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Year 7 05/09/2016 12/09/2016 19/09/2016 26/09/2016 03/10/2016 10/10/2016 17/10/2016 24/10/2016 HALF 31/10/2016 07/11/2016 14/11/2016 21/11/2016 28/11/2016 05/12/2016 12/12/2016 19/12/2016 26/12/2016 XMAS 02/01/2017 09/01/2017 MID YEAR 16/01/2017 TESTS MID YEAR 23/01/2017 TESTS 30/01/2017 06/02/2017 13/02/2017 HALF 20/02/2017 27/02/2017 06/03/2017 13/03/2017 20/03/2017 27/03/2017 EASTER 03/04/2017 HOL EASTER 10/04/2017 HOL 17/04/2017 24/04/2017 01/05/2017 08/05/2017 15/05/2017 22/05/2017 29/05/2017 HALF End of 05/06/2017 year test 12/01/1900 06/01/1900 Set 2 Pathway A Numeracy skills 1. Number 1 2 DAY WK 2. Crossed Ends & Algebra 1 3. S,S & M 1 TERM 4. Number 2 5. Handling Data 1 Parents induction & tutor meeting 6. Algebra 2 2 DAY WK HOL 2 DAY WK 7. Understanding laws of Arithmetic & number 3 8. S,S & M 2 TERM 9. Algebra 3 10. Number 4 BANK HOL MON 11. Probability games & Probability BANK HOL MON, Parents Evening 2nd 12. Algebra 4 TERM 13. Ratio Page | 1 Year 7 12/06/2017 19/06/2017 26/06/2017 03/07/2017 10/07/2017 17/07/2017 24/07/2017 Set 2 Pathway A 14. S,S & M 3 15. S,S & M 4 3D nets Page | 2 Year 7 MODULE 1 Set 2 Pathway A Number 1 DURATION: 9 Lessons PRIOR KNOWLEDGE Understand place value in numbers up to 1000 Begin to use decimal notation in contexts e.g. money Recognise negative numbers in context e.g. temperature LEARNING OBJECTIVES N1 Understand place value to multiple and divide whole numbers & decimals by 10, 100 & 1000 and explain its effects N2 To use a number line to order positive and negative numbers (in context) To understand and use the symbols > and < To order decimals F2/N4: Solve problems with/without a calculator To use written methods for decimals – 4 operations To add numbers involving negatives and decimals To use number line to calculate with negatives N13 Round decimals to the nearest decimal place N14 To estimate calculation in order to recognise possible errors RESOURCES Collins Framework 7 1-2 Ex 1B, C, D Ex 4A, B, C, D, E Links 7B Ch 1 Ex 1A, B, C, D, E, F, G, H KEYWORDS Positive, negative Decimal Tenths, hundredths Number line Order Estimate Round Add, subtract, multiply, divide Decimal Places Rank Reciprocal DIFFERENTIATION AND EXTENSION Check mental methods for 4 operations Probing Questions* Financial skills Pg 80-81 PAST EXAM QUESTION FS Pg 22 Q4 Bank Balance PS Pg 22 Q5 Negative Numbers FS Pg 23 Q6 Bank Statement PS Pg 23 Q7 Negative Numbers Page | 3 Year 7 Set 2 Pathway A Task: Year 7 module A1 Nrich –Crossed Ends Teachers notes : Learning Objectives: Introduce and develop an understanding of algebraic notation Reinforce 2 digit addition Resources: Activity sheet, number grids (different sized), pencil, ruler, colours Grouping:- 2s or 4s Display a number grid select a square cross – add the top(north) and bottom(south) numbers, then add left(west ) and right(east) numbers. What do you notice? Was it a fluke draw another cross and repeat Change size of square cross? Change size of grid Discuss in pairs why? Explain? Lead to describing using “n” What about adding the north value to the West value similarly with the south and east values still the same? Pupils’ notes Draw square crosses on your grid add the north value to the south value. Add the west and east values together. What do you notice? Repeat for 4 more square crosses Can you explain why this is happening? Change size of square cross? Change size of grid Discuss in pairs why? Explain? Lead to describing using “n” -Can you write each number in terms of n which is the middle number of your cross? What if you used a rectangular cross? Would the rule be the same if you added north to east and then added south to west? Investigate… Can you explain what you are finding? Page | 