

3 MODULE 2 Shape, space and measure 1 DURATION: 7 Lessons How to identify and label parallel and perpendicular lines How to calculate angles at a point, on a line or opposite angles How to calculate angles in a triangle Recognise symmetry of a quadrilateral How to plot co-ordinates in 4 quadrants Use a compass to draw a circle Translation, reflection & enlargement with positive scale factor Construct the midpoint and the perpendicular bisector of a line Construct an angle bisector Know and use the geometric properties of triangles and quadrilaterals Understand how to rotate and translate a shape Construct triangles To calculate angles in intersecting and parallel lines New Collins Frameworking Yr 8 2:2 Ex 2A, B, C, D, E Need additional resources for constructions and angle rules. AQA F Tier Ex 9B, 32B Collins F Tier Ex 20A, B Ex 15F, G We teach maths My maths Mathswatch 49, 50, 120, Corbett maths KEYWORDS For the More Able EXAM STYLE QUESTIONS Perpendicular, parallel Geometric properties Square, rectangle, parallelogram, rhombus, kite, trapezium, delta/arrowhead Allied angles, alternate/ corresponding angles Angle/Centre/Direction of rotation Transversal Translate, translation Angle/Perpendicular bisector, bisect Construction Loci AQA Ex 32 C & D Collins F Ex 20 C, D MR Pg 46 Q2 Translation MR Pg 46 Q4 Angle rules PS Pg 46 Q5 MR Pg 46 Q6 Pg Inscribed & circumscribed circles Can you construct a 30 angle? Page 3

4 MODULE 3 Handling Data 1 DURATION: 5 Lessons Understand and use simple vocabulary associated with probability Record data in a table or chart Place events in order of likelihood and use appropriate words to identify chance Use a probability scale to represent a chance Write probability of an event as a fraction Recognise mutually exclusive outcomes Calculate probabilities from experiments Use knowledge that the probability of an event is the number of desirable outcomes divided by the number of possible outcomes if these are all equally likely Understand and use 0&1 as the limits of the probability scale Understand p-1 Use sample space diagrams to calculate probabilities When dealing with a combination of 2 independent experiments, identify all the outcomes and calculate probabilities in the case of equally likely outcomes Understand relative frequency as an estimate of probability and use this to compare outcomes of an experiment New Collins Frameworking Yr 8 2:2 Ex 3A, B, C, D (Q2 & 5 & PS task) AQA F Tier Ex 19 B - F Collins F Tier Ex 18 B - H We teach maths My maths Mathswatch , Corbett maths KEYWORDS For the more able EXAM STYLE QUESTIONS Event Probability Outcomes Likely Experiment PS Pg 66 Q2 angles and probability Mutually exclusive And Or Rules PS Pg 66 Q3 Sample space Tree diagrams & PS Pg 66 Q7 Diagram using algebra PS Pg 66 Q8 Experimental probability Venn diagram Union, set Intersection Probability scale Page 4

5 MODULE 4 Number 2: Percentage DURATION: 3 Lessons Equivalence between fractions, decimals and percentage How to calculate a percent of a quantity with or without a calculator Understand the relationship and equivalences between fractions, decimals and percentages Write one quantity as a percent of another Use percent to compare quantities Use a multiplier to calculate percent change Work out a change in value as a percent increase/decrease New Collins Frameworking Yr 8 2:2 Ex 4A, B, C AQA F Tier Ex 13 A - E Collins F Tier Ex 12 B F good starter Ex 12A Q 24 We teach maths My maths Mathswatch 86 89, 108, 109 Corbett maths KEYWORDS For the More Able EXAM STYLE QUESTIONS Percentage Multiplier Percent increase/ decrease Reduction Simple & Compound Interest AQA F Tier Pg 626 & 631 Ex 38B Reverse Percentages FS Pg 80 Q3, 4 & 5 Percentages & money FS Pg 81 Q10, 11 & 12 Percentages, formulae & money PS Challenge pg 82 Page 5

