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   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
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   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
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   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.
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   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 .
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   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.
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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
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   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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