Mathematics
Blue Course
Teachers’ Notes
Mathematics
G
BG1
BG2
BG3
BG4
BG5
Distance, Speed and
Time with Revision of
Scientific Notation.
Right Angled
Trigonometry.
Money Topics.
Length, Area and
Volume (including
Tolerance).
Factorisation.
Mathematics
BG1 Distance, Speed and Time
Math 4 Real video is available for this topic.
BG1.1 I have revised how to make distance, speed and time calculations.
Int 2 Book 1
•
•
•
•
P30 – P32
Ex 3.3 – Ex3.5
Hours/Minutes
>
Decimal Time
Decimal Time
>
Hours/Minutes
Time/Distance/Speed Problems (Easier)
Time/Distance/Speed Problems (Harder)
• Time/Distance/Speed Problems (Hardest)
Ex 3.4
Ex 3.5
Ex 3.3
Ex 3.4
Ex 3.5
Ex 3.5
Q 1, 2, 3
Q 3, 4
Q 4, 5, 6
Q 10
Q 7, 8
Q 9, 10
Past Paper Questions (See SQA website) will include information
given or presented in Scientific Notation.
BG – Homework 1
BG1.2 I have revised how to interpret distance/Time graphs
Int 2 Book 1
P34
Ex 3.6
1 ,3 ,4 and 6
Staff should extend this section to include a wider variety of
Qualitative Graphs. A collaborative group activity based on
the Shell Package (University of Nottingham) will be
developed here.
Powerpoint “distanceTimeGraphs” and
“distanceTimeGraphs2” are available
BG – Homework 2
BG2 Right Angled Trigonometry
Maths 4 Real videos with real life examples covering Sine and
Tangent Ratios are available.
BG2.1 I can use Trig to calculate a side (unknown on numerator)
Int 2 Book 1
Int 2 Book 1
Int 2 Book 1
Page 122
Page 18
Page 18
Ex 11.1
Ex 11.4
Ex 11.5
Q2
Q3
Q3

Pupils should investigate Trig Ratios before formally
tackling this topic. Tangent ratio being constant for a
given angle is the most obvious way to tackle this.

Show me boards should be used to check for
understanding before textbook exercises are set. All three
ratios should be tackled simultaneously so SohCahToa
can be introduced early.
BG2.2 I can use Trig to calculate a side (unknown in denominator)
Int 2 Book 1
Page 130
Ex 11.6
All

Initially this should be tackled by inverse operations
which is consistent with the development of algebra in the
course. Cross multiplication can be introduced as a
special case for two ratios set equal to each other.

Show me boards should be used to check for
understanding before textbook exercise is set.
BG2.3 I can use Trig to find and angle
Int 2 Book 1
Int 2 Book 1
Int 2 Book 1
Page 123
Page 127
Page 129
Ex 11.3
Ex 11.4
Ex 11.5
Q4
Q9
(Q8 to 10)

This will be a recap and formal treatment of the
introduction to the topic.

Show me boards should be used to check for
understanding before textbook exercises are set.
BF – Homework 3 and 4
BG2.4 I Trig to solve problems
Int 2 Book 1
Page 133
Ex 11.7
(Q3 to 13)
The Powerpoint “TrigExamQuestions” is available.

