Download To: - Bridge of Don Academy – Faculty of Mathematics and Numeracy

FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
Summary:
National 4 course
Term
3a
3a
3a
3a
3a
3b
3b
3b
3b
3c
3b
3c
3c
3c
3d
3d
3d
3d
4a
4a
4a
4a
4b
4b
4b
4b
4b
4b
Evidence
Task
Content
Sig figs, Negatives, Scientific notation
Mean, mode etc
Pythagoras
Equations and brackets
Fractions of n, ratio, speed and time
Money: wages, interest, tax, exchange
Probability
Freq tables, scattergraphs, stem-and-leaf
Factors and factorising
Area and perimeter
Formulae and sequences
Symmetry
Volume and Surface Area
Gradient of a line
Scale drawing
Trig (SohCahToa)
Money: Profit and loss (inc. n/m = x%), HP
Reading and interpreting graphs
Proportion and variation
NU assessment
Drawing a line given equation
Similarity
Angles and shape properties
Trig revision and practice
Area and volume revision and practice
Fractions and %s revision and practice
Algebra revision and practice
AV exam
Unit Test Ques.
1
2
r6 r10
e1 e3 e13 e14 r3
3
e12 e15 r13
4
5
e7 e8
e2 e4 e5 r4 r5
6
e6 e10 e11
7
r11 r12
8
r1 r2 r7 r8 r9
Pages
2 to 4
5
6
7
8 and 10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
Resources
The main resources will be:
 “Maths in Action National 4” published by Nelson Thornes and
 “CfE Maths Fourth Level Pupil Book” published by Leckie and Leckie.
Throughout each and every topic please bear in mind that the following should be addressed:
Expressions and Formulae and Relationships Reasoning Skills:
1. Interpreting a situation where mathematics can be used and identifying a valid strategy.
Can be attached to any Assessment Standard in the other Outcomes to require analysis of a
situation.
2. Explaining a solution and relating it to context. Can be attached to any other Assessment
Standard to require explanation of the solution given.
PAGE 1 OF 28
FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
S3 Term 1
Topic
Significant
Figures
Syllabus Area (National 4 Course Unit Support Notes)
NU 1.2 Selecting and carrying out calculations (involving
whole numbers, fractions, decimals, percentages, ratio and
proportion): round answers to the nearest significant figure or
two decimal places.
Resources
L&L4:
Ch 1
Notes
Topic N20: Rounding II
[N5E1.3]
a) Appreciate the difference between zero as a place holder and a value (e.g. the hundreds digit
in 6000 and 6030).
b) Round off an integer value to a given number of significant figures.
c) Round of any real number to a given number of significant figures.
d) Be aware of how to choose an appropriate level of accuracy for a problem.
In addition, pupils should:
 Be aware of suitable degrees of accuracy.
 Know to always write down a more accurate answer before rounding off.
PAGE 2 OF 28
FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
S3 Term 1
Topic
Syllabus Area (National 4 Course Unit Support Notes)
Negative
NU 1.2 Selecting and carrying out calculations (involving
Numbers
whole numbers, fractions, decimals, percentages, ratio and
proportion): add and subtract whole numbers including
negative numbers.
NU 1.3 Reading measurements using a straightforward scale
on an instrument: use measuring instruments with
straightforward scales to measure temperature.
Resources
L&L4: Ch
3
Notes
Topic N18: Direct Proportion
[308a, N3M1.4]
a) Use direct proportion.
b) Draw a graph for direct proportion and recognise direct proportion from a graph.
c) Find products that offer “best value” (e.g. 300ml for £4 or 500ml for £5.50).
Topic N19: Ratio
[308a] {n4n7} {n5n2a}
a) Simplify a ratio.
b) Share a quantity out in a given ratio.
Topic G02: Reading a Scale
{n4n9} {n5n2b}
a) Interpret and read a scale that has subdivisions representing whole numbers (e.g. 0 and 10
labelled with ten subdivisions between them).
b) Interpret and read a scale that has subdivisions representing multiples of whole numbers
(e.g. 0 and 10 labelled with five subdivisions between them).
c) Interpret and read a scale that has subdivisions representing decimal fractions of numbers
(e.g. 0 and 1 labelled with ten subdivisions between them, 0 and 1 labelled with five
subdivisions between them etc.).
Topic N13: Negatives
[304a] {n4n8}
a) Use a number line to add/subtract whole numbers to/from integers (e.g. 5 – 8 = –3).
b) Able to add/subtract integers to/from integers (e.g. 7 + (–2) = 7 – 2 = 5). Make sure they use
brackets so that no two operators are touching (e.g. 5  3  5  (3) ).
c) Know how to multiply an integer by a whole number.
Topic N24: Negatives II
a) Multiply any integer by any other integer.
b) Divide any integer by any other integer.
c) Calculate using any of the four basic operations with any Real numbers
d) Calculate a n where a  R and n  N .
In addition, pupils should:
 Be familiar with a wide variety of different contexts.
 Interpret their calculations in the context of the problem.
 Make decisions based on their calculations.
