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7C e-resources Chapter Source Reference Activity Sect. Comments TG Starters MM Number / Number Number line This 'counting stick' starter can be used with whole numbers or operations / Number line decimals. You can hide the 'Start' (First number on the stick), the 'Step' and the numbers on the stick itself. Then uncover two numbers and decide what the others are. Use 'Automate' to set the start and step at random. MM Games / Mental games / Twenty 4 Different puzzles where you are given a set of four numbers Twenty 4 and have to use all of them to make 24 in three minutes. 1 First bites 2 Symmetry MM Shape / Symmetry / 3: Symmetry in a C Decide whether a flag design has rotational symmetry and, if it Rotation symmetry flag design does, state the order of rotational symmetry. There is some repetition. 4: Symmetry in a C Decide whether a design has rotational symmetry and, if it random design does, state the order of rotational symmetry. 3 Number skills MM AT1 / Number / Mini 6: Addition and A Introductory activity. Puzzles where numbers have to be investigations subtraction puzzles dragged into boxes to make correct addition and subtraction sums. You get a new pair of puzzles each time you go back to them. MM Games / Grid games / Times it out A Multiplying single digits. A timed puzzle where you have to 'zap' Times it out sets of numbers that multiply to make a target. You can repeat to try and improve your score. MM Games / TV Games / A As the TV programme except all totals are possible and the Countdown time limit can be altered to a maximum of 5 minutes. MM Number / Number Tool 1: Generate B Up to three-digit by three-digit multiplications are generated operations / Multiply your sums and reveal and then you uncover the various bits of the table method. double digits the solution MM Number / Number 7: Baseball teams - C Problems where one set demands rounding down and one operations / Division rounding down rounding up. chunking 8: Party balloons - rounding up 4 Growing FI Spotting numbers A, D The 'Draw/remove spots' option allows the flower bed patterns arrangements to be drawn in Section A and the different earrings in Section D. 5 Test it! 6 Number patterns MM Number / Powers and 3: Matching pairs B One memory matching puzzle that uses index notation for integers / Squares and game squares and goes up to 225. Cubes 4: Loop card game B One timed 'loop' puzzle that uses index notation for squares up to 400. 6: Beat the clock D Square roots of numbers up to 400. Repetition gives reinforcement. MM Number / Powers and D One memory matching puzzle that uses index notation for integers / Squares and squares and square roots up to 225. Cube Pairs 1 7 Angles and MM Shapes / Construction / 6: Constructing a A Animation to construct a 6 cm, 4 cm, 3 cm triangle. triangles Constructing shapes triangle from 3 lengths FI Cut outs B When a slider is operated, a net folds together to make a polyhedron (including three of those in Section B). Using the mouse pointer, you can rotate the shape in space or turn individual faces. MM Toolkit / AT1 / Shape Pinboard B, C, A flexible tool for drawing shapes on a square grid or a D triangular grid. You have a choice of three backgrounds: small squares, larger squares or triangles. A shape can be drawn with anything from 2 vertices (a line) to 16 vertices. The vertices can be repositioned to any gridline intersection. Triangles can be drawn on square and triangular grids and discussed: 'What is the special name for this triangle? 'Where could I move this vertex to make an isosceles triangle?' and so on. MM Shape / 2D and 3D shapes 4: Triangles in a C Name shapes using letters. / Properties of triangles pentagon 5: Investigation MM Shapes / Construction / 1: Construct a E Animations to draw a triangle from two sides and an angle and Constructing triangles triangle from S, A, S two angles and a side. 3: Construct a triangle from A, S, A FI Filling polygons H Equilateral triangles, squares, regular hexagons and dodecagons (all with the same edge length) can be used to create tiling patterns. This can be used to extend the ideas in H9 and H10. For example, you can decide by calculating angles whether or not a repeating tiling pattern can be made with the squares, regular hexagons and dodecagons and then use the applet to check your ideas. 