4 Year 7 MODULE 2 Set 2 Pathway A Algebra 1 DURATION: 6 Lessons PRIOR KNOWLEDGE Odd and even numbers 4 rules of arithmetic Tables to x12 LEARNING OBJECTIVES . A14 Generate sequences using term to term rule Work out missing terms in a sequence To recognise, describe and generate sequences that use a simple rule To know and understand the sequences of numbers known as square and triangular numbers Use function machines with 2 operations and find function where input & output are given A15 Find the nth term of an arithmetic sequence RESOURCES Collins Framework 7/1-2 Ex 2A, B, C MR Pg 42+43 Links 7B Ex 2A, B, C, D KEYWORDS Sequences Predict Function Machine Term, Position Rule Difference Term to Term Mappings Input, Output DIFFERENTIATION AND EXTENSION Rules from patterns pictorial/numerical PAST EXAM QUESTION FS Pg 41 Q4 Nth term Pg 41 Q5 Pattern in the Sequence Page | 5 Year 7 MODULE 3 Set 2 Pathway A Shape, space & measure 1 DURATION: 6 lessons PRIOR KNOWLEDGE Name and describe common 2D and 3D shapes LEARNING OBJECTIVES . G1 G2 Find perimeters of simple shapes Find areas by counting squares Derive and use simple formula to calculate the perimeter and area of a rectangle Solve problems with perimeter/area of 2D shapes Work out and use formula to find area/perimeter of compound shapes Calculate areas (and composite areas) of squares, rectangles, right angle triangles and volumes of cubes and cuboids Include area + circumference of circles? RESOURCES Collins Framework 7/ 1-2 Ex 3A Q 4 – 7, 10 Ex 3B, C, D Links 7B Ch 3 Ex 3A, B, C, D, E, F, G KEYWORDS Centimetre, metre, millimetre, kilometre Length, width Perimeter, area Square units (mm2 etc.) Metric units Formula Square, rectangle Compound shapes Volume, capacity Cube, cuboid Height Litre Estimate DIFFERENTIATION AND EXTENSION Surface area of cuboids & prisms PAST EXAM QUESTION PS Pg 60 Q3 Area of a rectangle PS Pg 61 Q5 Perimeter of the logo PS Pg 61 Q6 Compound shape PS Pg 61 Q7 Compound shape area PS Pg 61 Q8 Volume of cuboids Page | 6 Year 7 MODULE 4 Set 2 Pathway A Number 2 DURATION: 6 lessons PRIOR KNOWLEDGE How to square a number Tables to x12 Place value including decimals Use a calculator for simple calculations Convert units of a measure LEARNING OBJECTIVES N4 Choose a written methods for multiplying 2 numbers together and dividing Carry out written method for accurate multiplication and division N5 BIDMAS + Reciprocals -- need something on reciprocals e.g. pg. 70 “investigation” N7 Square + square roots, Cube + cube roots N13 Round numbers to appropriate degree of accuracy e.g. dp or sf N12 Standard units of measure, to convert between common metric units To use measurement in calculations To recognise and use appropriate metric units RESOURCES Collins Framework 7/1-2 Ex 5A, B, C, D, E KEYWORDS DIFFERENTIATION AND EXTENSION Power Square (root), squaring, square number Decimal place Round up/down, rounding Units, digit Cube (root), cubing, cube Extend square numbers and roots number into cube numbers and cube BIDMAS roots Order of operations Operation Reciprocal Methods of multiplication and Division Remainder PAST EXAM QUESTION PS Pg 79 Q7 Multiplying and Dividing by Decimals PS Pg 79 Q8 Volume and Estimation Page | 7 Year 7 MODULE 5 Set 2 Pathway A Handling Data 1 DURATION: 9 lessons PRIOR KNOWLEDGE Extract & interpret information presented in simple tables and lists Collect, display and interpret data in pictograms & bar charts in order to communicate information Create tally charts LEARNING OBJECTIVES S1 Understand and calculate the mode, median and range of data Understand and calculate the mean average of data Understand and use grouped frequencies S2 Read and interpret different statistical diagrams Create and use a tally chart, line graph, frequency