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Higher transition e-resources Chapter Source Reference Activity Sect. Comments 1 Calculation and MM Number / Decimals / 5: Ladder game A You are given eight numbers between 0 and 1 to place in a estimation Ordering decimals ladder in order. You have to place a number before you get the next one. Numbers can include 1, 2 or 3 d.p. though the majority have 3 d.p. MM Number / Decimals / 8: Beat the clock A Multiplying and dividing by 10 and 100. Multiply decimals by 10 and 100 MM Booster packs / Six 6: Loop card game A, B, A 'loop' puzzle multiplying and dividing by 1000, 100, 10, 0.1, boosters / Place value / C 0.01 and 0.001. A different puzzle when you return. Place value revision MM Number / Accuracy and 8: Beat the clock D Rounding whole numbers to the nearest 10, 100, 1000 . estimation / Rounding to 10, 100 MM Number / Accuracy and 7: Beat the clock E Rounding decimals to up to 6 d.p. (section goes up to 3 d.p.). estimation / Decimal places MM Number / Accuracy and 3: Beat the clock F Estimating answers to products of whole numbers such as 46 x estimation / Estimating 287 . introduction MM Booster packs / Six 1: Multiple Choice F Choose the option that best estimates the answer to a boosters / Calculators / game multiplication or division. Calculators revision 2: Number Jigsaw - F Puzzle where you estimate multiplications and divisions. Very Tricky 2 Graphing MM Algebra / Graphs / Real life 6: Fill the bath 1 A Filling a bath with a rectangular front view - choose the correct changes over graphs graph from four. time 7: Fill the bath 2 A Filling a bath with a sloping bottom - choose the correct graph from four. 8: Fill the bath 3 A Filling a bath with sloping sides - choose the correct graph from four. 3 Unitary method 4 Fractions MM Number / Fractions / 7: Multiple choice B You decide which fraction in a pair is bigger or if they are the Comparing fractions game same. MM Number / Fractions / 1: Multiplying a D 4 x 2/3 = 8/3 = 2(2/3) using pizzas. Multiply divide fractions fraction by a whole intro number 2: Another example D 5/7 x 4 = 20/7 = 2(6/7) using pizzas. 7: Pairs game - a D, E A matching puzzle on multiplying and dividing fractions by mixture whole numbers. A different puzzle when you return. 8: Beat the clock - a D, E You fill in a blank in a calculation that is either multiplying or mixture dividing a fraction by a whole number. MM Number / Fractions / 1: Multiplying two G 1/3 x 1/4 using a pizza diagram, noting the equivalence or 1/3 Multiplying fractions fractions x 1/4 and 1/3 of 1/4. 2: Another example G 2/3 x 3/5 using a pizza diagram, noting the equivalence or 2/3 x 3/5 and 2/3 of 3/5. 5: Multiplying mixed G Multiplying a mixed number by a fraction. A new problem when number fractions you return. 7: Pairs game G A matching puzzle with a mix of multiplying fraction calculations. A new puzzle when you return. 5 Parallel lines and angles 6 Percentages MM Number / Frac Dec Perc / 2: Drag and drop A Putting a set of five decimals, percentages and fractions in the Frac Dec Perc 2 activity correct order. A new set when you return. 8: Matching pairs A One matching puzzle on fraction, decimal and percentage game equivalences. MM Number / Percentages / 3: Random question D Non-calculator methods of percentage increase and decrease. Percentage change 1 generator You choose an amount from 60, 30, 400, 2000, 18 and 850. You choose to increase or decrease by 10%, 25%, 45%, 5% or 100% with the optional help of a 'working out box'. 7: Beat the clock E, F Finding multipliers for percentage increases and decreases. 7 Pie charts 8 Pythagoras's MM Shape / Pythagoras's 5: Random question D Calculating lengths in right-angled triangles, finding either the theorem theorem / Pythagoras's generator hypotenuse or a shorter side. theorem 9: Pythagoras D As in the Millionaire TV show with questions on Pythagoras. millionaire Tool 1: Distance D You choose two points on a coordinate grid (-10 to 10 on each between two points axis) by dragging A and B. You can show or hide the relevant line, triangle or calculation. 