New S1-S3 CfE Course Plan - Newbattle Community High School

INDEX 

(if viewing this file in MS Word, control+click takes you straight to that section) 

Index ...................................................................................................................................... 1 

Development Tasks .............................................................................................................. 2 

Course Aims ......................................................................................................................... 3 

Levels of Course ................................................................................................................. 3 

CfE Course Year Planners ................................................................................................... 4 

S1 Course Plan ................................................................................................................... 4 

S2 Course Plan ................................................................................................................... 5 

S3 Course Plan (three lessons a week) .............................................................................. 6 

NUMBER (NUNP) .................................................................................................................. 7 

ALGEBRA (NUAP) ................................................................................................................ 8 

Statistics ............................................................................................................................... 9 

S1 Statistics Experience (Census at School) ...................................................................... 9 

S2/S3 Statistics Outcomes ............................................................................................... 10 

Angle ................................................................................................................................... 13 

Time ..................................................................................................................................... 15 

Direction and Scale ............................................................................................................ 17 

Coordinates and Symmetry ............................................................................................... 19 

S1 Symmetry and Coordinates Experience (Christmas Symmetry and Coordinates) ....... 19 

S2 Symmetry and Coordinates Outcomes: “rigorous not reindeer!”.................................. 19 

Money .................................................................................................................................. 22 

S1 Christmas money task ................................................................................................. 22 

S2 Maths in a Social Context ............................................................................................ 22 

Perimeter, Area and Volume .............................................................................................. 24 

Shape and Trigonometry ................................................................................................... 29 

S1 Shape Course (3 rd level Shape) .................................................................................. 29 

S2/S3 Shape Course (Trigonometry) Pentagon and above only; S2 and after only ......... 30 

Measurement ...................................................................................................................... 31 

Probability and Risk ........................................................................................................... 34 

Mathematics – its impact on the world, past, present and future .................................. 36 

S1 Planet Maths 3rd level ................................................................................................. 36 

S3 Planet Maths 4th level ................................................................................................. 36 

Problem solving (last week of each year) ........................................................................ 37 

Proportion ........................................................................................................................... 38

Newbattle Maths Department 

S1/S2/S3 Course Planner (CfE) 

DEVELOPMENT TASKS 

Major tasks – will require whole department or a subgroup 

Write assessments: 

o Algebra starter exercises for triangle repeating classes, pentagon and octagon? 

o Algebra octagon and decagon finishing 

Develop work, resources and examples, then update course plan for areas we haven’t taught before: 

o sampling and validity of data 

o Problem Solving Week 

Minor tasks – will not require subgroup 

Discuss methods for going backwards (rearranging formula; substituting numbers then simplifying then rearranging) and how this will 

impact on reversing the change 

M1 check for group work task on scale drawing (fast track) 

- Page 2 -



COURSE AIMS 

 

 

 

 

 

 

 

 

 

To develop the mathematical skills and confidence of our pupils at a level that is appropriate for them. 

To give every pupil the opportunity to master mathematical skills at a level that is appropriate for them. 

To allow for number and algebra to be taught on an ongoing progressive basis, whilst other topics are taught in discrete blocks at 

appropriate points. 

To promote depth and breadth of learning and understanding by ensuring pupils to become secure at the previous level before moving on 

to the next level of study. 

To provide appropriate challenge at every level, including the lowest. 

To develop the mathematical skills that pupils will need for everyday life, the world of work and Further/Higher Education. 

To give pupils all the prerequisite skills they will need to be ready to complete the appropriate NQ course in S4 

To provide full coverage of all 3 rd level outcomes and experiences for all; and 4 th level for those who become secure at 3 rd level 

To ensure progression in all topics is based on prior understanding of number and algebra. 

