# for the Higher series - SMP Home

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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
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.
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
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
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
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
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.
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.
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.
SMP    H1p271ch27sectE.xls         The two tables of    E          As above.
Titanic on page 271
on a single
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.
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
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.
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.
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.
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

6: Adding vectors          B      Adding two vectors by joining them on a grid and 'walking' a
7: 5 questions - draw B           Dragging vectors to help you find the resultant of some vector
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.
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
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
centre
3: Square based            B      You can ask for various hints which add lines or rotate the solid
height
4: Square based            B      You can ask for various hints which add lines or rotate the solid
7: Pythagoras using        C      A new problem when you return.
3D coordinates

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