9 Working with MM Booster packs / Ds to Cs / 7: Matching pairs B One matching puzzle which includes expressions such as –8m + linear Expressions / Simplifying 1 game 4 which do not appear in the chapter. expressions FI Algebra arrows C, D Chains 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 output values. For example, the expressions 4(n + 2) and 4n + 8 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 appealling. A limitation is that when the coefficient of any variable is negative, you have to multiply by a negative number. Higher transition e-resources Chapter Source Reference Activity Sect. Comments 10 Representing 3- FI Building with blocks Building in the night A For each figure, you are shown an object made of black cubes D objects and told the number of cubes it contains. You can rotate it to look at it from different angles. You build it from cubes on the board provided. FI Guess the view C 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. You can rotate the object. FI Colouring sides 1 C One face of a pictured object is coloured red. You have to click on this face on the plan or one of the elevations. FI Colouring sides 2 C One face on a plan or elevation is coloured red. You have to click on this face on the pictured object. FI Building houses C You can build a solid and look at three views (called 'top', 'front' and 'right'). The views can be hidden and you can try to draw them. The edge lines for each cube are shown in the views which is not the case in the solutions for C6 here. You could try to draw each view as though you have a solid made from a single piece of wood rather than cubes. FI Building houses with side C Given the three views described above, you build a solid to fit views them trying to use the least number of cubes. To gain full marks in the problems you need to think of the 'houses' as structures which allow two cubes to be joined at an edge only. 11 Linear equations FI Linear equations practice A Levels 1 and 2 (Niveau 1 and 2) are suitable here. You need to state what is to be done to both sides and then give the correct next line of working. FI Solving equations with A, 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. 12 Multiples, factors MM Number / Powers and 5: Pairs game D One matching puzzle on numbers and their prime factorisation. and powers integers / HCF 7: Using factor trees E Animation of finding the HCF of 84 and 120 using factor trees. to find the HCF 13 Negative MM Number / Negatives / 9: Beat the clock A Adding, subtracting and multiplying negative numbers. numbers Negative numbers 2 MM Algebra / Formulae / 7: Beat the clock B You substitute negative numbers into simple linear expressions. Substitution 1 14 Drawing and using linear graphs 15 Using a MM Booster packs / Ds to Cs / 5: Multiple choice C, D Each time you are given a calculation involving decimals and calculator Arithmetic / Estimating test asked to choose the nearest estimate from three. calculations 6: Beat the clock C, D Estimating calculations by rounding each number to 1 s.f. 16 Changing the subject 17 Grid totals 18 Ratio MM Number / Ratio / Ratio Tool - match up A You make all possible equivalent ratios from a set of numbers. introduction activity 8: Make this ratio C You change the colour of the beads in a bag to make the challenge required ratio. Returning gives a different set of problems. 19 Substitution MM Algebra / Formulae / 8: Beat the clock B Substituting positive and negative numbers into expressions Substitution 2 with more than one variable but no squares. An emphasis on negative numbers. 7: Question B Three levels: simple, midi and hard. The hard level involves generator substituting positive and negative numbers into expressions with more than one variable including squares. An emphasis on negative numbers. 20 Scaling and ratio 21 Understanding inequalities 22 Sequences MM Algebra / Sequences / nth 8: Sequence search C Given the nth term, find nine linear sequences in a grid. term FI Sequences E This allows you to investigate the first and second differences of 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. FI Spotting numbers F The 'Draw/remove spots' option allows the light arrangements to be drawn. You can select a block of cells and move it to analyse the patterns. Higher transition e-resources Chapter Source Reference Activity Sect. Comments FI Spotting numbers F 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 F are Level 2 - F numbers 2, flip numbers, tile numbers 2, Z numbers and Level 3 - tile numbers 3. Good ones for section G are Level 2 - tile numbers 1, stair numbers and Level 3 - tile numbers 4. 