Levels of Course 

CfE reporting 

CfE Level 

National Qualifications 

(NB – could be argued that 3S and 4D are 

so similar it is almost impossible to 

distinguish) 

Circle Work on basic skills across levels 1 and 2 Roughly Access 2, though this is not formalised Maximum of 2D for number 

Maximum of 2C for other areas 

Triangle Consolidate then secure at level 2; begin to develop 

level 3 in some outcomes (not number/algebra) 

National 3: cover all content 

Maximum of 2S for number 

Maximum of 3D for other areas 

Pentagon Consolidate, then secure at level 3; begin to develop National 4: cover approx half of content 

Maximum of 3S for number 

level 4 for some outcomes (not number/algebra) 

Develop, then consolidate, then secure at level 4 (this 

course will be longer than the old top set S2 course) 

Octagon 

National 4: complete all units and finish with added 

value unit; 

Decagon Beyond 4 th level National 5: cover approximately two thirds of the 

course; only up to unit level in algebra 

Dodecagon Beyond 4 th level Pass National 5 exam. 

Classes who have enough time to cover dodecagon 

in full ought to be able to pass the exam with an A 

and be Ready for Higher. 

Teachers with less able classes will not necessarily 

cover the entire dodecagon course but will still be 

able to guide classes to an exam pass at National 5. 

Maximum of 4D for other areas 

Maximum of 4C for all areas. 

4S if added value unit is complete. 

If a pupil is working successfully at 

decagon, they are 4S for everything 

n/a 

- Page 3 -

S1 Course Plan 

NUNP 

NUAP 

Measure, 

Shape, 

Information 

Handling 

(do the upper topic 

before the lower topic) 

August to October 

(7 weeks) 

Starter Exercise 





CFE COURSE YEAR PLANNERS 

October to December 

(8 weeks) 

ongoing 

ongoing 

ongoing 

ongoing 

ongoing 

ongoing 

January to Easter 

(9 weeks) 

Easter to Change of 

timetable 

(9 weeks) 

Revise and sit finishing 

exercise immediately after 

Easter 

ongoing: Numerals, add/subtract, multiply, divide, fractions, integers, decimals, percentages, rounding 

Pentagon classes only: do the Triangle course 

Complete and sit finishing 

triangle course 

Pentagon course 

exercise at end May (not circle) 

ongoing: substitution, formulae, coordinates/linear graphical, simplifying, equations 

* Census at School 

(S1 Statistics 

Experience) 

* Angle 

Circle 

Triangle 

Triangle as needed, then 

pentagon in full 

* Time 

Circle 

Triangle 



* Symmetry and 

Coordinates 

(S1 Experience) 

* Measurement 

Circle 

Triangle 



* Perimeter Area Volume 

Circle: as much as time for 

Triangle: as much as time for 

Triangle: in full, no pentagon 

yet 

* Perimeter Area Volume 

continued 

Circle: continue 

Triangle: continue 

Triangle: ensure completed in full, 

some pentagon if time 

* Shape (S1 Shape Course) 

Special 

Lessons 

* Christmas Money task 

(2 periods) 

* Planet Maths 

[in 2013, was coordinated by M3] 

Not included in S1 course: Direction and Scale (S2 only), Probability (S2 only), Ratio and Proportion (start of S3), Money 

- Page 4 -

S2 Course Plan 

NUNP 

NUAP 

Measure, 

Shape, 

Information 

Handling 

(do the upper topic 

before the lower topic) 

June 

(4 weeks) 

Closing the gap: focus 

on areas of weakness 

from S1 as highlighted by 

finishing exercises 

* Money 

August to 

October 

(7 weeks) 

Starter exercise 






October to December 

(8 weeks) 

Ongoing 

Ongoing 

Ongoing 

Ongoing 

January to 

Easter 

(9 weeks) 

Ongoing 

Ongoing 

Ongoing 

Revision when 

needed. 

ongoing: rounding (cover first as it may have been missed in S1), numerals, 

add/subtract, multiply, divide, fractions, integers, decimals, percentages 

* Angle (in brief) 