table Construct and interpret pictograms where the symbol may represent a group of units Interrogate a simple data base for one criterion To develop greater understanding of data collection RESOURCES Collins Framework 7/1-2 Ex 6A, B, C, D, E, F Ex 15A, B, C Links 7B Ch 5 Ex 5A, B, C, D, E, F Ch 8 Ex 8A, B, C, D Ch 14 Ex 14,D, E, F, G KEYWORDS Interpret Mode, median, mean & range Pictogram, key Bar chart Compound bar chart Scale Data Axis Line graph Fluctuations Pie chart Modal class, spread Certain, unlikely, likely, impossible Probability (scale) Average Frequency DIFFERENTIATION AND EXTENSION Drawing Pie charts accurately Design questionnaire/compare averages of 2 sets of data PAST EXAM QUESTION PS Pg 124 Q3 Range PS Pg 124 Q4 Mean PS Pg 125 Q8 Mode and Mean PS Pg 296 Q3 Comparing averages PS Pg 297 Q4 Make a Datacollection sheet. FS Pg 297 Q7 Pie Chart Page | 8 Year 7 MODULE 6 Set 2 Pathway A Algebra 2 DURATION: 6 lessons PRIOR KNOWLEDGE Understand and use simple rules expressed in words Use more than 1 operation in a calculation Understand and use order of operations Know the meaning of term and expression LEARNING OBJECTIVES A2, A3 Construct and use simple expressions Substitute integers into an expression To use formulae Solve simple linear equations with integer coefficients with unknowns on 1 side A4 Simplify an expression F3 Use algebra to formulate mathematical relationships RESOURCES Collins Framework 7/1-2 Ex 7A, B, C, D Links 7B Ch 6 Ex 6A, B, C, D, E KEYWORDS Order of operations Amount, value Symbol, represent Expression Substitute Collect, like terms Simplify Term, formula Pattern Solve, expand, bracket Variable, coefficient Derive, generalise Subject DIFFERENTIATION AND EXTENSION PAST EXAM QUESTION PS Pg 144 Q2 Substitution Pg 145 Q7 Simplifying Expressions Page | 9 Year 7 Set 2 Pathway A Understanding the laws of arithmetic Year 7 Module N 3 Learning Objectives: Write expressions in a real life context Recognise the order of operations Simplify expressions Previous knowledge: Familiar with indices Finding the area of simple compound shapes see check (starter question) Starter Question What is the difference between 3 x 2 and 3²? Draw 2 different rectangles with area of 36. What is the area of this shape? Resources: Mini white boards Card set B Areas Sheet for brackets activity 4 3 1 3 Card set A Calculations Card set C Solutions Time: 40 mins to 8 mins Main Activity 1 Draw 3 compound shapes onto the board see smart board sheet saved Ask 1. If you work out 3 + 4 x 2 which area are you working out? Explain how you know. Ask 2. If you work out (3 + 4) x 2, which area are you working out? How do you know? Ask 3. What answers does your calculator give for the other area? Ask 4. Can you give me an expression for the other area? Ask 5. What is the difference between (2 + 3)² and 2² + 3² ? Ask 6. Can you show me a diagram to explain the difference? Ask students to explain BODMAS or BIDMAS & explain its meaning. Explain the danger of using such a rule without understanding it. What is wrong with workings below -identify the mistake 3 x (3 + 5) ² - 5 + 9 = 3 x 8² - 5 + 9 Brackets 4 4 = 3 x 64 – 5 + 9 Indices = 3 x 16 – 5 + 9 Division = 48 – 5 + 9 Multiplication = 48 – 14 Addition = 34 Subtraction Page | 10 Year 7 Set 2 Pathway A In pairs/groups of 4: Card sort sets A, B and C Match up the 3 sets and explain/discuss your mathematical reasoning. For the additional calculation cards they will need to create a matching card for the area and the solution. Differentiation: In pairs/groups of 4: sort sets A,shapes B and into C Match up theand 3 sets yourfinding the area Students could cutCard the compound rectangles findand theexplain/discuss area of each before mathematical reasoning. of the compound shape. ForStudents