PAGE 3 OF 28
FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
S3 Term 1
Topic
Syllabus Area (National 4 Course Unit Support Notes)
Scientific
[Extra] Express large numbers in the form n  10m .
Notation
Resources
L&L4: Ch
5
Notes
Topic N21: Standard Form I
[N5E1.2] {n5e2b}
a) Know that “standard form” is the proper name for this piece of maths but that in the SQA
Maths tests/exams it will be referred to as “Scientific Notation”
b) Represent x using standard form (where x  1 ).
c) Convert a number given in standard form into a fully written out number.
d) Perform calculations with values given in standard form (with and without a calculator).
In addition, pupils should:
 Be familiar with contextualised cases (e.g. molecular weights, astronomical units).
PAGE 4 OF 28
FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
S3 Term 1
Topic
Syllabus Area (National 4 Course Unit Support Notes)
Statistics I
EF 3.2 Determining statistics of a data set: mean, median,
mode, range.
EF 3.3 Interpreting calculated
Statistics: constructing Pie chart, (percentages and degrees),
Bar graph, Line graph.
Resources
MiAN4:
Ch 5
L&L4: Ch
33
Notes
Topic I05: Graphs and Charts II
[221a, 321a, N3M2.3, N3N2.1, N3N2.2, N4E3.4, N4N2.1] {n3m6b} {n4n12} {n5n1abc}
a) Draw pictograms, bar graphs, simple pie charts and line graphs.
b) Use and interpret combined bar charts (one section on top of another) and dual bar charts
(two bar charts on one diagram e.g. boys and girls columns next to each other).
Topic I07: Analysing Data II
[320b, 420b, N4E3.2, N4N2.2] {n4e13}
a) Revise mean.
b) Calculate median, mode and range.
c) Identify and deal with misleading data (e.g. when one piece of data causes mean and median
to be very different or when a conclusion is unjustified as the data has been misinterpreted).
d) Draw conclusions when presented with two (or more) sets of data using mean, median,
mode and range.
Topic I08: Graphs and Charts III
[320a, 321a, 420a, N4E3.4, N4N2.1, N4N2.2] {n4e14} {n5n1d, n5n3d}
a) Construct pie charts.
b) Construct stem-and-leaf diagrams (including back-to-back).
c) Gather data in an ungrouped frequency table and use this to calculate mean.
d) Gather data in a grouped frequency table.
e) Know the difference between discrete and continuous data (and which graphs charts are
suitable for each).
In addition, pupils should:
 Be aware of misleading statistics and diagrams.
 Be able to compare two (or more) diagrams and make decisions based on the information.
 Know statistical language and be able to relate it into ‘everyday-speak’ when stating a
conclusion.
PAGE 5 OF 28
FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
S3 Term 1
Topic
Syllabus Area (National 4 Course Unit Support Notes)
Pythagoras RL 2.1 Using Pythagoras’ theorem: given measurements,
given coordinates.
Resources
MiAN4:
Ch 8
L&L4: Ch
25
Notes
Topic G12: Pythagoras I
[312a, 416a, N4R2.1] {n4r6, n4r10}
a) Investigate the relationship between the sides of a right-angled triangle to discover the
Theorem of Pythagoras.
b) Use the Theorem of Pythagoras to calculate the hypotenuse of a right-angled triangle.
c) Find out about Pythagoras, the man.
d) Use the Theorem of Pythagoras to calculate one of the shorter sides of a right-angled
triangle.
In addition, pupils should:
 Know how to interpret a coordinate diagram and use Pythagoras to find the length of a line
segment.
 Be able to apply Pythagoras to isosceles/equilateral triangles (and then find e.g. area).
 Be able to apply Pythagoras to compound shapes, such as a trapezium.
Tasks:
 SEB Standard Grade Investigation: “All Ronders”
PAGE 6 OF 28
FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
S3 Term 1
Topic
Syllabus Area (National 4 Course Unit Support Notes)
Equations
EF 1.1 Using the distributive law in an expression with a
and
numerical common factor to produce a sum of terms: 3(4x ±
Brackets
2), 5(a ± 2c)
EF 1.3 Simplifying an expression which has more than one
variable: 3a + 4b – a + 6b
RL 1. 2 1.2 Solving linear equations: ax + b = c, ax + b = cx +
d
where a, b, c and d are integers
Resources
MiAN4:
Ch 1, 7
L&L4: Ch
22, 24
Notes
Topic A02: Expressions I (simplifying – avoiding negative algebraic terms in solution)
[314a, N4E1.3] {n4e3}
a) Tidy up expressions with an algebraic term (e.g. a  a  a  a  4  a  4a ).
b) Tidy up expressions with an algebraic term and arithmetic term (e.g. b  b  5  2  2b  3 ).
c) Tidy up expressions with algebraic terms (e.g. 2c  3d  c  d  c  4d ).
d) Tidy up expressions with algebraic terms and arithmetic term (e.g.
3e  9  f  e  4  5 f  2e  6 f  13 ).