Circle 

Triangle 

Pentagon 

Octagon 

* Measurement 

Circle 

Triangle 

Pentagon 

Octagon 

* Statistics 

Circle 

Triangle 

Pentagon 

Octagon 

All classes except circle 


timetable 

(8-9 weeks) 

Finishing exercises 

ongoing: substitution, formulae, coordinates/linear graphical, simplifying, 

equations 

* Proportion and Time 

Circle 

Triangle 

* Shape (Trigonometry) 

Pentagon 

Octagon 

* Direction Scale 

Enlargement 

Circle 

Triangle 

Pentagon 

Octagon 

* Perimeter 

Area Volume 

Circle 

Triangle 

Pentagon 

Octagon 

* Symm. and Coord. 

Circle S2/3 outcomes 

Triangle S2/3 outcomes 

Pentagon S2/3 outcomes 

Pentagon and octagon 

S2/3 outcomes 

* Probability 

Circle 

Triangle 

Pentagon 

Octagon 

Not included in S2 course: Time (pentagon/octagon), Shape (circle/triangle), Maths Impact on World, Ratio and Proportion 

(pentagon/octagon) 

- Page 5 -



S3 Course Plan (three lessons a week) 

NUNP 

NUAP 

Measure, 

Shape, 

Information 

Handling 

Special 

Lessons 

June 

(4 weeks) 

Closing the gap: 

focus on areas 

of weakness 

from S2 number 

and algebra as 

highlighted by 

finishing 

exercises 

* Proportion 

Circle 

Triangle 

Pentagon 

Octagon 

Decagon 

* Money 

August to October 

(7 weeks) 

October to 

December (8 weeks) 

January to Easter 

(9 weeks) 

Work through the NUNP course at the pace agreed for your class: 

Circle: then begin triangle when appropriate 

Triangle: then begin pentagon when appropriate 

Pentagon: then begin octagon when appropriate 

Octagon: then Added Value Unit, then begin decagon 

Decagon: then begin dodecagon when ready 

Work through the NUAP course at the pace agreed for your class: 

No algebra 

Triangle: then begin pentagon when appropriate 

Pentagon: then begin octagon when appropriate 

Octagon: then Added Value Unit, then begin decagon 

Decagon: then begin dodecagon when ready 

Work through the topics in this order at the pace agreed for your class: 


timetable (8-9 

weeks) 

Triangle course: measurement, perimeter area volume, time. Statistics, probability, coordinates and 

symmetry, shape, direction and scale, angle, then begin pentagon if ready 

Pentagon course: measurement, perimeter area volume, time. statistics, probability, coordinates and 

symmetry, shape, direction and scale, angle, then begin octagon if ready 

Octagon course: measurement, perimeter area volume, time. statistics, probability, coordinates and 

symmetry, shape, direction and scale, angle, Added Value Unit, then begin decagon 

Decagon course: perimeter area volume, coordinates and symmetry, shape, 

then begin dodecagon when ready 

* Planet Maths 4 th 

level (before sept w/e) 

- Page 6 -

I can round a number using an appropriate 

degree of accuracy, having taken into 

account the context of the problem. MNU 3- 

01a 

I can continue to recall number facts quickly 

and use them accurately when making 

calculations. MNU 3-03b 

I can use my understanding of numbers less 

than zero to solve simple problems in 

context. 

MNU 3-04a 

Having explored the notation and 

vocabulary associated with whole number 

powers and the advantages of writing 

numbers in this form, I can evaluate powers 

of whole numbers mentally or using 

technology. MTH 3-06a 

I can solve problems by carrying out 

calculations with a wide range of fractions, 

decimal fractions and percentages, using 

my answers to make comparisons and 

informed choices for real life situations. 

MNU 3-07a 

NATIONAL 4 MATHEMATICS CONTENT 



NUMBER (NUNP) 

I can apply my understanding of factors to 

investigate and identify when a number is 

prime. MTH 3-05b 

By applying my knowledge of equivalent 

fractions and common multiples, I can add 

and subtract commonly used fractions. MTH 

3-07b 

I have investigated strategies for identifying 

common multiples and common factors, 

explaining my ideas to others, and can apply 

my understanding to solve related problems. 