23 Paired data SMP HTp168ch23sectsA,C.xls The car database as A, C Various scatter diagrams can be drawn using the chart facility. a spreadsheet To select two non-adjacent columns for this purpose, drag- select the first, then hold down the Control key and drag-select the second. On some Macs you need to hold down the Apple key then drag-select the second column. SMP HTp172ch23sectB.xls The tables for B Having drawn a scatter diagram and line of best fit for B1 and questions B3 and B4 B2 students could use Excel to produce scatter diagrams for B3 on a single and B4. More recent versions of Excel let you add a line of best spreadsheet fit (which it calls a trendline). SMP HTp173ch23sectC.xls The bull elephant C For a scatter diagram. data in question C2 as a spreadsheet 24 Working with MM Shape / Coordinates / 7: Introducing B You are given two points in a vertical or horizontal line and you coordinates Coordinates 2 midpoints have to state the coordinates of the midpoint without the help of a grid. 8: Diagonal B You are given two points in a diagonal line and you have to midpoints state the coordinates of the midpoint without the help of a grid. 25 Brackets and FI Linear equations practice C Level 3 (Niveau 3) is suitable here. You need to state what is to equations be done to both sides and then give the correct next line of working. FI Solving equations with C Use the 'Make an equation yourself' option. See chapter 11 balance-strategy: game above for fuller notes. 26 Roots MM Number / Powers and Square and cube A, B One memory matching puzzle on squares, cubes, square and integers / Square and cube pairs cube roots. pairs 2 Higher 1 e-resources Chapter Source Reference Activity Sect. Comments 1 Triangles and polygons 2 Drawing and FI Algebra trees A An algebra tree can be set up so that there is an input box for using quadratic each of a, b and c in ax^2 + bx + c. Various values of a, b and graphs 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 in Section A. 3 Distributions and MM Data/Averages/Stem and 1: Creating a stem A Shows how to create a stem and leaf diagram. averages leaf and leaf diagram 2: You try this one 3: Finding the mode A Finding the modal group and the mode from a stem and leaf diagram. 4: Finding the A Finding the median from a stem and leaf diagram. median 5: Finding the range A Finding the range from a stem and leaf diagram. 6: You try this one A Comparing data using stem and leaf diagrams. 7: Back to stem and leaf diagrams MM GCSE Stats / The mean / 1: Neil gets girls data A Finding the mean from an ungrouped frequency table for girls Frequency tables and finds the mean and then boys and then drawing conclusions. 2: Find the mean for the boys 3: Compare the results MM Data / Charts and graphs / 4: Tallying B You complete one grouped frequency table. Grouping data continuous data 4 Fractions MM Number / Fractions / 1: Dividing a whole C Pizza diagrams to show that 3 ÷ 1/2 = 6 Dividing fractions number by a unit fraction 2: Another example C Pizza diagrams to show that 5 ÷ 1/4 = 20 6: Dividing a whole C Pizza diagrams to show that 4 ÷ 2/3 = 6 number by any fraction Tool: Fractions Wall C A slightly different visual than the one in the chapter for dividing a whole number by a fraction. For example, for 4 ÷ 2/3 choose 4 bars divided into 1/3s. 5 Accuracy MM Number / Accuracy and 8: Beat the clock A Finding upper and lower bounds of numbers given to the estimation / Upper and nearest whole number, ten or hundred. lower bounds 1 6 Linear equations FI Linear equations practice A Levels 2 and 3 (Niveau 2 and 3) are suitable here. You need to 1 state what is to be done to both sides and then give the correct next line of working. FI Solving equations with A Problems 1-13 are suitable. Use the red buttons to choose what balance-strategy: game 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. C, D Use the 'Make an equation yourself' option. After making the equation in the smaller box select 'Add' and the equation will appear in the larger box. Then go on as above. 7 Area and MM Shape / Area and 10: Beat the clock A perimeter perimeter / Area of a parallelogram MM Shape / Area and 9: Beat the clock D perimeter / Area of a trapezium MM Games / Beat the clocks / Area A, B, A mix of triangles, trapeziums and parallelograms. Shape / Area D 8 Percentages 9 Transformations MM Shape / Transformations / Tool 1 Reflection tool A 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. You can move the line of reflection and look at how the position of the image changes. MM Shape / Transformations / 1: Revision of draw A Showing the positions of the lines y = x, y = -x, y = 6 and x = All transformations lines from equations 2. 