6 MODULE 5 Algebra 2 DURATION: 5 Lessons Create sequences and describe them in words Substitute numbers into algebraic expressions Know the sequence of square and triangular numbers Use flow diagrams to generate sequence Know and understand the Fibonacci Sequence Use the nth term of a sequence Work out the nth term of a sequence New Collins Frameworking Yr 8 2:2 Ex 5A, B, C, D Need more on finding the nth term AQA F Tier Ex 18 A - D Collins F Tier Ex 23 A - E We teach maths My maths 37, 103, 104 Mathswatch Corbett maths KEYWORDS For the More Able EXAM STYLE QUESTIONS Finite, infinite Generate Algebraic expression Constant term Coefficient Nth term Substitute Flow diagram Find nth term of quadratic sequences FS Pg 96 Q3 in context PS Pg 96 Q4 nth term PS Pg 96 Q6 nth term Pg 96 Q7 generating sequence Page 6

7 MODULE 6 Shape, Space and Measure 2 DURATION: 5 Lessons Can work out the perimeters and areas of squares, rectangles and triangles Can work out the volume of cubes and cuboids To work out the area of a triangle Work out the area of a parallelogram Work out the area of a trapezium Find the surface area of cubes and cuboids Find the volume of cuboids Substitution into formula New Collins Frameworking Yr 8 2:2 Ex 6A, B, C, D Use Ex 6A Q1-4 as starters and Q5 8 as lesson Need resources for volume AQA F Tier Ex 11A, B D, E Collins F Tier Ex 5 D - K We teach maths My maths Mathswatch 54 56, 119 Corbett maths KEYWORDS For the more able EXAM STYLE QUESTIONS Perpendicular height Base Triangle Parallelogram Trapezium Compound shapes Surface area Cuboid, cube Find area of compound shapes involving the above Volume of prisms PS Pg 117 Q4 Area triangle PS Pg 117 Q5 Area compound shapes PS Pg 117 Q6 volume cuboid MR Pg 205 Q6 Area & ratio PS Pg 204 Q4 create equation for volume & solve Page 7

8 MODULE 7 Algebra 3 DURATION: 7 Lessons Plot coordinates in all 4 quadrants How to calculate with negative numbers Recognise and draw the graph of a linear function Recognise and draw the graph of a quadratic function Work out the gradient of a graph from a linear function Work out an equation of the form y = mx + c from the graph Draw graphs from real life situations to illustrate the relationship between two variables Solve linear and simultaneous equations graphically New Collins Frameworking Yr 8 2:2 Ex 7A, B, C, D 10 Ticks level 5 pg. 4&6 AQA F Tier Ex 28 A D & F, Ex 29 A & B Collins F Tier Ex 14 D & E We teach maths My maths Mathswatch 96 98, 140 Corbett maths KEYWORDS For the More Able EXAM STYLE QUESTIONS Substitute Rule Table of values Co-ordinates, axes Equation Straight line graphs, linear Gradient Constant Distance-time graphs Average speed Quadratic Y-intercept Variable Origin Use graphs of linear and quadratic equations to solve. Pg 132 Q1 Distance/time graph Pg 133 Q4equations of lines PS Pg 133 Q5 pendulum graph Page 8

9 MODULE 8 Number 3 DURATION: 4 Lessons To multiply and divide by powers of 10 To round to the nearest 10, 100 and 1000 Multiply and divide by powers of 10 Rounding to a given dp Multiply with numbers in standard form Round large numbers Round to 1 or more significant figures Use a calculator efficiently New Collins Frameworking Yr 8 2:2 Ex 8 C, D & E AQA F Tier Ex 12 C, Ex 15 A - E We teach maths My maths Mathswatch 82, 83 Corbett maths Use Ex 8A & B as starters only KEYWORDS For the More Able EXAM STYLE QUESTIONS Estimate Power Round, approximate Standard form Significant Significant figures Calculations with standard form Challenge pg 152 book 2:2 PS Pg 150 Q2 sf MR Pg 150 Q8 show that standard form MR Pg 150 Q9 show that. sf Page 9