MTH 3-05a 

I have developed my understanding of the 

relationship between powers and roots and 

can carry out calculations mentally or using 

technology to evaluate whole number powers 

and roots, of any appropriate number. MTH 4- 

06a 

Having used practical, pictorial and written 

methods to develop my understanding, I can 

convert between whole or mixed numbers 

and fractions. MTH 3-07c 

Mental/non calculator fractions, percentages (single digit %, multiples of 10% and 25%, 33 1/3 %) 

Adding two decimals with different number of d.p.s and subtracting from the result 

multiplying decimal by single digit 

Add and subtract integers 

Round to nearest significant figure 

Round to two decimal places 

Convert between fractions, decimals, percentages 

Percentage increase and decrease 

multiply whole numbers of any size, with up to four-digit whole numbers 

divide whole numbers of any size, by a single digit, 10 or 100 

I can solve problems involving fractions and mixed 

numbers in context, using addition, subtraction or 

multiplication. MTH 4-07b 

I can choose the most appropriate form of fractions, 

decimal fractions and percentages to use when 

making calculations mentally, in written form or using 

technology, then use my solutions to make 

comparisons, decisions and choices. MNU 4-07a 

I have investigated how introducing brackets to an 

expression can change the emphasis and can 

demonstrate my understanding by using the correct 

order of operations when carrying out calculations. 

MTH 4-03b 

Within real life contexts, I can use scientific notation 

to express large or small numbers in a more efficient 

way and can understand and work with numbers 

written in this form. MTH 4-06b 

Having investigated the practical impact of 

inaccuracy and error, I can use my knowledge of 

tolerance when choosing the required degree of 

accuracy to make real life calculations. MNU 4-01a 


Simplify surds 

Rationalise denominator 

Significant figures 

Compound interest and depreciation 

Reversing a percentage change 

Four operations with fractions 

- Page 7 -

I can collect like algebraic terms, simplify 

expressions and evaluate using substitution. 

MTH 3-14a 

Having discussed ways to express problems or 

statements using mathematical language, I can 

construct, and use appropriate methods to 

solve, a range of simple equations. MTH 3-15a 

Having explored number sequences, I can 

establish the set of numbers generated by a 

given rule and determine a rule for a given 

sequence, expressing it using appropriate 

notation. MTH 3-13a 

I can create and evaluate a simple formula 

representing information contained in a 

diagram, problem or statement. MTH 3-15b 



ALGEBRA (NUAP) 