2: Reflecting A Reflecting a triangle in any horizontal or vertical line, y = x or y triangles = -x on a coordinate grid. MM Shape / Transformations / Tool 1 Translating B 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 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˚ or 180˚ clockwise or turns. A small selection of shapes can then be rotated. You can move the centre and look at how the position of the image changes. 3: Describing C You are asked to fully describe a rotation that takes one shape rotations to another on a coordinate grid. A new pair of shapes when you return. Higher 1 e-resources Chapter Source Reference Activity Sect. Comments MM Shape / Transformations / Tool 1 Enlargement D 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 positive scale factors are considered in Section D). A small selection of shapes can then be enlarged. You can move the centre and look at how the position of the image changes. MM Toolkit / Shape / Transform tool 2 E On a coordinate grid (axes from -10 to 10) you can reflect a Transformations small selection of shapes in any vertical or horizontal gridline, rotate 90˚ or 180˚ clockwise or anticlockwise about any point on the grid with integer coordinates, enlarge with a positive scale factor of 1/3, 1/2, 1, 2 or 3 about any point on the grid or translate with any vector using integers from -10 to 10. You can hide the centres, lines of reflection, vectors, descriptions of the transformations and the images which allows a variety of questions. You can combine transformations in some cases but when a translation or enlargement is used it goes back to the original shape. 10 Powers and MM Number / Powers and 8: Matching pairs B, D One matching puzzle matching equivalent algebraic expressions indices integers / Indices part 1 game involving multiplying, dividing and powers. 11 Surveys and experiments 12 Speed, distance MM Shape / Measures / Speed 4: Working out C Short animations on working out distances and times. and time distances 6: Working out times taken 13 Volume, surface MM Shape / Volume / Volume 8: 5 questions A A question for discussion. Finding missing lengths when the area and density of cuboids working backwards to volume is known. find missing lengths MM Shape / Volume / Volume 3: Volume of a B Finding the volume of a prism by considering one slice first. of prisms triangular prism MM Shape / Volume / Volume 1: Finding the C Finding the volume of a cylinder by considering one slice first. of cylinders volume of a cylinder by breaking it into layers MM Shape / Area and 6: The surface area D Animation showing solid opening out into net followed by perimeter / Nets, surface of a triangular prism calculation of its surface area. area 8: Finding the D Animation showing cylinder opening out into net followed by surface area of a calculation of its surface area. cylinder 14 Cumulative MM Data / Cumulative 1: How to draw a box E Demonstration of drawing a box and whisker plot of a set of 12 frequency frequency / Box and and whisker plot from lengths. whisker plots a set of data 2: How to draw a box E and whisker plot from a CF (cumulative frequency) graph 3: Interpreting a box E and whisker 4: Making your own E Making your own plot from a cumulative frequency graph. box and whisker plot FI Minitool 2 E This applet creates dot plots. Set the max and min. As data is entered the dots appear. Two different colours can be used, say for males and females. The plots for the two colours can be shown separately by choosing 'Split colours'. Choosing the 'Four equal groups' option and check the 'Box plot' option to get a box plot for the data. 15 Working with MM Algebra / Formulae / 7: Question D Three levels: simple, midi and hard. The hard level involves expressions Substitution 2 generator substituting positive and negative numbers into expressions with more than one variable including squares. An emphasis on negative numbers. MM Algebra / Use of symbols / 5: Choose the correct D You are given a variety of expressions and have to choose 2 Simplifying 2 two buttons from 8 that multiply to give it. MM Algebra / Use of symbols / 1: Simplifying D Demonstration of (15a^2b^2)/(3a^2b). Cancelling algebraic 15a^2b^2 over fractions 3a^2b 16 Coordinates in MM Shape / Coordinates / 3D 2: The z-axis A Animation of all three axes. three coordinates 3: Plotting A Animation of plotting the point (3, 2, 4). dimensions coordinates in three dimensions 4: The helpful cuboid A A cuboid is drawn with one vertex on (0, 0, 0). You adjust the x, y or z coordinates on the diagonally opposite vertex and see the effect on the cuboid. 