the additional they will need to create a matching card for the area and the solution. could calculation progress to cards generalisation Differentiation: What happens when we change the numbers? students could the compound shapes andcalculation find the area of still eachmatch beforeinfinding theway? area Suppose wecut change the 4 in every cardinto to arectangles 5? Will the cards the same of the compound shape. Will this still be true when we change the 4 to a large number, a negative number or a decimal? Students progresshelp to generalisation Do thecould area pictures to explain why this happens? What happens when we change the numbers? Suppose we change the 4 in every card to a 5? Will the calculation cards still match in the same way? Will this still be true when we change the 4 to a large number, a negative number or a decimal? Plenary: DoUse the area helpQ& to explain why this happens? wipepictures boards and A Draw an area that requires this calculation: 3 x ( 4 + 5) Write a different calculation that gives the same area. Draw an area that requires this calculation 6 + 8 2 Plenary: Write a different calculation that gives the same area. Use wipe and Q& A this calculation: (10 + 5)². Draw an boards area that requires Draw that requires thisthat calculation: x ( 4area. + 5) Writeana area different calculation gives the3same Write a different calculation that gives the same area. Draw area requires this calculation + 8 emerged: Drawanout thethat general learning points that 6have 2 by 2 The equivalence of multiplying by ½ and dividing Write a different calculation that gives the same area. The order of operations Draw an area that Brackets first requires this calculation: (10 + 5)². Write a different calculation that gives the same area. Then powers or roots Draw out the general learning points that have emerged: Then multiplication or division The equivalence Then additionof ormultiplying subtraction by ½ and dividing by 2 The order of operations Equivalent expressions: 2 x (3 + 4) = 2 x 3 + 2 x 4 multiplication is distributive over addition Brackets 3 +first 4 = 3 + 4 division is distributive over addition Then powers 2 or rrots 2 2 Then multiplication or division Then addition or subtraction The Brackets activity (consolidation) Equivalent expressions: 2 x (3 + 4) = 2 x 3 + 2 x 4 multiplication is distributive over addition Use wipe boards: 3+4 = 3 + 4 division is distributive over addition 2 2 2 Sheet A Sheet B Sheet C 2+3x4+5 2x3+4x5 2 + 3 x 4² Call out a sheet name and a target number eg sheet A & 25 write answer onto wipe board showing use of brackets Page | 11 Year 7 Set 2 Pathway A Sheet Target Method A 29 2 + 3 x (4 + 5 ) A 45 (2+3)x(4+5) B 26 2x3+4x5 B 46 2x(3+4x5) B 50 (2x3+4)x5 B 70 2x(3+4)x5 C 80 ( 2 + 3 ) x 4² C 146 2 + ( 3 x 4 )² C 196 ( 2 + 3 x 4 )² C 400 ( ( 2 + 3 ) x 4 )² Page | 12 Year 7 MODULE 7 Set 2 Pathway A Number 3 DURATION: 6 lessons PRIOR KNOWLEDGE Common multiples Recognise and use simple fractions Compare and order fractions with the same denominator LEARNING OBJECTIVES N9 Find simple equivalent fractions Write fractions in simplest form N2 Compare and order two fractions N4 Add/subtract fractions with same/different denominators, including mixed numbers Convert mixed numbers to improper fractions and vice versa RESOURCES Collins Framework 7/1-2 Ex 8A, B, C, D, E, F, G KEYWORDS Equivalent (fractions) Denominator, numerator Simplest form Simplify, cancel Addition, subtraction LCM Convert Improper fraction Mixed number DIFFERENTIATION AND EXTENSION PAST EXAM QUESTION PS Pg 165 Q7 Halfway between the two fractions Pg 165 Q12 Adding and Subtracting fractions Page | 13 Year 7 MODULE 8 Set 2 Pathway A Shape, space & measure 2 DURATION: 9 Lessons PRIOR KNOWLEDGE Recognise and name different