Topic A07: Expressions III
[314a, N4E1.1] {n4e1}
a) Evaluate expressions where an algebraic term is assigned a negative value (e.g. evaluate 3x
+ 2y when x = –3 and y = 5).
b) Simplify expressions involving brackets (e.g. 3(2b – 7) = 6b – 21).
c) Evaluate expressions involving algebraic fractions (e.g. when x = 2 and y = 7, find the
3y
5 y  4x
values of (i)
and (ii)
).
2x
3
Topic A08: Equations III
[414a, 415a, N5R1.2] {n4r3}
a) Solve equations to give negative solutions (e.g. 3a + 10 = 4).
b) Solve equations involving brackets (e.g. 2(3x + 1) = 20).
c) Solve equations that have rational solutions (e.g. 3y – 1 = 7).
d) Solve equations that have letters on both sides and/or brackets, with negative/rational
solutions (e.g. 5(2n – 3) = 3n + 8).
In addition, pupils should:
 Create an equation form a text or diagram.
PAGE 7 OF 28
FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
S3 Term 1
Topic
Syllabus Area (National 4 Course Unit Support Notes)
Fractions of NU 1.2 Selecting and carrying out calculations (involving
a Quantity
whole numbers, fractions, decimals, percentages, ratio and
proportion): convert equivalences between common fractions,
decimals and percentages; find simple percentages and
fractions of shapes and quantities, eg 50%, 10%, 20% and
25%, 33%; ½, ⅓, ¼, 1/10, 1/n.
Resources
L&L4: Ch
6
Topic N02: Fractions I and Percentages I
[207b, 207c, 307b, 207a, 307a, N3N1.2N4N1.2]
a) Equivalent fractions (focussing on 1 s to 1 s , 1 s and 1 s ).
2
6
10
100
35
b) Fractions of a quantity (including e.g.
of £9 but not mentioning percentages).
100
20
of £3 ).
c) Percentages of quantities (treating them as fractions e.g. 20% of £3 
100
In addition, pupils should:
 Know how to calculate percentages without a calculator.
 Be aware of a wide variety of context where these skills can be used.
 Make judgements based on their calculations.
PAGE 8 OF 28
Notes
FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
S3 Term 1
Topic
Ratio
Syllabus Area (National 4 Course Unit Support Notes)
NU 1.2 Selecting and carrying out calculations (involving
whole numbers, fractions, decimals, percentages, ratio and
proportion): calculate ratio and direct proportion, calculate
rate eg miles per hour or number of texts per month.
Resources
L&L4:
Ch8
Notes
Topic N18: Direct Proportion
[308a, N3M1.4]
a) Use direct proportion.
b) Draw a graph for direct proportion and recognise direct proportion from a graph.
c) Find products that offer “best value” (e.g. 300ml for £4 or 500ml for £5.50).
Topic N19: Ratio
[308a] {n4n7} {n5n2a}
a) Simplify a ratio.
b) Share a quantity out in a given ratio.
In addition, pupils should:
 Know how to calculate proportion using a ‘non-unitary’ method without a calculator (e.g. 80
pencils cost £7.20 so 10 pencils cost 90p and 10 pencils cost £9).
 Be aware of a wide variety of context where these skills can be used.
 Make judgements based on their calculations.
PAGE 9 OF 28
FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
S3 Term 1
Topic
Time,
Speed and
Distance
Syllabus Area (National 4 Course Unit Support Notes)
NU 1.2 Selecting and carrying out calculations (involving
whole numbers, fractions, decimals, percentages, ratio and
proportion): calculate rate eg miles per hour or number of
texts per month, calculate distance given speed and time,
calculate time intervals using the 12- and 24-hour clock.
Resources
L&L4: Ch
12, 13
Notes
Topic N17: Speed, Distance and Time
[310a, N4N1.2] {n4n6}
a) Revise calculation of time intervals (e.g. 05:45 to 10:20) and time conversions (e.g. 1 hour
30 minutes = 1 1 hours = 1 5 hours). Keep time conversions to simple fractions of an
2
hour.
b) Understand the idea of average speed.
c) Know the relationships between speed, distance and time and use this triangle:
.
d) Read simple information from Distance-Time graphs.
e) Create simple Distance-Time graphs.
In addition, pupils should:
 Know how to express time (e.g. hours and minutes) as a decimal hours (e.g. 5min 24sec =
5∙4 min).
 Know how to convert decimal time into ‘proper’ time (e.g. 3∙2 hours = 3 hours 12 minutes).
 Know that the steeper a line on a distance-time graph is then the greater the speed.
PAGE 10 OF 28
FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
S3 Term 2
Topic
Money I
Syllabus Area (National 4 Course Unit Support Notes)
Wages, simple interest, tax, exchange rates.
NU 1.1 Selecting and using appropriate numerical notation
and units: money (pounds and pence)
Resources
MiAN4:
Ch
L&L4: Ch
10, 11
Notes
Topic N14: Money and Percentages
[303b, 307a, 309a, 309b, N3M1.3] {n3m4} {n4n1, n4n3, n4n13}
a) Revise decimal skills (add, subtract, multiply and divide) in the context of money.
b) Discuss banking: What is interest? Why do banks pay/charge interest? Why does it vary
from bank to bank, year to year? What does percent mean? [stress that percent is a fraction].
c) Know how to calculate simple interest for one year or whole number multiples of years.
d) Know how to use exchange rates.