7: Beat the clock A 17 Cubic graphs and equations Higher 1 e-resources Chapter Source Reference Activity Sect. Comments 18 Gradients and FI Shooting balls A, B The object of this game is to shoot the balls on the grid in as rates few shots as possible by firing arrows through them. The arrow is aimed by choosing a starting point on the y-axis and a gradient. The coordinates of the balls are shown if they are clicked on. At level three only the starting point of the arrow is shown and at level four nothing is shown until it is fired. In the two player game, players must only hit balls of their colour. 19 Changing the subject 20 Probability MM Data / Probability / Play B Five cards from the same suit are given face down. You click on your cards right the first card and then gamble on the next card being higher or lower. You cannot go on until you have worked out the probability that you will win. MM Data / Probability / Listing 7: 2-reeled fruit C, D Two reels each have pictures of a frog, cat and dog. The two outcomes machine simulator reels are spun at once and you 'win' if they both show the same animal. You can run the simulation as long as you like till you feel you have a good estimate of the probability of a win. 8: Listing outcomes D Listing the outcomes in a grid. for the fruit machine 21 Large and small MM AT1 / Number / Billionaire 1: Are you a billion A Leads you through the problem and then poses the same with numbers seconds old? minutes, hours and days. 2: How bad is a A Leaves it up to you to find this out. billion pound debt? 3: What do a billion 1 A Leaves it up to you to find this out. cm cubes look like? MM Number / Standard form / 1: Animation: large E Zooming in on a picture going from 10^8 to 10^-3. Standard form small numbers to small 2: Patterns in the E Carrying a pattern from 2 x 10^4 to 2 x 10^-3. index number MM Number / Standard form / 1: Using a calculator D, F Shows how to enter numbers in standard form onto a calculator Standard form calcs with an EXP key. 2: Calculations on D, F Multiplication of numbers in standard form. A new problem your calculator when you return. 4: Calculations G Multiplication of numbers in standard form without a calculator. without a calculator A new problem when you return. 5: Another example G Division of numbers in standard form without a calculator. A new problem when you return. 7: Pairs game G One matching puzzle using standard form calculations without a calculator. 22 The tangent function 23 Linear equations 2 24 Loci and MM Shape / Loci / Drawing loci 1: Equidistant from a A Placing a golf ball a certain distance from a hole. constructions point MM Shape / Construction / 6: Constructing a A Constructing shapes triangle from 3 lengths MM Shape / Loci / Drawing loci 2: Equidistant from B Placing a (slightly odd looking) boat the same distance from two points two lighthouses. MM Shape / Construction / 1: Constructing a B Animation. Constructing shapes perpendicular bisector 5: Perpendicular from C Animation. a point to a line MM Shape / Loci / Drawing loci 3: Equidistant from D Placing a golf ball equidistant from two lines. two lines MM Shape / Construction / 4: Constructing an D Animation. Constructing shapes angle bisector 8: Construct angles D Animation. of 60˚ and 30˚ 9: Construct a 45˚ D Animation. angle 2: Perpendicular line E Animation. from any point on a line 25 Equations of FI Find the function B, C, You need to be familiar with basic function notation f(x) = 2x + linear graphs D 3. Level 1 (Niveau 1): problems 1 to 5 each ask for the equation of a straight line on a coordinate grid. You sometimes have to move the axes to find points to give an accurate gradient. 26 Quadratic MM Algebra / Use of symbols / 9: Beat the clock A, C Multiplying out expressions of the form (x ± a)(x ± b) . expressions and Brackets equations MM Algebra / Use of symbols / 9: Beat the clock D Factorising quadratic expressions where the coefficient of x^2 Factorising quadratics 1 is 1. 