types of angles Recognise and name different triangles and quadrilaterals LEARNING OBJECTIVES G7, G12 Know that the sum of angles in a triangle is 180 and of a quadrilateral is 360 Understand and use the properties of triangles and quadrilaterals G10 Use a protractor to measure/draw angles Calculate opposite angles, angles at a point and angles on a straight line G10, G11 Understand the properties of parallel, intersecting and perpendicular lines RESOURCES Collins Framework 7/1-2 Ex 9A, B, C, D, E KEYWORDS Acute, obtuse, right, reflex Degrees Calculate Vertically opposite Isosceles, equilateral Quadrilateral Diagonal Geometrical properties Intersect, parallel Perpendicular Vertex, vertices DIFFERENTIATION AND EXTENSION Constructing triangles and bisecting angles PAST EXAM QUESTION MR Pg 191 Q5 Angles in quadrilateral MR Pg 191 Q6 Angles in triangle MR Pg 191 Q7 Geometrical properties Page | 14 Year 7 MODULE 9 Set 2 Pathway A DURATION: 6 lessons Algebra 3 PRIOR KNOWLEDGE Know how to plot coordinates in the first quadrant LEARNING OBJECTIVES A8 Understand and use co-ordinates to locate points in all 4 quadrants A9, F6, M1 Work out coordinates that fit a simple relationship A11 Recognise and draw line graphs with fixed values of x and y Recognise and draw lines in the form of y = ax and y + x = a A13 Learn how graphs can be used to represent real life situations RESOURCES Collins Framework 7/1-2 Ex 10A, B, C, D, E, F KEYWORDS Axes, origin X-axis, Y-axis Coordinate, quadrant X co-ord, Y coord Straight line graph Coordinate grid Equation Relationship Conversion graph DIFFERENTIATION AND EXTENSION PAST EXAM QUESTION FS Pg 212 Q3 Real life situation graph MR Pg 213 Q4 Equation of a line Page | 15 Year 7 MODULE 10 Set 2 Pathway A DURATION: 12 lessons Number 4 PRIOR KNOWLEDGE Able to write ¼ and 1/10 as decimal/percent Simplify fractions Work out a simple % of a whole number LEARNING OBJECTIVES N10 Recognise approximate proportions of a whole and use simple fractions and percentages to describe these N11 Find a percent of a quantity Find a fraction of a quantity N15, M8, M9 Use understanding of equivalence to add and subtract simple fractions Understand the relationship between simple fractions, decimals and percentages Understand and use the equivalences between fractions, decimals and percentages Calculate percent increase/decrease RESOURCES Collins Framework 7/1-2 Ex 11A, B, C, D, E Links 7B Ex 4A, B, C, D, E, F DIFFERENTIATION AND EXTENSION KEYWORDS Numerator, denominator Fraction Equivalent Improper, mixed Decimal, whole Tenth, hundredth, unit Percentage, percent Cancel HCF Terminating decimal Integer Number line Place value Deposit Quantity PAST EXAM QUESTION PS Pg 231 Q10 Percentage of an amount FS Pg 231 Q11 Percentage decrease FS Pg 231 Q12 Percentage increase FS Pg 231 Q14 Percentage decrease FS Pg 231 Q15 Percentage increase FS Pg 231 Q17 Percentage decrease Finance & percentages Pg 224, 229 & 232 Page | 16 Year 7 Set 2 Pathway A Probability Games Year 7 Probability Choose 2 from the following 4 games:- either Hare & Tortoise or Dice difference and Grand National or Motorway Need dice &/ counters In Pairs: For each game agree you understand the rules and how to play Decide upon how you will record your results Play the game 3 /4 times Discuss whether game is fair or not For Hare & Tortoise or dice difference design a sample space diagram for rolling 2 dice and calculating the difference. See below a partially completed diagram difference 1 2 0 1 1 1 2 2 3 3 4 4 5 5 6 3 2 4 3 5 4 6 5 Work out the probability of getting a difference of 0, 1 or 2 Work out the probability of getting a difference of 3, 4 or 5 Is the game fair? What evidence could you use from your sample space diagram and calculations can you provide to