Having explored the distributive law in practical 

contexts, I can simplify, multiply and evaluate 

simple algebraic terms involving a bracket. MTH 

4-14a 

Having explored how real-life situations can be 

modelled by number patterns, I can establish a 

number sequence to represent a physical or 

pictorial pattern, determine a general formula to 

describe the sequence, then use it to make 

evaluations and solve related problems. MTH 4- 

13a 

Having investigated the pattern of the 

coordinate points lying on a horizontal or 

vertical line, I can describe the pattern using a 

simple equation. MTH 4-13c 


Linear equations (possibly including distributive law [mentioned in unit 

spec]); including letters on both sides 

Create then use a formula from a numerical or diagram sequence 

Multiply bracket by constant and factorise with numerical common factor 

Simplifying an expression with more than one variable 

Evaluate linear expression with more than one variable 

Extend number pattern or pattern in diagram and identify formula 

Gradient using V/H 

Draw straight line graph – horizontal, vertical, diagonal 

Know meaning of m and c in y=mx+c 

Change subject of a basic formula 

I can find the factors of algebraic terms, use my 

understanding to identify common factors and 

apply this to factorise expressions. MTH 4-14b 

Having discussed the benefits of using 

mathematics to model real-life situations, I can 

construct and solve inequalities and an 

extended range of equations. MTH 4-15a 

I have discussed ways to describe the slope of 

a line, can interpret the definition of gradient 

and can use it to make relevant calculations, 

interpreting my answer for the context of the 

problem. MTH 4-13b 

I can use a given formula to generate points 

lying on a straight line, plot them to create a 

graphical representation then use this to 

answer related questions. MTH 4-13d 


Multiply and factorise – double brackets, or common factor of letter 

Complete square with unitary coefficient 

Simplify and four operations with algebraic fractions 

FUNCTION NOTATION 

Identify equation of straight line using y-b=m(x-a) 

Linear equations and inequations 

Simultaneous equation – algebraic and graphical 

Changing subject 

Parabola equations 

Sketch quadratics 

Quadratic equations and discriminant 

Gradient formula 

Transformation graphs of sin, cos, tan including phase angle, multiple 

angle, vertical translation 

Trig identities; trig equations; non calc trig 

Laws of indices 

- Page 8 -



STATISTICS 

Areas to work on: develop work and resources on sampling and validity – including examples 

3 rd /4 th level CfE Statistics outcomes: 

I can work collaboratively, making appropriate use of 

technology, to source information presented in a 

range of ways, interpret what it conveys and discuss 

whether I believe the information to be robust, vague 

or misleading. MNU 3-20a 

I can evaluate and interpret raw and graphical 

data using a variety of methods, comment on 

relationships I observe within the data and 

communicate my findings to others. MNU 4-20a 

When analysing information or collecting data 

of my own, I can use my understanding of how 

bias may arise and how sample size can affect 

precision, to ensure that the data allows for fair 

conclusions to be drawn MTH 3-20B 

In order to compare numerical information in 

real-life contexts, I can find the mean, median, 

mode and range of sets of numbers, decide 

which type of average is most appropriate to 

use and discuss how using an alternative type 

of average could be misleading. MTH 4-20b 

Cross Curricular Links (whole school numeracy record): to be inserted here 

- Page 9 - 

I can display data in a clear way using a 

suitable scale, by choosing appropriately from 

an extended range of tables, charts, diagrams 

and graphs, making effective use of technology. 

MTH 3-21a 

I can select appropriately from a wide range of 

tables, charts, diagrams and graphs when 

displaying discrete, continuous or grouped 

data, clearly communicating the significant 

features of the data. MTH 4-21a 

PROGRESSION SUGGESTIONS FOR ACTIVITIES FOR LEARNING RESOURCES 

S1 Statistics Experience (Census at School) 

In S1, the following will apply: 

Pupils should be aware that surveying 

and interpreting is part of this process: 

ASK: Ask questions that can be answered by 

carrying out a survey or investigation and 

comparing sets of data. 

COLLECT: gather and record data from a 

variety of sources including class surveys, data 

from internet, books and newspapers. 

ORGANISE: design and use tables and 

diagrams 

DISPLAY: construct graphs, using technology if 

possible. 

INTERPRET: draw and communicate 

conclusions 

S1 classes must follow the Census at School structure: 

See the circle, triangle, pentagon sections below for details of what 

type of graphs and questions we would expect a class to cover 

1. Ask/Collect In their first lessons, all classes will complete the 

Census at School (CaS) questionnaire. 

2. Organise and Display Drawing tables, charts and graphs based 

on Census at School results for class (or year group) by hand. 

There should be a clear focus on drawing axes, writing good 

titles, and labelling graphs. All S1 classes should have an 

opportunity to draw graphs based on the CaS data using a 

computer (e.g. Microsoft Excel) 

3. Interpret The results and graphs will be collated and used to 

compare the data across classes and year groups. 

4. Interpret Pupils also need to be able to analyse somebody else’s 

information in context. Real-life graphs should be used as nonroutine 

questions. A key skill to develop here is to understand 

what the question is asking; as much as what the graphs or 

calculated statistics are showing. 