27 Handling SMP H1p264ch27sectA.xls The distance A The percentage of road use that is by car and van, for example, secondary data travelled table as a could be calculated for each year. spreadsheet 27 Handling Higher 1 e-resources secondary data Chapter Source Reference Activity Sect. Comments SMP H1p265ch27sectAqA9.xls The table for A The number of people per doctor could be calculated, for question A9 as a example. spreadsheet SMP H1p268ch27sectD.xls The table on pages D Various scatter diagrams could be drawn using the Excel chart 268-269 as a facility. To select two non-adjacent columns for this purpose, spreadsheet drag-select the first, then hold down the Control key and drag- select the second. On some Macs you need to hold down the Apple key then drag-select the second column. In some early versions of Excel, after you have made a selection of this kind you can't just click on the scatter diagram button but must use the chart wizard. SMP H1p270ch27sectE.xls The two tables on E For use in answering the questions set and in further page 270 on a single exploration of the data. spreadsheet SMP H1p271ch27sectE.xls The two tables of E As above. data about the Titanic on page 271 on a single spreadsheet SMP H1p272ch27sectF.xls The A level data on F You can selecting the whole table, sort on one column and then pages 272-273 as a analyse the subsets created. spreadsheet 28 Solving inequalities 29 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. It fits the early part of Section B. 30 Sine and cosine MM Shape / Trigonometry / 7: Random question D When you return you get a new problem. You first identify the Trig missing angles generator known sides and then the correct trig ratio. You are then given the appropriate formula and you fill in the missing lengths. You then continue to find the missing angle. Higher 2 e-resources Chapter Source Reference Activity Sect. Comments 1 Graphing MM Algebra / Inequalities / 7: Inequalities tool - D, E This allows you to set up problems and demonstrates solutions inequalities Shading inequalities Create and solve by shading unwanted regions. your own questions 2 Enlargement and MM Shape / Transformations / 8: Investigating E On a plain background you have a triangle and its image with similarity Enlarging shapes negative scale factors the centre of enlargement and the lines from the 'ray method'. You can adjust the scale factor through the integers 5, 4, … –4, –5 and move the centre of enlargement. Tool 1 Enlargement E Allows a variety of centres (which can be hidden) to be chosen tool on a coordinate grid but no non-integer coordinates. Possible negative scale factors are -1 and -2. A small selection of shapes can then be enlarged. You can move the centre and look at how the position of the image changes. 3 The reciprocal FI Algebra arrows B To create a table of values for y=1/x and its graph, set up a function chain using '1/...' with '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. Click on the arrows on the graph to alter the scale and values in the tables for discussion of the behaviour of the function for large and small x. 4 Arc, sector and MM Shape / Circles / Arc, 1: Naming the parts A, B Defines sector, arc, chord and segment. segment sector, segment of a circle 5 Investigating MM Algebra / Graphs / 1: Drag and drop for B Shows the general equation and some properties of linear, and identifying Recognising graphs definition of curves quadratic, cubic and reciprocal graphs. graphs 6 Combining MM Data / Probability / 4: Using a tree D Demonstrates using a tree diagram to find the probability of a 2 probabilities Independent probability diagram on an ordinary dice and a heart from an ordinary pack of cards. 5: Using the AND D Demonstrates using a tree diagram to find the probability of 3 rule spades and exactly 2 spades when three cards are drawn and replaced from an ordinary pack. 7 Direct and MM Number / Proportion / 6: Inversely F You answer questions about the time taken for various numbers inverse Direct and inverse proportional of builders to build a patio and this leads up to the formula t = proportion proportion 216/n which is then used. 8 Quadratic expressions and equations 1 9 Dimension of an MM Shape / Dimensions / 6: Beat the clock A You are given ten expressions and identify if each one is a expression Dimensions of formulae length, area or volume. 8: Multiple choice - A You are given five expressions and identify if each one is a you decide length, area or volume. New expressions when you return. 10 Sequences FI Spotting numbers D 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 here are Level 3 - pentagonal numbers, spiral numbers and triangle numbers 4. 