support your theory? Task: Make the game fair by changing the rules then test your game by playing it 3 / 4 times and recording the results. Motorway Place your 10 counters Can I place more than 1 counter onto the same number? Play the game 3 / 4 times Is the game fair? Did you change your strategy? What advice would you give to someone playing the game? What evidence could you provide to support your advice? Use a sample space diagram see below a partially completed diagram Sum total 1 2 3 4 2 3 4 5 1 3 2 4 3 5 4 6 5 7 6 5 6 6 7 Page | 17 Year 7 Set 2 Pathway A Grand National Play the game 3 / 4 times Is the game fair? Use a sample space diagram see below a partially completed diagram Sum total 1 2 3 4 2 3 4 5 1 3 2 4 3 5 4 6 5 7 6 5 6 6 7 How can you use this diagram to support your argument ? Change the rules to make your game fair You may wish to handicap some horses – how? Make the race longer for some horses – how Or you may have a better suggestion Test your game 3 / 4 times to show that it is now fair. Page | 18 Year 7 MODULE 11 Set 2 Pathway A DURATION: 9 lessons Probability PRIOR KNOWLEDGE Basic ideas about chance and probability How to collect data from a simple experiment How to record data with table/chart LEARNING OBJECTIVES P1, P2 To learn and use the correct words about probability Learn about and use probability scales from 0 to 1 To work out probabilities based on equally likely outcomes RESOURCES Collins Framework 7/1-2 Ex 12A, B, C KEYWORDS Chance At random Event, outcome Probability (scale) Biased, Fair Equally likely Probability fraction Experimental probability Theoretical Trial DIFFERENTIATION AND EXTENSION PAST EXAM QUESTION PS Pg 247 Q7 Sample Space Diagram Pg 247 Q3 Probability Pg 247 Q5 Probability Financial & Easter Ch 12 Pg 248-249 Venn Diagrams Key maths GCSE Statistics text Chap 6 Page | 19 Year 7 MODULE 12 Set 2 Pathway A DURATION: 9 lessons Algebra 4: Solving Equations PRIOR KNOWLEDGE How to write and use expressions Able to substitute numbers into expressions to work out their values Can write and use simple formulae LEARNING OBJECTIVES A7, F3 Find missing numbers in simple calculations Solve equations involving 1 and 2 operations Use algebra to set up and solve equations RESOURCES Collins Framework 7/1-2 Ex 14A, B, C, D KEYWORDS Algebra Unknown number Variable Equations Solve Inverse, balancing Operation DIFFERENTIATION AND EXTENSION PAST EXAM QUESTION Pg 282 Q3 Linking algebra to angles Pg 283 Q3 Solving equation Pg 283 Q8 Writing and solving equation Page | 20 Year 7 MODULE 13 Set 2 Pathway A Ratio DURATION: 6 lessons PRIOR KNOWLEDGE Can simplify fractions Find a fraction of a quantity Equivalence between simple fractions and percentages Can interpret bar and pie charts LEARNING OBJECTIVES R4 Use ratio notation Write ratios as simply as possible R4, R6 Use ratio to compose quantities R5 Use ratios to find totals or missing quantities R6 Understand the connections between fractions and ratios R9, R10 Understand how ratios can be useful to everyday life RESOURCES Collins Framework 7/1-2 Ex 17A, B, C, D KEYWORDS Ratio Quantity Fraction Simplify DIFFERENTIATION AND EXTENSION PAST EXAM QUESTION MR Pg 326 Q1 Proportion (Recipe) PS Pg 326 Q5 Ratio (Perimeter) PS Pg 327 Q6 Ratio (Age) PS Pg 327 Q7 Finding the unknown PS Pg 327 Q8 Ratio and comparing Page | 21 Year 7 MODULE 14 Set 2 Pathway A Shape, Space and Measure 3 DURATION: 6 lessons PRIOR KNOWLEDGE Recognise symmetrical shapes Can plot co-ordinates LEARNING OBJECTIVES G5, G7 Recognise shapes with reflective symmetry G5, G8 Draw lines of symmetry on a shape Recognise shapes that have rotational symmetry Find the order of rotational symmetry for a shape G8 Understand how to reflect a shape Use co-ordinates to reflect shapes in all 4 