In this outcome, we should be putting pupils in a situation where 

literacy is a major part of the outcome. We should be developing 

their ability to interpret graphs or calculated statistics in a written and 

oral way and to write conclusions in proper sentences. 

Item Banks of level D/E questions 

Smartboard File on literacy in folder 

 

Pie chart template: Active Maths 

website Q7

S2/S3 Statistics Outcomes 

By the end of the topic, pupils should be 

able to: 

Construct: 

line graphs 

frequency tables 

Describe and compare key features of: 

bar graphs (no decimal numbers at all). 

line graphs 

pictographs 

pie charts 

Conduct a survey on a topic of their choice 

Construct: 

line graphs (whole numbers only) 

scatter graphs 

frequency tables (ungrouped) 



Notes on approaches and activities for 

learning 

Using real-life or made up data as appropriate 

One lesson could involve going to the computers 

Class should do all of this: Design questionnaire, 

decide who to ask, collect results, create graphs 

on computers (not by hand) 

Real life or made up data as appropriate 

RESOURCES 

Smartboard File on Circle level bar graphs 

ICT Resources: Maths Pack 2 (bar graphs/ 

/pictographs); supermathsworld.com 

(games) 

Smartboard file on triangle level 

Smartboard Files containing example 

graphs to select suitable examples from 

Graphs should be created using a computer package 

when appropriate. 

Calculate the mean, and compare data set using 

means, giving answer in a sentence 

Describe and compare (in sentences) key features of: 

bar graphs (including non-routine ones) 

line graphs (including non-routine ones) 

scatter graphs (basic comment only, no best fit 

line) 

pie charts (recognise max/min sectors; For sectors 

that are quarters and halves, should be able to 

evaluate frequency when they know population 

size – basic examples only) 

tables (including non-routine) 

Discuss whether data is valid 

Discuss basic sampling strategies 

Likely to be mostly with a calculator at this level, 

with no decimals 

Reference to cross-curricular links and real-life contexts 

Dynamic Worksheet Statistics-04 

ICT Resources: Maths Pack 2 (bar 

graphs/line graphs/pie charts/pictographs) ; 

supermathsworld.com (games) 

At least one lesson must focus on literacy, reasoning, sampling and validity, with class writing 

answers in full sentences. Every class MUST have experience of: 

Identify key words in question and discuss their meaning 

Writing multiple sentences in their own words describing what a graph is showing in their 

putting sentences up on boards; discussing as a class which sentences were stronger or 

weaker interpretations of graphs (i.e. identifying when a pupil’s sentence actually doesn’t 

answer the question; or where a pupils sentence makes no sense to a reader (“Mayfield was 

most”) ) 

questions that ask pupils to evaluate the validity of the data (e.g. a pie chart showing 10 pupils at 

Newbattle. 80% of them support Celtic. The chart says that most Newbattle pupils support 

Celtic. Do you agree? What if the same survey was repeated in London) 

- Page 10 -




Mean without calc requiring rounding 

Freq table with class intervals from ungrouped data 

Mean, median, mode, range 

Comparing data sets with MMMR 

Pie charts from raw data 

Construct scatter, add best fit, use to estimate 

 

 

 

 

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 

NATIONAL 5 MATHEMATICS 

CONTENT 

Comparing data sets using 

standard deviation/IQR 

Scattergraphs, line of best 

fit 

Construct: 

Pie charts from raw data 

Scatter graphs 

Line graphs including decimals where appropriate 

Grouped frequency tables 

Draw a line of best fit on a scatter graph and use to 

estimate one value given another 

Calculate mean, median, mode and range 

Describe and compare (in sentences) key features of: 

Two data sets represented by mean, median, 

mode or range, including difference between 

concept of average and concept of spread 

Non-routine line graphs or bar charts, including the 

word trend 

Scatter graphs, using the word correlation 

Pie charts (e.g. “before” and “after”); including 

examples where percentages are shown on the 

slices 

Non routine graphs (possible examples including 

stem and leaf diagrams, dot plots or Venn 

diagrams) 