11 Enlargement, MM Shape / Similarity / Area 1: Comparing two A Animation showing nine 2 by 2 squares fitting into a 6 by 6 area and volume scale factor squares for their square. scale factor 12 Algebraic fractions and equations 1 13 Time series MM Data / Averages / Moving 1: Ice cream sales A Demonstrates calculation of moving averages and shows them averages on a graph. 14 Trigonometric MM Shape / Trigonometry / 1: What is the sine of A You produce the sine curve for angles between 0˚ and 360˚ by graphs Sine and cosine graphs an angle - Meet the dragging a point round a unit circle. unit circle 2: Where does a sine B You produce the cosine curve for angles between 0˚ and 360˚ curve (sic) come by dragging a point round a unit circle. from? 8: Multiple choice A, B You are given the sine curve and the cosine curve for angles random questions between 0˚ and 360˚. You are then given one angle that satisfies a simple trig equation such as cosx˚ = 0.96 and you have to choose one angle out of three that also satisfies it. A new problem when you return. MM Shape / Trigonometry / 1: What is the C The tangent is defined as the gradient of the line OP as you Tan graphs tangent of an angle? - move P round the unit circle. You produce the tangent graph for What curve does it angles between 0˚ and 360˚ by dragging a point round a unit produce? circle. MM Shape / Trigonometry / 4: 4 questions - drag D You match four sine and cosine graphs with four functions. Transforming trig graphs and drop the Reviews Section D. equation 15 Pyramid, cone MM Games / Pairs games / B One memory matching puzzle on matching area and volume and sphere Shape pairs formulas with 2D and 3D shapes. 16 Rearranging a formula 17 Sampling 18 Using graphs to solve equations Higher 2 e-resources Chapter Source Reference Activity Sect. Comments 19 Histograms MM Data / Charts and graphs / 5: Question C Given the intervals and frequencies in a table, you work out the Histograms frequency densities. The bars are drawn when the densities are correct. 6: Tool for setting C You set your own intervals and frequencies. When you click on and drawing your 'Draw graph', the frequency densities are calculated and the own question graph is drawn. You can hide the frequency and/or the frequency density column. 20 Quadratic expressions and equations 2 21 Working with MM Number / Accuracy and 7: Beat the clock A Finding the upper and lower bounds of quantities given to rounded estimation / Upper and different degrees of accuracy. quantities lower bounds 2 22 Using exact values 23 Fractional MM Number / Powers and 4: Matching pairs D One matching puzzle using algebraic expressions, roots, indices indices / Indices part 2 game fractional and negative powers. 24 Exponential MM Number / Exponentials / 2: How bacteria grow A Working out the number of bacteria after 24 hours if you start growth and Exponential growth (exponentially) at 500 and double the number each hour. decay 3: Graphing A Graphing the numbers of bacteria above in the first 10 hours. exponential growth 7: Plotting a graph of A Plotting the graph for values of x from -3 to 3 (rounding to two y = 3^x decimal places where appropriate). FI Growth A, B You can plot two curves of the form y = ba^t on the same axes to compare growth (you also get windows that show the growth like bacteria in a dish). For example, in the investigation in A7, you can start with b = 1 in both cases and compare, say a = 2 and a = 3. Other values for a can be compared and you can look at the effect of changing the time interval. Click on 'Step' to speed things up. Click on 'Stop' to draw another pair of graphs. Negative values for t are not an option. FI Playing with functions A, B You need to be familiar with basic function notation. Set function f to be exponential. A panel appears with the general function f(x) = a*b^x. You can alter the values of a and b by typing in values or moving the sliders. Choose 'Show table' from the 'Options' menu to see the table of values. You can alter the range of values for x (which can include negatives) using the 'View' menu. Two functions can be compared by choosing function g to also be exponential. 25 Angle properties MM Shape / Circles / Circle 2: Proof of the B Demonstration of the proof in B3. of a circle theorem proof 'Arrow' theorem 3: Proof of the B Demonstration of the proof in B5. 