8 Fractions MM Number / Fractions / 6: Beat the clock B You fill in a gap to make two fractions equivalent. Equivalent fractions 7: Matching pairs B One memory matching puzzle that uses equivalent fractions. MM Number / Fractions / 7: Multiple choice C You decide which fraction in a pair is bigger or if they are the Comparing fractions game same. MM Number / Fractions / Tool: Build your own B, C, Allows you to build up to eight different fraction 'strips'. Can be Equivalent fractions fraction wall E used to look at equivalent fractions, compare fractions and add/subtract fractions where the denominator does not exceed 15. MM Number / Fractions / 9: Matching pairs E, F One matching puzzle that uses mixed numbers and simple Improper and mixed game operations. fractions 7C e-resources Chapter Source Reference Activity Sect. Comments MM Games / Golf / Fractions F You need to select a club value and a fraction. You multiply golf them together to get the length of your shot. Only whole numbered lengths are possible. 9 Action and result puzzles 10 Chocolate 11 Health club FI Minitool 2 A, B, This applet creates dot plots. Set the max and min. As data is C entered the dots appear. Two different colours can be used, say for the males and females in Health Club. The plots for the two colours can be shown separately by choosing 'Split colours'. By choosing the 'Two equal groups' option, the median(s) can be shown/found. SMP 7Cp082ch11sectDresshts8 The health club D After work with the cards, you could use the spreadsheet to do 0,81.xls database cards as a sorting, filtering, comparing and finding medians (see p 76 of spreadsheet the teacher's guide). Identical to the spreadsheets for Health club in 7S and 8T. 12 Balancing FI Solving equations with C Use the 'Make an equation yourself' option (the problems get balance-strategy: game too complex too quickly). After making the equation in the smaller box select 'Add' and the equation will appear in the larger box. Use the red buttons to choose what you want to do to each side. Then key in what you think the next line should be and you will be told if you are right or wrong. Continue till the value of the unknown is found. 13 Multiples and MM Number / Powers and 2: Game Multiples A A game against the computer that uses multiples of 2, 3, 4, 5, factors Integers / Multiples connect 4 6 and 7. MM Number / Powers and 6: Prime numbers: A Integers / Factors and Sieve of Eratosthenes primes FI Hit the safe B At the 0-100 level you are given any number between 1 and 100. You select which numbers from 1 to 10 are factors of that number and hit the handle of the safe to open it. 101-999 is more challenging. MM Number / Powers and 5: Pairs game D One matching puzzle that uses prime factorisations. Integers / HCF 7: Using factor trees F Animation of finding the HCF of 84 and 120 using factor trees. to find the HCF 14 Work to rule FI Spotting numbers The 'Draw/remove spots' option allows the tile arrangements to be drawn with dots for tiles. You can select a block of cells and move it to analyse the patterns. 15 Decimals 1 MM Number / Decimals / 7: Making sums A Make as many calculations as you can with a set of numbers Multiply decimals by 10 game and x/÷ 10 or 100. and 100 MM Number / Accuracy and 7: Beat the Clock C Rounding to the nearest whole number and 1 d.p. Estimation / Rounding Decimals MM Booster packs / Six 1: Multiple Choice E Choose the option that best estimates the answer to a boosters / Calculators / game multiplication or division. Calculators revision 2: Number Jigsaw - E Puzzle where you estimate multiplications and divisions. Very Tricky 16 Gravestones MM GCSE Stats / Presenting 2: Why is a long data B Group some discrete data into groups and complete a data / Collating data table no good? frequency table (using tally marks if you like). SMP 7Cp122ch16sectD.xls The age/frequency D For experimenting with producing different styles of charts table as a using Excel. Identical to the spreadsheet for Gravestones in 7S. spreadsheet 17 Area and perimeter 18 Negative MM Number / Negatives / 6: Ordering positive A Revision of ordering integers. numbers 1 Negative numbers 1 and negative temperatures MM Booster packs / Four Stepping stones A The hard version gives practice in ordering positive and boosters / Decimals / (hard) negative decimals with 1 and 2 d.p. A hiker gets stepping Game: Stepping stones stones to cross a river, gets to the other side, pitches his tent and makes a fire! Otherwise falls in the river … MM Booster packs / Six 2: Loop Card Game A You have to find the next term in a linear sequence. Many boosters / Sequences / involve negative numbers. Sequences revision MM Number / Negatives / Tool: Interactive B Adding and subtracting positive numbers from positive or Negative numbers 1 number line negative numbers. FI Tic Tac Go C Use in addition or subtraction mode. 19 Spot the rule MM Algebra / Formulae / 5: Teacher tool - 1 A Supports the teacher-led introduction. Function machines stage 6: Teacher tool - 2 stage 20 Chance MM Data / Probability / 2: Dice and counters B Game seems fair to begin with as it's even/odd but the Probability fair computer has more of a chance of winning because of the number of spots. 