Discuss whether data is valid and using sampling 

strategies and making informed choices 

Discuss discrete and continuous data 

Pie charts: link to work on fractions. Pupils may 

need revision on how to use a protractor 

See comments above about interpretation of 

graphs. Class activity: find the mean, median, 

mode and range of the ages of all the people 

living in your house. What does it tell us? (M7) 

At least one lesson must focus on literacy, 

reasoning, sampling and validity, with class writing 

answers in full sentences to an exam standard 

response. Every class MUST have experience of: 

Identify key words in question and discuss 

their meaning 

Writing multiple sentences in their own words 

describing what a graph is showing in their 

putting sentences up on boards; discussing 

as a class which sentences were stronger or 

weaker answers to questions and improving 

on sentences through class discussion 

Smartboard File for pentagon level 

statistics 

Smartboard Files containing example 

graphs to select suitable examples from 

Dynamic worksheets Statistics-03, 04, 05 

ICT Resources: Maths Pack 2 (bar 

graphs/line graphs/pie charts/pictographs) ; 

supermathsworld.com (games) 

See Int 1 past paper questions for ideas of 

what to interpret 

- Page 11 -



Construct graphs: 

Revise all pentagon 

Describe and compare in sentences key features of 

graphs, compare graphs, compare data sets using 

statistics 

Revise all pentagon, plus introduce stem and leaf 

diagrams 

Come across the words standard deviation and 

interquartile range, and interpret them in practice 

Discuss whether data is valid and using sampling 

strategies and making informed choices 

Discuss difference between qualitative and 

quantitative; discrete and continuous data 

No content at decagon 

Calculate sample standard deviation (n

Areas for Development: none at present 

3 rd /4 th level CfE Angles outcomes: 

I can name angles and find their sizes using my knowledge of the 

properties of a range of 2D shapes and the angle properties associated 

with intersecting and parallel lines. MTH 3-17a 



ANGLE 


Having investigated the relationship between a radius and a tangent 

and explored the size of the angle in a semi-circle, I can use the facts I 

have established to solve related problems. MTH 4-17a 

By the end of the topic, pupils should be able to: 

Recognise right, acute and obtuse angles 

Draw angles in degrees using a protractor to within 5° 

Identify and know: 

Right angle = 90º 

Acute angles90º and




Angles with parallel lines, symmetry and circle properties: 

o Angles with parallel lines 

o Angles with intersecting lines 

Naming angles 

Check class know how to measure angles with a 

protractor 

Know the facts and solve basic problems using: 

90° in a right angle, 180° in a straight line 

360° round a point 

vertically opposite angles are equal 

angles in a triangle add up to 180°. 

angles in a quadrilateral add up to make 360° 

facts about angles in parallel lines 

o 

o 

o 

Sum of angles in triangle/quadrilateral 

Angle in semicircle 

Relationship between tangent and 

radius 

i.e. using three letters. Put a diagram on the board and ask 

pupils to come to the board and (e.g.) identify angle BCA or say 

what type of angle EBD is. 

Use an investigative approach to discover angle properties 

Class should meet some more complex questions where more 

than one rule will be needed; followed by occasional angle 

problem solving starters throughout year 


CONTENT 

Nothing specific, though 

properties of shapes are 

mentioned 

Maths Pack 1 

Angles in a Straight 

Line 

Active Maths Worksheet 

pQ10/Q10b 

Parallel line angles on laminated 

card.(to be made) 

Some examples should be angles in diagrams of 

quadrilaterals with the diagonals marked 

Know and use all previous facts in diagrams 

requiring use of three or more rules, including all 

rules from pentagon, plus: 

angle in a semicircle 

angle between tangent and radius 


No content at dodecagon 

Use an investigative approach to discover the properties of 

angles in circles 

Past General exam questions, 

and some Int 2 exam questions 

(not the hardest Int 2 examples) 