Topic N15: Money II (Deductions)
{n3n4b, n3n5}
a) Know the meaning of the terms: gross pay, net pay, income tax, national insurance,
superannuation, overtime, bonus, profit and loss.
b) Calculate net pay given gross pay and deductions.
c) Calculate Value Added Tax (as a percentage of value) and add to price of items.
In addition, pupils should:
 Know how to find out the interest paid by a bank for savings and research to find good
deals.
 Be able to search for jobs (newspaper and/or internet) and interpret the advert to work out
the weekly/monthly pay.
 Know about the reasons for different types of pay (e.g. wage, salary, commission).
 Have calculated over-time using different rates (e.g. time-and-a-half, time-and-a quarter).
 Be aware that there is “tax allowance”, different tax rates.
 Have seen how income tax and national insurance are calculated (e.g. using the online
calculator: http://www.thesalarycalculator.co.uk/salary.php).
 Have an awareness of why we pay income tax, national insurance and VAT.
Tasks:
 SEB Standard Grade Investigation: “Bank Charges”
PAGE 11 OF 28
FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
S3 Term 2
Topic
Syllabus Area (National 4 Course Unit Support Notes)
Probability NU 2.3 Making and explaining decisions based on
probability: recognise patterns and trends and use these to
state the probability of an event happening, make predictions
and use these predictions to make decisions
Resources
MiAN4:
Ch 11
L&L4: Ch
35
Notes
Topic I06: Probability I
[222a, N3N2.3, N4E3.5, N4N2.3] {n4n16. n4n17, n4e15}
a) Calculate probability given relevant information (as a fraction or a decimal between 0 and
1).
b) Conduct a simple experiment or survey to determine or check a probability (e.g. coin toss).
Topic I09: Probability II
[322a, N4E3.5, N4N2.3] {n5n4}
a) Use tree diagrams and organised lists to identify all possible outcomes and calculate
probability of specific results.
b) Calculate probability and use this to make predictions.
In addition, pupils should:
 Be able to compare probabilities and make an informed choice based on this.
PAGE 12 OF 28
FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
S3 Term 2
Topic
Statistics II
Syllabus Area (National 4 Course Unit Support Notes)
EF 3.1 Constructing a frequency table: Using ungrouped data.
EF 3.4 Representing data in a diagram: constructing Pie
chart (percentages and degrees), Bar graph and Line graph.
RL 4.1 Constructing a scattergraph: Given a set of data.
RL 4.2 Drawing and applying a best-fitting straight line: The
line should have roughly the same number of data points on
either side; Use the line of best fit to estimate one variable
given the other.
NU 2.2 Making and explaining decisions based on the
interpretation of data from straightforward graphical forms:
make decisions based on observations of patterns and trends
in data; make decisions based on calculations involving data;
make decisions based on reading scales in straightforward
graphical forms; offer reasons for the decisions made based on
the interpretation of data.
Resources
MiAN4:
Ch 6
L&L4: Ch
32, 33, 34
Notes
Topic I02: Data I
[220b, N3M2.1, N4E3.1, N4N2.2] {n3m6a} {n4e12}
a) Gather data through experiment or survey.
b) Order data (e.g. put it into a frequency table).
Topic I10: Graphs and Charts IV
[N4R4.1, N4R4.2, N5A4.2] {n4r13} {n5n3ab}
a) (Refer to G04) Plot points using suitable axes to create a scattergraph.
b) Draw a ‘line of best fit’ on a scattergraph (visual approximation).
c) Use the ‘line of best fit’ to make estimates and predictions.
In addition, pupils should:
 Complete a frequency table with grouped data.
 Compare data sets from analysis or diagram and make decisions/judgements based on
findings.
 Be able to understand statistical language.
 Be able to translate statistical language into layman’s’ terms when coming to conclusion.
PAGE 13 OF 28
FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
S3 Term 2
Topic
Syllabus Area (National 4 Course Unit Support Notes)
Factors and EF 1.2 Factorising a sum of terms with a numerical common
Factorising factor: eg 7x ± 21 = 7(3x ± 7), 9 ± 27x = 9(3 ± 3x).
Resources
MiAN4:
Ch 1
L&L4:
Ch23
Notes
Topic A10: Factorising I (Common Factors)
[N4E1.2] {n4e2}
a) (See N09) Look at common factors of numbers and algebraic terms (e.g. 12 and 4n).
b) Factorise a linear algebraic expression (e.g. 4n + 12 = 4(n + 3)).
c) Factorise a ‘linear’ algebraic expression involving more than one algebraic term (e.g. 15 +
5x – 20y = 5(3 + x – 4y)).
d) Factorise an algebraic term involving a ‘squared’ term (e.g. 6x2 + 3x = 3x(2x + 1)).
PAGE 14 OF 28
FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
 S3 Term 2
Topic
Syllabus Area (National 4 Course Unit Support Notes)
EF
2.1 Calculating the circumference and area of a circle: Given radius or
Length,
diameter.