'Triangle' theorem 4: Proof of the 'Bow B Demonstration of the proof in B6. tie' theorem 5: Proof of the 'Cyclic C Demonstration of the proof in C2. Quadrilateral' theorem 8: Proof of the D Demonstration of the proof in D2. 'Alternate Segment' theorem 26 Algebraic fractions and equations 2 27 Vectors MM Shape / Vectors / Vectors 2: Activity - Draw A You choose points A and B and then decide on the vector 1 any vector and then (called a matrix here) AB represents. guess the matrix 5: 5 questions - draw A Dragging vectors to help you draw scalar multiples of some your own vectors vectors. 6: Adding vectors B Adding two vectors by joining them on a grid and 'walking' a ladybird along the route. 7: 5 questions - draw B Dragging vectors to help you find the resultant of some vector your own vector additions. addition 8: Subtracting C Subtracting two vectors a and b by adding a and -b on a grid vectors and 'walking' a ladybird along the route. MM Shape / Vectors / Vectors 2: Random questions C Select two points on a grid of parallelograms and express the 2 parallel pipe. Drag resulting vector as a linear combinations of two vectors. your own vectors and solve 4: Random question C Select two points on a grid of equilateral triangles and express triangle. Drag your the resulting vector as a linear combinations of two vectors. own vectors and solve 28 Circles and MM Algebra / Graphs / 6: Multiple choice A You are given the equation of a circle with centre (0, 0). You equations Equations of circles test are given three points and choose which one lies on the circle. Surds are used. 29 Congruent MM Shape / Congruency / 7: Matching pairs A One matching puzzle on congruent triangles. triangles Congruent triangles game Higher 2 e-resources Chapter Source Reference Activity Sect. Comments 30 Proof MM AT1 / Algebra / Frogs B You can first try to find and prove a rule for the minimum number of moves to swap n red frogs and n green frogs. Then extend to n red frogs and m green frogs. 31 Extending trigonometry to any triangle 32 Transforming FI Playing with functions A You need to be familiar with basic function notation. Set graphs function f to be quadratic. A panel appears with the general function f(x) = a*(x - b)^2 + c in completed-square form. You can alter the values of a, b and c by typing in values or moving the sliders. Choose a = 1. Now you can look at the effect of changing b and c on the minimum point on the graph. MM Algebra / Quadratics / 4: Matching pairs B Matching quadratic expressions with the completed square Completing the square game form. FI Playing with functions C See the description above. Set function f and g to be quadratic. For f, choose a = 1, b = 0 and c = 0 for f(x) = x^2. Then alter a, b and c for g to see which transformation makes g the image of f. FI Find the function C You need to be familiar with basic function notation. Level 1 (Niveau 1): problems 6 to 10 and Level 2: problems 1 to 2 each ask for the equation of a quadratic on a coordinate grid. You sometimes have to move the axes to find key points. 33 Rational and MM Number / Decimals / 8: Pairs game A One matching puzzle on fractions and recurring decimals. irrational Recurring decimals 1 numbers MM Number / Decimals / 5: Loop card game B One matching puzzle on fractions and recurring decimals. Recurring decimals 2 MM Number / Surds / Surds 6: Matching pairs D One matching puzzle on manipulating surds. game 34 Pythagoras and FI Seeing through objects A, B Choose the 'Block' from the 'Objects' menu to get a cuboid trigonometry in (which cannot be altered). You can add letters to points by three choosing 'Add letters to points' from the 'Options' menu. Add dimensions (and fill) lines and planes to the cuboid by clicking on the appropriate icons. Then the object can be rotated and the lengths and angles discussed. MM Shape / Pythagoras's 1: Larry Cotter and B Demonstrates using Pythagoras to find the length of a diagonal theorem / Pythagoras 3D his magic wand in a in a cuboid. box 2: Square based B You can ask for various hints which often rotate the solid to pyramid with apex off help you. centre 3: Square based B You can ask for various hints which add lines or rotate the solid pyramid finding the to help you. height 4: Square based B You can ask for various hints which add lines or rotate the solid pyramid 2 to help you. 7: Pythagoras using C A new problem when you return. 3D coordinates

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