Q9 and Q13 should be used to exemplify a numerical
comparison. It may be best to set question 9 (perhaps as
homework) then go over the solution on the board (or get
pupils to present the solution to the class). Q13 could
then be tackled and Peer Assessment used to ensure the
answer is justified with a numerical comparison.
BF – Homework 5
BG3 Money Topics
N5
National 5
Applications
Sub outcome 1.3
This outcome is touched on here but it completely
covered in the Blue Course in Block D and Block E.
BG3.1 I have revised Using Money contexts such as Hire Purchase,
Insurance, interest, Wages and Foreign Exchange.
Insert Required
The Powerpoints “Money” and “Foreign Exchange” are available.
BF – Homework 6
BG3.2 I can calculate percentage profit and loss.
Int 2 Book 1
P10
Ex 1.3
All
BF – Homework 7
BG3.3 I can calculate compound interest.
Int 2 Book 1
P11
BF – Homework 8
Ex 1.4
All
BG3.4 I can compare and contrast a range of financial products including
credit and debit cards, personal loans, mortgages and pay monthly
plans.
Insert Required
BF – Homework 11
BG3.5 I can determine what I can afford using my knowledge of income,
savings, VAT, bills, discounts, surcharges, and insurance.
Insert Required
BG4 Length, Area and Volume (including
Tolerance)
N5
National 5
Expressions and Formulae
Sub outcome 1.4
Partially covered in this outcome (also includes
equation of a straight line given two points)
Use interactive whiteboard, prepared shapes, composite shapes and sectors
to calculate areas and volumes. 3D shapes are available in the department.
Relate examples to real life objects where possible. This topic provides an
opportunity for pupils to develop skills in measurement
BG4.1 I can calculate the perimeter and area of a triangle.
Revision
BG4.2 I can calculate the circumference and area of a circle.
Int 2 Book 1
Int 2 Book 1
Int 2 Book 1
P47
P50
P43
Ex 5.1
Ex 5.3
Ex 5.5
All
All
All
BG4.3 I can calculate the perimeter and area of common quadrilaterals
given the formula (including composite shapes).
Int 2 Book 1
P77
Ex 8.1
All
BG4.4 I can calculate the perimeter and area of a sector of a circle.
Int 2 Book 1
Int 2 Book 1
Int 2 Book 1
P101
P102
P103
Ex 10.1
Ex 10.2
Ex 10.3
Q2, 4, 5
Q2, 4, 5
Q2 to 9
BF – Homework 9
BG4.5 I can find the angle in a sector given the arc length or area of the
sector.
Int 2 Book 1
P104
Ex 10.4
Q4 and 5.
Int 2 Book 1
P105
Ex 10.5
Q4 and 5.
BG4.6 I can calculate the surface area of cuboids, triangular prisms and
cylinders.
Int 2 Book 1
Int 2 Book 1
P79
P85
Ex 8.2
Ex 8.6
Q12 to 16
Q4 to 8
BG4.7 I can find the volume of cuboids, prisms (including cylinders), cones
and spheres.
Int 2 Book 1
Int 2 Book 1
Int 2 Book 1
Int 2 Book 1
Int 2 Book 1
P78
P80
P81
P83
P86
BF – Homework 10
Ex 8.2
Ex 8.3
Ex 8.4
Ex 8.5
Ex 8.7
Q1 to 10
All
All
Q7 to 13
All
BG4.8 I can find the volume of prisms with composite cross sections.
Volume of Composite Solids PowerPoint
The PowerPoint “VolumeCompositeSolids” is available.
Word document “Area&VolumePastPapers”
BF – Homework 11
BG5 Factorisation
N5
National 5
Expressions and Formulae
Sub outcome 1.2
Partially covered in this outcome (also includes
multiplying out brackets which has previously been
covered)
BG5.1 I can factorise expressions which contain a common factor.
Int 2 Book 1
P94
Ex 9.5
All
Revision of common factor (common factor already covered
in course). Ensure that all pupils can factorise using common
factor by employing a “show me” technique. Stress Highest
Common Factor and illustrate with examples where the HCF
includes algebraic symbols as well as numerical values.
Then set tasks for pupil to enable them to practise the skill of
factorising an expression using common factor.
BG5.2 I can factorise expressions which contain a difference of two squares.
Int 2 Book 1
P95
Ex 9.6
*All (see note)
Pupils should be allowed sufficient time multiplying out
brackets of the type (A+B)(A-B) where A is a variable such as
x or 2y and B is a constant or a variable.
Working in pairs pupils will examine their results so that
they can spot the pattern to both the brackets and their
products.
Now ask pupils to make up a question of their own that fits
the pattern of brackets and products. Collect in responses
and question the class “does this fit into the pattern?” You
can then start to talk about the products of the brackets
always being a “take away” which could then be replace by
the word difference. You should also note that the product is
the difference of A2 and B2.
Now ask the question “If I started with a difference of two
squares what would the answer be?” On show me boards
get the pupils to make up a difference of two squares
question.
Collect responses and use them to both rule out questions
which are not difference of two squares and to highlight
what is meant by difference of two squares.
At this point a formal note would be appropriate and set
pupils examples from the textbook.
* Ensure the examples set are sufficiently challenging which
my require missing out many of the examples early in the
exercise.
BG5.3 I can factorise quadratic expressions of the form,
Int 2 Book 1
P96
Ex 9.7
Q3
Pupils should be allowed time to multiply out pairs of
brackets which will result in quadratic trinomials. Use
examples which will produce a quadratic coefficient which is
greater than 1.
Then give pupils a trinomial which can be factorised again
with a coefficient of x which is greater than 1. Allow the
pupils think time to try to factorise it on their own. If any
pupil manages to factorise the trinomial, ask them to explain
how they managed it. If pupils don’t manage this show the
solution on the board and then check it by multiplying out
the brackets. Do not restrict the pupils’ think by showing a
method just give them the solution. Repeat this process
several times.
Once pupils are clear in what the process of factorising a
quadratic is and how it is vital to check your solution by
multiplying out, any of the ROTE factorisation schemes can
be formally taught and a formal note made.
Pupils should then be given examples from the textbook.
Avoid exercises where the questions only have the coefficient
of quadratic term = 1 as this can result in pupils developing a
simplified rule of how to factorise quadratic expressions
which will ultimately fail once the coefficient become greater
than 1. Reinforce throughout the course as a lesson starter
from this point onwards.
Types of quadratic trinomials which can be factorised:
Basic examples with a = 1, and ‘c’ prime, such as:
(x2 + 3x + 2); (x2 + x – 2); (x2 – 2x – 3)
Slightly more complex examples with ‘c’ non-prime:
(x2 + 5x + 6); (x2 +x – 6)
Most complex examples with a > 1:
(3x2 + 5x – 2); (6x2 + 13x + 2); (1 + 3x – 18x2)
.
BG5.4 I can factorise expression which have a combination of common
factor, difference of two squares or trinomial quadratic.
Int 2 Book 1
P78
Ex 8.2
Q1 to 10
It is important that pupils realise that there is an order to
factorisation. From this point onwards all factorisation
questions should be attempted by asking, in this order



Can we take out a common factor?
Is there a difference of two squares?
Is there a Quadratic Trinomial?
BF – Homework 12
BG5.5 I can express a quadratic in the form
Int 2 Book 1
P78
Ex 8.2
–
Q1 to 10