Perimeter
EF 2.2 Calculating the area of a parallelogram, kite, trapezium: Composite
and Area
shapes by splitting into triangles.
NU 1.3 Reading measurements using a straightforward scale on an
instrument: use measuring instruments with straightforward scales to
measure length, weight, volume, read scales to the nearest marked,
unnumbered division with a functional degree of accuracy
NU 1.4 Interpreting the measurements and the results of calculations to
make decisions: use appropriate checking methods, eg check sums and
estimation; interpret results of measurements involving time, length,
volume; recognise the inter-relationship between units in the same family,
eg mm/cm, cm/m and ml/l; use vocabulary associated with measurement
to make comparisons for length, volume.
Resources
MiAN4:
Ch 2
L&L4: Ch
14, 15, 26
Notes
Topic G03: Measurement II (Length)
[211a, 211b, N3S1.1, N4N1.3] {n3n3, n3s4a} {n4n5, n4n11a}
a) Use a ruler to measure a length in cm or mm.
b) Convert metric units of length (e.g. 56mm = 56cm).
c) Use metre sticks, tape measures and trundle wheels to measure large lengths (e.g. length and
breadth of classroom).
d) Calculate perimeter of a compound shape.
Topic G07: Measurement II (Basic Area and Volume)
[211c, N3S1.1, N3S1.2, N4E2.2] {n3s2, n3s4b}
a) Calculate area of a rectangle ( A  l  b ).
b) Calculate area of a triangle ( A  1 of b  h ).
2
c) Calculate area of compound shapes.
d) Calculate volume of a cuboid ( V  l  b  h ).
e) Convert cm3 in millilitres or litres.
Topic G14: Measurement IV (Areas)
[N4E2.2] {n4e8}
a) Calculate the area of a kite/rhombus by splitting them up into triangles.
b) Calculate the area of a trapezium by splitting it into constituent parts (e.g. two triangles and
a rectangle).
c) Calculate the area of a parallelogram by splitting it into constituent parts (e.g. two triangles
and a rectangle).
1
d) Calculate the area of a kite/rhombus using the formula Area = lb .
2
e) Understand why a parallelogram’s area can be calculated using Area = bh and use this to
calculate the area of parallelograms.
In addition, pupils should:
 Be able to use these skills in a variety of situations and context.
 Be aware of imperial units and have some idea of the magnitude of each (e.g. pint, lb).
 See that imperial measurements can be converted to metric.
 Have practical experience of calculating areas, length and volumes (e.g. area of the
classroom).
PAGE 15 OF 28
FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
S3 Term 2
Topic
Syllabus Area (National 4 Course Unit Support Notes)
Formulae
EF 1.4 Evaluating an expression or a formulae which has
and
more than one variable: Evaluate linear expressions for given
Sequences
variables (eg w=1, t=3, k=5 find 4w + 6t – 3k).
EF 1.5 Extending a straightforward number or diagrammatic
pattern: eg 4, 7, 10, 13,… and 4, 9, 16, 25,… and well known
sequences.
EF 1.6 Determining a formula from information or a
diagrammatic pattern: Evaluate the formula for a given
variable.
RL 1.3 Changing the subject of a formula: Change the subject
of the formulae: G = x+a, T = xc, E = wx + k.
Resources
MiAN4:
Ch 1
L&L4: Ch
18
Notes
Topic A03: Expressions II (evaluating – for examples below a  1, b  2, c  3 )
[315b, N4E1.4] {n4e4a}
a) Expressions with an algebraic term (e.g. a  5  1  4  5 ) where algebraic term has no
coefficient.
b) Expressions with one algebraic term (e.g. 2  a  5  2 1  4  6 progressing quickly to
3b 1  3 2 1  5 ).
c) Expressions with two algebraic terms (e.g. a  b  1  2  3 ) where the algebraic terms have
no coefficients.
d) Expressions with two algebraic terms (e.g. 7a  2b  7 1  2  2  3 ).
e) Expressions with two algebraic terms and an arithmetic term (e.g.
7a  2b  5  7 1  2  2  5  8 ).
Topic A05: Formulae I
[315b, N3S2.2, N4E1.4] {n4e4b}
a) Substitute values into a given basic formulae (e.g. Area  l  b  7  9  63cm2 ).
Topic A09: Formulae II
[313a, NFE1.5, N4E1.6] {n4e5} {n5n3c}
a) Substitute values into a formula involving brackets.
b) Create a formula for a simple scenario.
c) Create an nth term formula for a sequence.
In addition, pupils should:
 Know the importance of setting the working out properly.
 Be able to create a table/sequence from diagrams/pictures and extend the pattern.
 Be able to create an expression from a diagram.
 Be aware that final answers can be algebraic expressions (and know that these are different
from equations).
PAGE 16 OF 28
FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
 S3 Term 3
Topic
Syllabus Area (National 4 Course Unit Support Notes)
Symmetry
EF 2.6 Using rotational symmetry: with straightforward linear
shapes.
Topic G06: Symmetry
[219a, 319a, N4E2.6] {n4e11}
a) Reflect in a horizontal or vertical line.
b) Rotate by 90 or 180 .