3: Horse race B Like Three way race. 21 Translation MM Shape / Transformations / 1: Introduction A Translating shapes 2: Using vectors 3: Practise using vectors 22 Stretchers 7C e-resources Chapter Source Reference Activity Sect. Comments 23 Number grids 24 Constructions MM Shape / Constructions / 1: Constructing a C Animations. Constructing shapes perpendicular bisector 2: Perpendicular line from any point on a line 4: Constructing an angle bisector 5: Perpendicular from a point to a line 25 Comparisons 1 26 Further areas MM Shape / Area and 10: Beat the clock A perimeter / Area of a parallelogram MM Shape / Area and 9: Beat the clock C perimeter / Area of a trapezium MM Games / Beat the clocks / Area A, B, A mix of triangles, trapeziums and parallelograms. Shape / Area C 27 Inputs and FI Algebra arrows Can be used in a variety of ways throughout the section. Chains outputs of machines can be made (you click and drag the arrowheads to join up the machines) and either numbers or expressions can be input. Checking the 'table' box gives sets of input and ouput values. For example, the expressions 2(4x + 1) and 8x + 2 can be demonstrated to give the same outputs for any set of inputs by making the two appropriate chains. Two chains can be made from the same input which is nice visually. MM Algebra / Use of symbols / 3: Matching pairs E One matching puzzle on expanding single brackets. Brackets game 28 Decimals 2 MM Shape / Measures / 10: Beat the clock A Converting metric measures. Converting measures MM Booster Packs / Six 6: Loop card game A Multiplying and dividing by 1000, 100, 10, 0.1, 0.01, 0.001 . boosters / Place value / Place value revision MM Number / Accuracy and 9: Beat the clock H Rounding a variety of numbers up to six significant figures. Estimation / Significant figures 29 Investigations 30 Parallel lines 31 Percentage MM Number / Percentages / 6: Floating bubbles B You get a starting value and then work out 50%, 25%, 75%, Percentages of amounts 1 10% one at a time in that order. Then you work out 5%, 20% and 30% in any order. Finally 15%. 8: Beat the clock B MM Games / Golfs / B You need to select a club value and a percentage. The Percentages golf percentage of the value of the club gives you the length of your shot. MM Number / Frac dec Perc / 7: Matching pairs C, E One matching puzzle that uses 1/2s, 1/4s, 1/5s and 1/10s and Frac dec Perc 1 their equivalent decimals and percentages. 8: Beat the clock C, E Equivalent, fractions, decimals and percentages. 32 Think of a MM Algebra / Equations / 10:Beat the clock C, D Solving simple equations. number Simple equations 33 Quadrilaterals MM Shape / 2D and 3D shapes 8: 'What am I?' game A You are given a set of six quadrilaterals (the ones in Section A / Lines and Quadrilaterals with the exception of the arrowhead) and a series of statements that are all true about just one of the shapes. When you think you know what it is you click on that shape. 9: Properties of A You are asked a series of questions about a kite, square, quadrilaterals parallelogram, rectangle, rhombus and trapezium. MM Toolkit / AT1 / Shape Pinboard A Quadrilaterals can be drawn and discussed: 'What is the special name for this shape?', 'What is the area of this quadrilateral?', 'Where could I move this vertex to make a kite?' and so on. 34 Negative MM Number / Negatives / 9: Beat the clock A, B Addition, subtraction and multiplication of negative numbers. numbers 2 Negative numbers 2 FI Tic Tac Go B Use in multiplication mode. MM Algebra / Formulae / 7: Beat the clock B, C Substituting negative numbers into expressions, including those Substitution 1 that involve division and brackets. 35 Comparisons 2 MM Booster packs / Six 2: Mean, median, D Each puzzle gives a set of six cards with some hidden. Given boosters / Handling data / mode card 2 some information about the mean, median, mode or range you Handling data revision 3: Mean, median, find the missing cards. mode card 3 4: Mean, median, mode card 4 36 Know your MM Algebra / Formulae / Order 4: Pairs game A One matching puzzle where different calculations with the same calculator of operations value are matched up. 5: Puzzles A You have to insert two operations to make each calculation correct. 10: Beat the clock A, B Goes a little further than Section B so a challenge. FI Broken calculator B You try to reach each target using three numbers under 10 (any number of times), three operations (chosen for you) and brackets. 