quadrants G7, G16? Understand how to tessellate shapes RESOURCES Collins Framework 7/1-2 Ex 13A, B, C, D KEYWORDS Line of symmetry Mirror line Reflect Reflective symmetry Order of rotational symmetry Image Object Reflection Tessellation, tessellate DIFFERENTIATION AND EXTENSION PAST EXAM QUESTION MR Pg 262 Q3 Order of rotational symmetry MR Pg 263 Q7 Tessellation Rotation, Reflection, Translations and Enlargements Page | 22 Year 7 MODULE 15 Set 2 Pathway A 3D Shapes DURATION: 6 lessons PRIOR KNOWLEDGE How to draw a net of a cube Meaning of face, edge and vertex How to draw a cuboid LEARNING OBJECTIVES G5, G7 Be familiar with the names of 3D shapes and their properties Use isometric paper to draw 3D shapes made from cubes Draw nets of 3D shapes M5 Construct 3D shapes from nets Work out the relationship between face, edges and vertices for 3D shapes G15, F7 Solve problems involving 3D shapes RESOURCES Collins Framework 7/1-2 Ex 16A, B, C Problem Solving pg 312-313 KEYWORDS 3D Net Cube Face, edge, vertex Isometric Tetrahedron Hexagonal, pentagonal, triangular prisms Construct Pentomino DIFFERENTIATION AND EXTENSION 3D nets PAST EXAM QUESTION PS Pg 311 Q4 Volume and isometric grid MR Pg 311 Q5 Net of a cuboid/Volume/Percentage Page | 23 Year 7 Set 2 Pathway A Crossed Ends – Teacher Notes These crosses can be drawn on number grids of various sizes. Add opposite pairs of orange numbers (i.e. north + south, east + west). Notice anything? Try a few more. Now try the same questions on crosses with two lines of symmetry, like these: Experiment with grids of various sizes until you know that it's a coincidence, or until you know why it must always work. A sheet of number grids is available here What happens if you add the orange squares in adjacent pairs? (try N + W, S + E ) Can you predict in advance how the totals will relate to each other? What does it depend on? Is it the same if you added them the other way round? (i.e. N + E, S + W) Can you explain what you are finding? Page | 24 Year 7 Set 2 Pathway A Back to topic Page | 25 Year 7 Set 2 Pathway A Crossed Ends – Resource Grid 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9 8 9 10 11 12 13 14 9 10 11 12 13 14 15 16 10 11 12 13 14 15 16 17 18 15 16 17 18 19 20 21 17 18 19 20 21 22 23 24 19 20 21 22 23 24 25 26 27 22 23 24 25 26 27 28 25 26 27 28 29 30 31 32 28 29 30 31 32 33 34 35 36 29 30 31 32 33 34 35 33 34 35 36 37 38 39 40 37 38 39 40 41 42 43 44 45 36 37 38 39 40 41 42 41 42 43 44 45 46 47 48 46 47 48 49 50 51 52 53 54 43 44 45 46 47 48 49 49 50 51 52 53 54 55 56 55 56 57 58 59 60 61 62 63 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 64 65 66 67 68 69 70 71 72 57 58 59 60 61 62 63 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 64 65 66 67 68 69 70 73 74 75 76 77 78 79 80 82 83 84 85 86 87 88 89 90 71 72 73 74 75 76 77 81 82 83 84 85 86 87 88 91 92 93 94 95 96 97 98 99 78 79 80 81 82 83 84 89 90 91 92 93 94 95 96 100 101 102 103 104 105 106 107 108 85 86 87 88 89 90 91 97 98 99 100 101 102 103 104 109 110 111 112 113 114 115 116 117 Back to topic Page | 26 Year 7 Set 2 Pathway A Mini White Board Starter Back to topic Page | 27 Year 7 Set 2 Pathway A Card Set A: Calculations A2 A1 2 x (3 + 4) 3² + 4² A3 A4 (3 + 4)² A5 3 x 4² A6 3+4 (3 x 4)² A7 2 2 A8 2x3+4 A9 4+3x2 A10 3² x 4² A11 2x3+2x4 A12 ½(3 + 4) A13 3² + 4² + 2 x 3 x4 A14 3+4 2 3+ 4 2 Back to topic Page | 28 Year 7 Set 2 Pathway A Back to topic Page | 29 Year 7 Set 2 Pathway A Card Set C—Solutions 144 48 49 3.5 5.5 14 Back to topic Page | 30 Year 7 Set 2 Pathway A Motorway: Back to topic Page | 31 Year 7 Set 2 Pathway A The Grand National: Back to topic Page | 32 Year 7 Set 2 Pathway A Dice Difference: Back to topic Page | 33 Year 7 The Hare & the Tortoise Set 2 Pathway A Back to topic Page | 34