In addition, pupils should:
 Be able to complete reflections/rotations on a diagram.
 Use the property of symmetry when finding angles/lengths/areas.
PAGE 17 OF 28
Resources
MiAN4:
Ch 4
L&L4: Ch
31
Notes
FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
S3 Term 3
Topic
Syllabus Area (National 4 Course Unit Support Notes)
Volume
EF 2.3 Investigating the surface of a prism: Know face,
and Surface vertex, edge; Draw nets; Calculate surface area.
Area
EF 2.4 Calculating the volume of a prism: Triangular prism,
cylinder, other prisms given the area of the base.
NU 1.2 Selecting and carrying out calculations (involving
whole
numbers, fractions, decimals, percentages, ratio and
proportion): calculate volume (cube and cuboid), area
(rectangle and square) and perimeter (shapes with straight
lines).
NU 1.3 Reading measurements using a straightforward scale
on an instrument: use measuring instruments with
straightforward scales to measure length, volume; read scales
to the nearest marked, unnumbered division with a functional
degree of accuracy.
NU 1.4 Interpreting the measurements and the results of
calculations to make decisions: use appropriate checking
methods, eg check sums and estimation; interpret results of
measurements involving time, length, volume; recognise the
inter-relationship between units in the same family, eg
mm/cm, cm/m and ml/l; use vocabulary associated with
measurement to make comparisons for length, volume.
Resources
MiAN4:
Ch 2
L&L4: Ch
15, 16
Notes
Topic G16: Measurement VI (Volume of a Prism)
[N4E2.4, N5E3.3] {n4e10}
a) (Refer to G06) Understand that for a cuboid Volume = lbh = Ah.
b) (Refer to G06) Know for a triangular prism that V = Ah where A = (area of an end) and h =
(distance between ends).
c) Extend this to the circle and the cylinder. Calculate volume of a cylinder using V  r 2 h .
d) Find the volume of any prism using V = Ah (possibly where A is already calculated).
Topic G15: Measurement V (Surface Area)
[N4E2.3] {n4e9}
a) (Refer to G01) Sketch the net of a cuboid, triangular prism and cylinder.
b) (Refer to G06, G08) Calculate the area of a rectangle, triangle and circle.
c) Calculate the area of the faces of a cuboid and find the total surface area.
d) Sketch the net of a triangular prism and find the surface area.
e) Sketch the net of a cylinder (and understand that the length of the curved surface is the
circumference of the circular end) and find the surface area.
In addition, pupils should:
 Know how to draw a net of cuboid/cube and cut it out to create the 3D shape.
 Know how to draw a net of triangular prism and cut it out to create the 3D shape.
 Apply these skills to contextualised problems.
Tasks:
 SEB Standard Grade Investigation: “Which Container?”
 SEB Standard Grade Investigation: “Wooden Display Boxes”
PAGE 18 OF 28
FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
S3 Term 3
Topic
Syllabus Area (National 4 Course Unit Support Notes)
Gradient of EF 2.5 Investigating the gradient of a straight line: vertical
a Line
distance over horizontal distance; positive and negative
gradients; parallel lines have equal gradient.
Resources
MiAN4:
Ch 3
L&L4: Ch
19, 20
Notes
Topic G17: Gradient I
[N4E2.5, N5E3.1] {n4e6}
a) Understand the term gradient referring to steepness. Know that a horizontal surface has
“zero” gradient and that a vertical surface has an infinite gradient (and is therefore
undefined).
horizontal
b) Know to calculate gradient using the formula: gradient 
.
vertical
c) Understand that on a graph we can have negative gradients (sloping downwards).
d) Appreciate that parallel lines have equal gradients.
In addition, pupils should:
 Be able to apply these skills to contextualised problems.
PAGE 19 OF 28
FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
S3 Term 4
Topic
Scale
Drawing
Syllabus Area (National 4 Course Unit Support Notes)
NU 1.3 Reading measurements using a straightforward scale
on an instrument: use measuring instruments with
straightforward scales to measure length; read scales to the
nearest marked, unnumbered division with a functional degree
of accuracy.
NU 1.4 Interpreting the measurements and the results of
calculations to make decisions: use appropriate checking
methods, eg check sums and estimation; interpret results of
measurements involving length; recognise the interrelationship between units in the same family, eg mm/cm,
cm/m; use vocabulary associated with measurement to make
comparisons for length.
Resources
L&L4: Ch
15
Notes
Topic G11: Scale
[317b, 317c, N3S2.3, N3S2.4, N4R2.2] {n3s3b} {n4r7}
a) Able to enlarge and reduce given a scale factor.
b) Able to calculate a scale factor.
c) Create scale drawings, given a suitable scale, and use these to answer problems.
d) Know the points of an 8-point compass.
e) Know how to measure bearings and how to draw them on a scale drawing.
f) Able to read a basic map and use it to calculate distances and directions/bearings.
In addition, pupils should:
 Gather required measurements to create a scale drawing of a real-life problem (e.g. finding
the height of the school).
 Be able to apply these skills to contextualised problems.