7C e-resources Chapter Source Reference Activity Sect. Comments 37 Three FI 3-D object viewer B A picture of an object is shown together with a plan view and dimensions three elevations (eight different objects). This could provide an opportunity for discussion at the start of Section B. FI Rotating 3-D objects B Using the fact that an arrow shows the front view, you have to turn the object so that a stated view is showing. FI Guess the view B You are given a picture of an object with its front indicated by an arrow, together with a view. You have to choose which view (out of six) it is. MM Shape / 2D and 3D shapes 1: Opening a cube to F Animations of a cube, cuboid and triangular prism opening up / Nets of 3D shapes find a net to show the net. Dimensions are shown for the cuboid and the 3: Opening a cuboid triangular prism. to find a net 5: Opening a triangular prism to find a net MM Shape / Area and 3: Finding the G Finding the surface area of a 5 cm by 5 cm by 5 cm cube. Perimeter / Nets, Surface surface area of a area cube 4: Finding the G Finding the surface area of a 3 cm by 4 cm by 6 cm cuboid. surface area of a cuboid 38 Finding formulas FI Spotting numbers A You are given the first three in a sequence of dot patterns. You problems can show the next four patterns. You can predict the number of dots in the 4th, 5th and 10th patterns. You can decide whether a pattern exists made from a certain number of dots and finally give the number of dots in the nth pattern. Good for discussion in Section A. Ones particularly suitable for discussion in this chapter are Level 1 - V numbers, W numbers, Plus numbers and Tower numbers. MM Algebra / Sequences / nth 8: Sequence search D Given the nth term, find nine linear sequences in a grid. term FI Number strips with labels D, E, The result of different operations on the whole set of natural F numbers can be investigated. It can be used to support discussion in Sections D, E and F. 39 Ratio MM Number / Ratio / Ratio 5: Ratio target game D One matching puzzle matching up equivalent ratios. introduction Tool - match up D You make all possible equivalent ratios from a set of numbers. activity 8: Make this ratio E You change the colour of the beads in a bag to make the challenge required ratio. Returning gives a different set of problems. 40 Using a SMP 7Cp331ch40top.xls The Furry festivals Contains what is shown in the spreadsheet on the page. spreadsheet spreadsheet Formulas have to be added then quantities experimented with to get an answer. Identical to the spreadsheet for the second Furry festivals problem in 8T and the Furry festivals spreadsheet in 8S. SMP 7Cp331ch40bottom.xls The Breakfast time Contains what is shown in the spreadsheet on the page. The spreadsheet required data and formulas have to be added. Identical to the Breakfast time spreadsheet in 8S. SMP 7Cp332ch40.xls The Mean, median, Contains the data on the cans collected. Formulas for mean, range spreadsheet median and range are to be added then the investigations carried out. 41 Functions and FI Algebra arrows B To create a table of values for a function and its graph, set up graphs the appropriate chain and use 'x' in the input box. Check the 'graph' option and link the output box to the graph. You need to click the 'table' option to see the individual points. A limitation is that it will not draw graphs for implicit equations such as x + y = 10 . 8C e-resources Chapter Source Reference Activity Sect. Comments 1 Graphs that tell MM Algebra/Graphs/Real Life 6: Fill the bath 1 B Filling a bath with a rectangular front view - choose the correct stories Graphs graph from four. 7: Fill the bath 2 B Filling a bath with a sloping bottom - choose the correct graph from four. 8: Fill the bath 3 B Filling a bath with sloping sides - choose the correct graph from four. 2 Scaling 3 Graphs and charts 4 Solving FI Solving equations with A, C Use the 'Make an equation yourself' option (the problems get equations balance-strategy: game too complex too quickly). After making the equation in the smaller box select 'Add' and the equation will appear in the larger box. Use the red buttons to choose what you want to do to each side. Then key in what you think the next line should be and you will be told if you are right or wrong. Continue till the value of the unknown is found. 5 Solids 6 Units MM Shape / Measures / Bonus: Multiple C You estimate conversions of imperial and metric measures. Imperial measures Choice Game Each time you are given a metric/imperial measure and asked to choose the nearest imperial/metric measure from three. 