10 MODULE 9 Handling Data 2 DURATION: 5 Lessons Interpret data from tables, graphs and charts Read pie charts where the sectors are percent or simple fractions Find the mode, median, mean and range for small data sets Work out the size of sectors in pie charts by their angles at the centre Use a scaling method to draw pie charts Read scatter graphs Understand correlation Create scatter graphs New Collins Frameworking Yr 8 2:2 Ex 9A, B, C, D 10 Ticks L5 P6 & L6 P6 AQA F Tier Ex 2D, Ex 3 D, E Collins F Tier Ex 22 A, B We teach maths My maths Mathswatch 128, 129 Corbett maths KEYWORDS For the More Able EXAM STYLE QUESTIONS Pie charts Scatter graphs Frequency table Sector Correlation Total frequency Scaling Frequency Interpolate/extrapolate using line of best fit Pg 168 Q2 Pie Chart Pg 169 Q3 interpret Scatter graph PS Pg169 Q4 scatter graph Page 10

11 MODULE 10 Algebra 4 DURATION: 5 Lessons What an algebraic expression is How to interpret simple algebraic expressions Write a simple algebraic expression Identify equivalent expressions Write algebraic expressions involving powers Simplify algebraic expressions involving the 4 basic operations Simplify algebraic expressions by combining like terms Remove/expand brackets from an expression Manipulate an algebraic expression Product of two brackets (binomials) New Collins Frameworking Yr 8 2:2 Ex 10C, D, E Use Ex 10A & B as starters to recap simplifying expressions 10 Ticks L6 P1&4, AQA F Tier Ex 16 A, B Ex 7A - D Collins F Tier Ex 7B E, G Collins H Tier Ex 12 A - C We teach maths My maths Mathswatch 33 35, 93, 134 Corbett maths Need more resources for substitution into formula (also done in area) KEYWORDS For the More Able EXAM STYLE QUESTIONS Expression Like terms, collect Substitute Brackets Expand Power, index Manipulate Equivalent Multiply out Index notation Simplify Algebraic expression Product of 3 binomials MW 178 PS Pg 185 Q8 Mean & algebra Pg 185 Q9 volume& algebra Pg 185 Q8 surface area & algebra Use algebra in context creating expressions/equations Page 11

12 Representing 3D shapes Plans And Elevations Learning Objectives: 1. To interpret 2 D representations of 3D shapes 2. To analyse 3D shapes using plans, elevations and isometric drawings 3. To develop their reasoning ability in spatial contexts Starter: to be able to draw multi-link cubes onto isometric paper practise Time: 1-2 hours or if possible 80 mins Resources: Building Houses 1& 2 OHT 1 Plans & Elevations OHT 2 Isometric drawing Card set A Perspectives Card set B - Plans & Elevations Card set C - Isometric drawing Squared & triangular grid paper & isometric graph paper Multi-link cubes Need a set of each card set for each group of 4 Lesson: Building house 1: In groups of 2 or 4 ask what they think this house looks like from above (plan), from the front (front elevation), from the right side ( right side elevation) draw onto squared grid paper. Discuss: Could add colour to picture plan in red, front elevation coloured in blue, and right side elevation coloured in green this helps focus Repeat with Building house 2, OHT 1 In groups of 2/4 using card sets A & B match up the perspectives to the plans & elevations give reasons for each match. Do not pack these away but leave out (needed later) Sketch a cube house for the remaining 3 plans & elevations cards onto perspective card F (& make it using multi-link cubes) Using 4 multi-link cubes make all possible arrangements & draw onto isometric paper. OHT 2 Isometric drawings -which shows perspective card F together with isometric drawing. Explain how this shows how cubes can be hidden in the isometric view. Give out Card set C & match the drawings to the previous card set A & B Plenary: Present them with a front and side elevation & ask them to draw a plan, sketch or to make it using multi-link cubes. See below for example Page 12