PAGE 20 OF 28
FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
S3 Term 4
Topic
Trig
Syllabus Area (National 4 Course Unit Support Notes)
RL 3.1 Calculating a side in a right-angled triangle: Given a
side and an angle.
RL 3.2 Calculating an angle in a right-angled triangle: Given
two sides.
Resources
MiAN4:
Ch 10
L&L4: Ch
25
Notes
Topic G20: Trigonometry I (Soh Cah Toa)
[N4R3.1, N4R3.2] {n4r11, n4r12}
a) Know how to label the sides of a right-angled triangle relative to an angle: opposite,
adjacent and hypotenuse.
b) Investigate the ratio of sides of mathematically similar right-angled triangles.
c) Know the terms sine (sin), cosine (cos) and tangent (tan). Able to identify which one is
appropriate (Soh Cah Toa) and find the ratio with respect an angle using a calculator (e.g.
sin(30)).
d) Use basic trig to find an unknown length on a right-angled triangle, given an angle and one
other side.
e) Use basic trig to find an angle in a right-angled triangle, given the length of any two sides.
In addition, pupils should:
 Gather required measurements to create a scale drawing of a real-life problem (e.g. finding
the height of the school).
 Be able to apply these skills to contextualised problems.
PAGE 21 OF 28
FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
S3 Term 4
Topic
Money II
Syllabus Area (National 4 Course Unit Support Notes)
Profit and Loss (including m/n = x%), Hire Purchase
NU 1.1 Selecting and using appropriate numerical notation
and units: money (pounds and pence).
NU 1.2 Selecting and carrying out calculations (involving
whole
numbers, fractions, decimals, percentages, ratio and
proportion): round answers to the nearest significant figure or
two decimal places; find simple percentages and fractions of
shapes and quantities, eg 50%, 10%, 20% and 25%, 33%; ½,
⅓, ¼, 1/10, 1/n; calculate percentage increase and decrease;
convert equivalences between common fractions, decimals
and percentages.
NU 1.5 Explaining decisions based on the results of
calculations: give reasons for decisions based on the results
of calculations.
Resources
L&L4: Ch
6, 11
Notes
Topic N22: Money III (Hire Purchase and Loans)
[N3M1.4] {n3m5} {n5n2e}
a) Calculate and apply discount.
b) Calculate HP cost (given deposit amount or when deposit is a percentage of cash price).
c) Compare overall HP costs and reason to which is the better buy.
d) Look at personal loans and compare with HP/finance options offered by companies.
Topic N27: Amounts Expressed as a Percentage
[N5A3.1] {n5n2d}
a) Know how to express one amount as a fraction of another (e.g. bought for £10, sold for £12
2 1
 of buying price).
so profit =
12 6
b) Express one amount as a percentage of another (using contexts such as profit/loss, scores
from tests, errors, tolerances, depreciation/appreciation).
In addition, pupils should:
 Gather required information to perform these calculations for a real-life problem (e.g. (a)
finding the net annual pay for a joiner. (b) comparing finance options to buy a specific TV.
(c) calculating the percentage profit on a sale).
 Be able to apply these skills to wide variety of contextualised problems.
PAGE 22 OF 28
FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
S3 Term 4
Topic
Syllabus Area (National 4 Course Unit Support Notes)
Statistics III Reading and interpreting Graphs
NU 2.1 Extracting and interpretation data from at least two
different straightforward graphical forms: Straightforward
graphical forms should include a table with at least four
categories of information; a chart where the values are given
or where the scale is obvious, eg pie; a graph where the scale
is obvious, eg bar, pie, scatter or line graph; a diagram, eg
stem and leaf, map or plan.
NU 2.2 Making and explaining decisions based on the
interpretation of data from straightforward graphical forms:
make decisions based on observations of patterns and trends
in data: make decisions based on calculations involving data;
make decisions based on reading scales in straightforward
graphical forms; offer reasons for the decisions made based on
the interpretation of data.
Resources
MiAN4:
Ch 5, 6
L&L4: Ch
34
Notes
Topic I05: Graphs and Charts II
[221a, 321a, N3M2.3, N3N2.1, N3N2.2, N4E3.4, N4N2.1] {n3m6b} {n4n12} {n5n1abc}
a) Draw pictograms, bar graphs, simple pie charts and line graphs.
b) Use and interpret combined bar charts (one section on top of another) and dual bar charts
(two bar charts on one diagram e.g. boys and girls columns next to each other).
Topic I08: Graphs and Charts III
[320a, 321a, 420a, N4E3.4, N4N2.1, N4N2.2] {n4e14} {n5n1d, n5n3d}
a) Construct pie charts.
b) Construct stem-and-leaf diagrams (including back-to-back).
c) Gather data in an ungrouped frequency table and use this to calculate mean.
d) Gather data in an grouped frequency table.
e) Know the difference between discrete and continuous data (and which graphs charts are
suitable for each).
Topic I10: Graphs and Charts IV
[N4R4.1, N4R4.2, N5A4.2] {n4r13} {n5n3ab}
a) (Refer to G04) Plot points using suitable axes to create a scattergraph.
b) Draw a ‘line of best fit’ on a scattergraph (visual approximation).
c) Use the ‘line of best fit’ to make estimates and predictions.