7 Simplifying expressions 8 Fractions and decimals 9 Transformations MM Shape / Transformations / Tool 1 Reflection tool B Allows a variety of horizontal and vertical lines of reflection Reflecting shapes (which can be hidden) to be chosen on a coordinate grid but no diagonal. A small selection of shapes can then be reflected in them. MM Shape / Transformations / Tool 1 Rotation tool C Allows a variety of centres (which can be hidden) to be chosen Rotating shapes on a coordinate grid but no non-integer coordinates and 90 deg or 180 deg clockwise or anticlockwise rotation. A small selection of shapes can then be rotated. MM Shape / Transformations / Tool 1 Translating D Allows a variety of vectors (which can be hidden) to be chosen Translating shapes tool but no non-integer values. A small selection of shapes can then be translated on a coordinate grid. MM Shape / Transformations / Tool 1 Enlargement E Allows a variety of centres (which can be hidden) to be chosen Enlarging shapes tool on a coordinate grid but no non-integer coordinates. Possible scale factors are 3, 2.5, 2, 1.5, 1, 1/2, 1/3, 1/4, -1 and -2 (though only 2 and 3 are considered here). A small selection of shapes can then be enlarged. SMP 8Cp070ch09sectG.xls The data for the G For this activity to work, you need to use the Excel 'chart triangle that is to be wizard'; the route to it depends on the version of Excel you are transformed using. When you have activated it, select scatter diagram, then select the scatter diagram sub-type in which data points are connected by lines. You may not be able to adjust the axes, but the required axes should appear as the activity proceeds. 10 True, iffy, false 1 11 Linear equations FI Shooting balls A The point here is to shoot all the balls using the least number and graphs of shots. You set the height and gradient of each shot. More than one ball can be hit in one shot. The balls can be hit anywhere and not just in the centre. Level one allows the slope to be set by adjusting the line at the side. Level 2 shows you the height and direction of your shot before you take it. Level 3 just shows you the height and level 4 shows you neither. 12 Percentage MM Number / Percentage / 7: Beat the Clock C Finding multipliers for percentage increases and decreases. changes Percentage change 1 13 True, iffy, false 2 14 Probability from experiments 15 Bearings 16 Forming equations 17 Ratio and proportion 18 No chance! MM Data / Probability / Listing 1: 2 dice bingo C You choose six numbers to put on your bingo card (numbers outcomes can be repeated). The computer 'rolls' two dice repeatedly until all the numbers on your card have been crossed off. You can repeat and try to reduce the number of rolls. 2: Possible sums on C Listing outcomes and making a grid. 2 dice 3: Sample space for 2 dice 19 Strips 20 The right SMP 8Cp141ch20sectsC,D.xls The tables for C, D Having drawn scatter diagrams at the start of the chapter connections questions C4, C5 and pupils could learn how produce a scatter diagram as an Excel D2 in a single chart for these later questions. For D2 they can use the spreadsheet MEDIAN function, print out the chart, draw the median lines on their printout then count points in the quarters. 8C e-resources 21 Triangles and MM Shape / Angles / Angle 6: Interior and B The tool allows you to look at the exterior angle and the two polygons proofs exterior angles (just opposite angles as an introduction to the proof. the tool) MM Shape / Angles / Interior 1: Finding the D These use the 'sliding pieces' idea. Exterior Angles interior and exterior angles in a regular pentagon 2: Finding the interior and exterior angles in a regular hexagon 3: Finding the interior and exterior angles in a regular nonagon 22 Moving around 23 Substitution 24 Locus MM Shape / Loci / Drawing loci 1: Equidistant from a A Placing a golf ball a certain distance from a hole. point 2: Equidistant from B Placing a (slightly odd looking) boat the same distance from two points two lighthouses. 3: Equidistant from C Placing a golf ball equidistant from two lines. two lines 25 Distributions MM Data/Averages/Stem and 1: Creating a stem B Shows how to create a stem and leaf diagram. leaf and leaf diagram 2: You try this one 9C e-resources Chapter Source Reference Activity Sect. Comments 1 Circumference of a circle 2 Solving FI Solving equations with A, C Use the 'Make an equation yourself' option (the problems get equations balance-strategy: game too complex too quickly). After making the equation in the smaller box select 'Add' and the equation will appear in the larger box. Use the red buttons to choose what you want to do to each side. Then key in what you think the next line should be and you will be told whether you are right or wrong. Continue until the value of the unknown is found. FI Linear equations practice A, C Up to level 3 is appropriate here, although the questions at the end of each level are very tricky. They include for example –5x + 4 = 3 which is a type not explicitly dealt with in the chapter. FI True-makers E Any equation with two possible solutions allows either to be marked correct but it should be pointed out that there is no option to enter both solutions at once. The use of a raised dot to mean multiply may be unfamiliar. Level 3 is challenging. 3 Rates 4 Vectors MM Shape / Vectors / Vectors 2: Activity - Draw A You draw any vector that fits on a 5 by 5 grid and then decide 1 any vector and then what it is. The term 'matrix' and the use of the AB notation are guess the matrix not explicit in the chapter. 