13 Front Side elevation Page 13

14 MODULE 11 Shape, space and measure 3 DURATION: 6 Lessons Identify lines of symmetry in 2D shapes Recognise shapes in different orientations Reflect shapes in vertical/horizontal mirror lines Describe position and movement, translate 2D shapes Use ratio Know how to use map ratios Understand and use scale drawings Recognise congruent shapes Enlarge a 2D shape by a scale factor Use ratio to compare lengths, areas and volumes of 2D and 3D shapes Plans & elevations New Collins Frameworking Yr 8 2:2 Ex 11A, B, C, D 10 Ticks L5 P7 AQA F Tier Ex 21 E, F, Ex 33 B, Ex 34 A, B Collins F Tier Ex 19A, F, Ex 17C We teach maths My maths Mathswatch 12, 148 Corbett maths KEYWORDS For the More Able EXAM STYLE QUESTIONS Congruent Transformations Enlargement Centre of enlargement Scale factor Ray Scale drawing Scale Map ratio Hectare Congruent triangles Enlarge using fractional & negative scale factors Pg 204 Q2 enlargement Pg 204 Q3 enlargement Pg 204 Q5 map ratios Pg 204 Q7 Page 14

15 MODULE 12 Proportion DURATION: 4 Lessons How to write a simple formula algebraically Know what a ratio is How to draw graphs To understand the meaning of direct proportion Find missing values in problems involving proportion Represent direct proportion graphically and algebraically Understand what inverse proportion is Use graphical and algebraic representations of inverse proportions Recognise direct and inverse proportion and work out missing values New Collins Frameworking Yr 8 2:2 Ex 13A, B, C, D AQA F Tier Ex 27 A - E Collins F Tier Ex 9E, F We teach maths My maths Mathswatch 42, 199 Corbett maths KEYWORDS For the More Able EXAM STYLE QUESTIONS FS Pg 228 Q2 direct proportion Direct proportion Pg 228 Q5 direct proportion Proportional FS Pg 229 Q13 direct proportion Find the equation Variable FS Pg 229 Q14 direct proportion linking the 2 Formula FS Pg 234 exchange rates task A, B & C variables (using k) Graph Pg 243 Q10 inverse proportion Inverse proportion Page 15

16 MODULE 13 Shape, Space and Measure 4 DURATION: 3 Lessons Know the words radius and diameter Use a compass to draw a circle Know what a regular polygon is Know the definition of a circle and the name of its parts Work out the relationship between the circumference and diameter of a circle Calculate the circumference of a circle Calculate the area of a circle New Collins Frameworking Yr 8 2:2 Ex 14A Ex 14A, B, C, D Ex 14A chiefly checks can use a compass Activity: pg Athletics stadium AQA F Tier Ex 10 C E, Ex 11 C,D Collins F Tier Ex 16 A - D We teach maths My maths Mathswatch Corbett maths Arc Chord Diameter Sector Semi-circle Centre Circumference Radius Segment Tangent Pi KEYWORDS For the More Able EXAM STYLE QUESTIONS Find length of arc, area of sector MR Pg259 Q6 circumference PS Pg 259 Q7 area circle & rectangle PS Pg 259 Q8 Area circle, square & percentages Page 16

17 MODULE 14 Algebra 5 DURATION: 5 Lessons How to solve a simple equation How to write a simple equation Solve equations involving brackets Solve equations with the variable on both sides Solve equations with a fractional coefficient Solve equations with bracket & fractions Change the subject of a formula New Collins Frameworking Yr 8 2:2 Ex 15A, B, C, D Pg AQA F Tier Ex 17 A, B, Ex 22C Collins F Tier Ex 13 B G, I We teach maths My maths Mathswatch 100, 101, 135, 136 Corbett maths KEYWORDS For the More Able EXAM STYLE QUESTIONS Inverse operation Variable Subject Formula Solve Equation Expand Expression Using graphs to solve equations (e.g. simultaneous equations) book 2:2 pg 276 PS Pg 274 Q5 create an equation & solve PS Pg 275 Q6 create an equation & solve Page 17