In addition, pupils should:
 Gather required data to draw a scattergraph for two different groups and make a comparison
(e.g. age and height from two year groups).
 Be able to apply these skills to contextualised problems.
 Use information gathered to draw two different types of charts/diagrams for two different
groups of data and use these to present and justify a conclusion.
PAGE 23 OF 28
FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
S4 Term 1
Topic
Proportion
and
Variation
Syllabus Area (National 4 Course Unit Support Notes)
NU 1.2 Extracting and interpretation data from at least two
different straightforward graphical forms: calculate rate: eg
miles per hour or number of texts per month; calculate ratio
and direct proportion
Resources
L&L4: Ch
8
Notes
Topic N18: Direct Proportion
[308a, N3M1.4]
a) Use direct proportion.
b) Draw a graph for direct proportion and recognise direct proportion from a graph.
c) Find products that offer “best value” (e.g. 300ml for £4 or 500ml for £5.50).
Topic N19: Ratio
[308a] {n4n7} {n5n2a}
a) Simplify a ratio.
b) Share a quantity out in a given ratio.
In addition, pupils should:
 Be able to see how these skills apply in different subject areas across the school (e.g.
proportion in Home Economics).
 Research and use these skills to find the best deal for buying a particular product (e.g. a real
life scenario for Topic N18c).
 Be able to apply these skills to contextualised problems.
PAGE 24 OF 28
FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
S4 Term 1
Topic
Drawing
Graphs of
Straight
Line
Syllabus Area (National 4 Course Unit Support Notes)
RL 1.1 Drawing and recognising a graph of a linear equation:
Draw using a table of values or chosen values of x; For y =
mx +c, know the meaning of m and c; Recognise and use y =
a, x = b.
Resources
MiAN4:
Ch 3
L&L4: Ch
21
Notes
Topic A11: Graphs of Linear Equations
[N4R1.1] {n4r1, n4r2}
a) (Referring to A09c) Take a “formula” and create a table of values/coordinates, plot the
points and draw the graph. Emphasize that the line is a collection of all the points generated
by the “formula” (including those between the coordinates originally plotted).
b) Given any Linear Equation (of the form y = mx + c) they can create a table of values (at
least three points) and draw the graph.
c) Given any Linear Equation (in any form) they can create a table of values (at least three
points) and draw the graph.
d) Reference should be made to the steepness of the graph (m) and the y-intercept (c).
e) Sketch the graph of a linear equation given in the form y = mx + c.
In addition, pupils should:
 Appreciate the term “linear” and see the association with sequences.
 Know that linear means that there are no powers (larger than 1) on the variables.
 Realise that their line is only part of the line given by the equation.
 See that m is the gradient and appreciate what it means when m > 0, m = 0 and m < 0.
 See that c is the gradient and appreciate what it means when c > 0, c = 0 and c < 0.
 See how this ties in with a scattergraph and a line of best fit.
PAGE 25 OF 28
FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
S4 Term 1
Topic
Similarity
Syllabus Area (National 4 Course Unit Support Notes)
RL 2.2 Using a scale factor to enlarge or reduce a shape:
Linear, non-rectangular shape.
Resources
L&L4: Ch
28
Topic G11: Scale
[317b, 317c, N3S2.3, N3S2.4, N4R2.2] {n3s3b} {n4r7}
a) Able to enlarge and reduce given a scale factor.
b) Able to calculate a scale factor.
c) Create scale drawings, given a suitable scale, and use these to answer problems.
d) Know the points of an 8-point compass.
e) Know how to measure bearings and how to draw them on a scale drawing.
f) Able to read a basic map and use it to calculate distances and directions/bearings.
In addition, pupils should:
 Be able to apply these skills to contextualised problems.
PAGE 26 OF 28
Notes
FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
S4 Term 2
Topic
Angles and
Shape
Properties
Syllabus Area (National 4 Course Unit Support Notes)
RL 2.3 Using properties of shapes: Triangles, quadrilaterals
and
Circles using: angle in a semi-circle; relationship between
tangent and radius; combinations of angle properties.
Resources
MiAN4:
Ch 9
L&L4: Ch
27
Notes
Topic G19: Circle Geometry
[N4R2.3, N5R3.2] {n4r9} {n5r14}
a) (Refer to G03 and G09) Able to use the properties of alternate angles, corresponding
angles, vertically opposite angles, complementary angles, supplementary angles and sum of
angles in a triangle.
b) Investigate, understand and use the property of that a triangle formed by a diameter and two
chords in a semi-circle will be a right angled triangle (angle in a semi-circle).
c) Know what a “tangent to a circle” is and that it is perpendicular to the radius at point of
contact.
d) Know that if a chord is bisected by a radius then they are perpendicular (and vice versa).
In addition, pupils should:
 Be able to apply these skills to contextualised problems (e.g. bearings, angles in a polygon).
Tasks:
SEB Standard Grade Investigation: “Presentation Pack of Golf Balls”
PAGE 27 OF 28
FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY
PAGE 28 OF 28