5 Manipulation MM Algebra / Use of symbols / 5: Choose the correct A You are offered eight expressions and have to choose two that Simplifying 2 two buttons multiply to produce a given expression. FI Spotting numbers H, I You can draw the various diagrams using dots to denote the Smarties in Section H or tins in Section I. Then diagrams can be analysed by moving blocks of dots. FI Spotting numbers H, I You are given the first three in a sequence of dot patterns. You problems can show the next four patterns. You can predict the number of dots in the 4th, 5th and 10th patterns. You can decide whether a pattern exists made from a certain number of dots and finally give the number of dots in the nth pattern. Ones particularly suitable for discussion in Section H are Level 1 - F numbers 1, Level 2 - F numbers 2, Level 3 - Tile numbers 3, Block numbers 2 and Block numbers 3. Level 3 - Pentagonal numbers is a good addition to Section I. Some of the patterns already in the chapter appear here too. 6 Area of a circle MM Shape / Volume / Volume 1: Finding the E Animation of how to find the volume of a cylinder by splitting it of cylinders volume of a cylinder into layers. by breaking it into layers MM Shape / Area and 8: Finding the E Animation of how to find the surface area of a cylinder. perimeter / Nets, Surface surface area of a area cylinder 7 Over to you 8 Trial and improvement 9 Exploring MM Data / Probability / 4: Spinner frenzy This can be tried before or after 'Routes on a grid'. Pascal's triangle Probability fair 10 Fractions and MM Number / Fractions / 1: Multiplying 2 A Using a square pizza to show multiplying 1/3 by 1/4; can be probability Multiplying fractions fractions used with the introduction here. 2: Another example A Using a square pizza to show multiplying 2/3 by 3/5. FI Flowcharts C This creates diagrams for traffic flow that can show the total traffic at each point on the route. Click on the arrow on the right of each box to split the flow. The correct fractions can be entered into the boxes (using the slash on the keyboard). Put the number of cars into the first box and then clock 'flow on' to see the result. MM Number / Fractions / 1: Dividing a whole E 3/(1/2) = 6 using pizza diagrams. Dividing fractions number by a unit fraction 2: Another example E 5/(1/4) = 20 using pizza diagrams. 6: Dividing a whole E 4/(2/3) = 6 using pizza diagrams. number by any fraction 11 Linear equations and graphs 12 Using and MM GCSE Stats / Presenting 1: Misleading bar A The effect of not starting the vertical scale at 0. misusing data / Misleading Graphs chart statistics 2: Dodgy line graph A The effect of not using even intervals on the horizontal axis. MM Data / Sampling / 1: Introduction to B Sampling. Sampling sampling 2: Some surveys: good or bad? 13 Pythagoras's MM Shape / Pythagoras's 7: Finding the D Animation of finding the distance between two points. theorem Theorem / Pythagoras distance between 2 Theorem points Tool 1 - Distance D You can pick any two points on a set of axes that each go from - between 2 points 10 to 10 and find the distance. The lines, triangles and distances can all be hidden and shown. 9C e-resources Chapter Source Reference Activity Sect. Comments 14 Simultaneous MM Algebra / Simultaneous 1: Mr Jones set up a B Given the price of 2 coffees and a tea, look at all the possible equations equations / Sim equations tea and coffee shop pairs of prices. Then, given the price of 2 coffees and a tea, and 1 2: How much did he 3 coffees and a tea, set up equations and solve by looking at charge for tea and the difference. how much for coffee? 5: Beat the clock B The coefficients of one unknown are the same so it is possible to solve them quite quickly. 15 Spot the errors 16 Changing the subject 17 Similar shapes 18 Functions and FI Algebra trees B An algebra tree can be set up so that there is an input box for graphs each of a, b and c in ax^2 + bx + c. Various values of a, b and c can then be entered in the boxes. Use 'x' in the appropriate input box and the graph can be drawn each time by linking the final output box with the graph image. This can be used with the investigation at the end of Section B. 19 Inequalities 20 More MM Algebra / Use of symbols / 9: Beat the clock B, C Expanding pairs of brackets where the coefficient of x is 1 each manipulation Brackets time. 21 Quadratic FI Sequences D This allows you to investigate the first and second differences of sequences quadratic sequences. First enter a quadratic expression at the top of the strip on the left. Then pull it out to the right. Then choose 'Sequence of differences' on the drop down menu. The sequence of differences appears on the left. Pull that sequence out and repeat to get the second differences. This can be repeated with various expressions.

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