18 MODULE 15 Handling Data 3 DURATION: 4 Lessons Construct a frequency table from given data Find mode, median and range and modal class from grouped data Calculate the mean from a set of data Construct graphs and diagrams to represent data Interpret & construct line graphs Create a grouped frequency table from raw data Interpret frequency diagrams Draw a frequency diagram from a grouped frequency table Use mean and range to compare data from 2 sources Understand when each different type of average is most useful New Collins Frameworking Yr 8 2:2 Ex 16A, C, D Assumed mean Key maths statistics Pg 87 Ex 3:7 AQA F Tier Ex 3A, B Collins F Tier Ex 11 A - H We teach maths My maths Mathswatch 62, 65, 128, 130 Corbett maths Use Ex 16B as a starter KEYWORDS For the More Able EXAM STYLE QUESTIONS Class Discrete Grouped frequency table Continuous Frequency Raw data Mean Median Mode, modal class Range Average Estimate mean of grouped frequency tables MR Pg 290 Q1 averages PS Pg291 Q8 mean, median, mode & algebra PS Pg291 Q9 mean & algebra Page 18

19 MODULE 16 Number 4 DURATION: 5 Lessons Order fractions Use the 4 rules of fractions including mixed numbers To find equivalent fractions To add & subtract fractions & mixed numbers To multiply a fraction & an integer To divide a fraction or a mixed number by an integer To divide an integer by a unit fraction To multiply with combinations of large & small numbers mentally To divide with combinations of large & small numbers mentally To find the LCM & HCF New Collins Frameworking Yr 8 2:2 Ex 12A - E AQA F Tier Ex 5A - D Collins F Tier Ex 2B, C, E - G We teach maths My maths Mathswatch 25, 26, 27, 70 74, 84, Corbett maths KEYWORDS For the More Able EXAM STYLE QUESTIONS Improper fraction Numerator Convert recurring decimals to Denominator fractions MW 177 PS: Q8 & Q12 Pg 223 Mixed number Apply fraction MR: Q11 Integer methods to Unit fraction algebra MW 210 Divisor Page 19

20 MODULE 17 Number 5 DURATION: 4 Lessons 4 rules of basic arithmetic using integers Find percentages of an amount To use written methods for long multiplication & division To carry out the 4 basic operations on decimals without a calculator To understand & use simple & compound Interest New Collins Frameworking Yr 8 2:2 Ex AQA F Tier Ex 38 A, B, Ex 6C- E Collins F Tier Ex 8A, B, E - H We teach maths My maths Mathswatch 17, 18, 66, 67, 111, 164, Corbett maths KEYWORDS For the More Able EXAM STYLE QUESTIONS Simple Interest Compound Interest Multiplier Percentage Principal Reverse interest/percenta ges Page 20

21 MODULE 18 SSM6 DURATION: 5 Lessons Square numbers To use & apply Pythagoras Theorem to find the longest/shorter side of a right angled triangle TO convert metric units of measure New Collins Frameworking Yr 8 2:2 Ex AQA F Tier Ex 35A - F Collins F Tier Ex 26A - C We teach maths My maths Mathswatch 150 Corbett maths KEYWORDS For the More Able EXAM STYLE QUESTIONS Real life questions Page 21

22 Number Pyramids Speed up sheets Page 22

23 Back to Pre-Module 1 Teacher Notes N1 Number Pyramids Speed up sheets 2 Page 23

24 Back to Pre-Module 1 Teacher NotesBuilding Houses 1 Building Houses 2 Back to Pre-Module 11 Teacher Notes Page 24

25 SSM 3 OHT 1 Plans and Elevations Year 8 Sets 2, 3 & 4 Pathways Back to Pre-Module 11 Teacher Notes Page 25

26 SSM3 OHT 2 Isometric Drawing Year 8 Sets 2, 3 & 4 Pathways Back to Pre-Module 11 Teacher Notes Page 26

27 Perspectives Card set A Back to Pre-Module 11 Teacher Notes Page 27

28 Perspectives Card set B Year 8 Sets 2, 3 & 4 Pathways Back to Pre-Module 11 Teacher Notes Page 28

29 Perspectives Card set C Year 8 Sets 2, 3 & 4 Pathways Back to Pre-Module 11 Teacher Notes Page 29

30 Page 30

31 Page 31

32 Year 7 Set 1 Pathway Fast Track Page 32