Laminated card activity 

- Page 14 -


3 rd /4 th level CfE Time outcomes: 

Using simple time periods, I can work out how long a journey will 

take, the speed travelled at or distance covered, using my knowledge 

of the link between time, speed and distance. MNU 3-10a 



TIME 

I can research, compare and contrast 

aspects of time and time management 

as they impact on me. MNU 4-10a 

(our interpretation is this means timetables, 

“being on time” etc) 


By the end of the topic, pupils should be able 

Notes on approaches and activities for learning 

to: 

Know the facts: 

60 seconds in an minutes 

60 minutes in an hour 

24 hours in a day 

7 days in a week 

52 weeks in a year 

365 days in a year 

Read time from analogue clocks 

Understand simple time equivalences and use of am and 

pm 

Understand 24 hour times used in context 

Teachers should use their discretion as to how much time to 

spend on analogue time. 

e.g. quarter to six = 5.45, half past twelve = 12.30 

The bus arrives at 14.30. What time is that? Class discussion 

I can use the link between time, speed 

and distance to carry out related 

calculations. MNU 4-10b 

RESOURCES 

Active Maths 

Worksheets pP23 

Teaching Time 

Class Clock 

DW Time-02 

AW pP27/P28 

Smartboard file 

Interpret a simple bus or train timetable 

Know and use all basic facts from circle 

Convert between 12 and 24-hour time 

Calculate time intervals (12 and 24 hour time) (multiples of 

5 minutes) 

Interpret and solve problems using bus and train timetables 

Class discussion, worksheets 

Whiteboards; splitting time interval into smaller intervals and 

adding. “A film starts at 7.35pm and finishes at 10.20pm – how 

long does it last?” 

 

Smartboard file – class discussions/whiteboards: if I get the 

8am train from Edinburgh, when will I arrive at Glasgow? if I 

need to be in London by 11am which is the last train I can 

get from Edinburgh? If I am at Dundee station at 7.15am, 

how long do I have to wait for the next train? 

Worksheets and group activities on reading the number 3 

and number 29 bus timetables (M5). 


sP24 

DW Time-02 

DW Time-01 

Teaching Time, Maths 

Pack 1 Class Clock 

Lothian Bus timetable, 

worksheets and group 

activity (M5) 

- Page 15 -


using appropriate units for time (min, sec, year, week 

etc) 

Calculate time intervals 

Be aware of terms GMT, BST, “+1” (in context of time 

zones) 

Meaning of speed and units used for it 

Calculate speed, distance or time taken (whole hours) in 

routine problems 

Interpret distance-time graphs 

Convert 15 minutes, 30 minutes, 45 minutes into hours as 

a decimal 

Calculate and solve problems involving speed, time 

(decimals) and distance 





time intervals with 12 and 24 hour clock 

speed distance time (time in hrs&mins) 

I go to sleep at 2148 and wake up at 0824. How long did I sleep 

for? 

Class should experience questions including: 

Moving from one time zone to another (including a brief 

class discussion on other countries and their time zones) 

Interpreting information (e.g. what time do I need to leave 

the house to get to the airport on time? Which of the trains 

on this timetable should I take to be at work by 8.30am?) 

Class discussion: km/h, mph, m/s etc. What does it mean to say 

a car is travelling at 30mph? 

Basic numbers; formulae given. Class should be explicitly 

aware that this topic is algebraic formulae – teach after Triangle 

formulae have been covered in NUAP. At end of topic, practice 

choosing which of the three formulae to use each time. 

e.g. 3 hours 45 minutes = 3.75 hours (link NUNP decimal) 

Able sets should be able to convert any decimal into hours and 

minutes and vice versa 

Class discussion, mini whiteboards, non routine questions, 

questions with a number of steps. One or two lessons should be 

spent on this, and class should experience questions including: 

Moving from one time zone to another 

Interpreting information (see pentagon) 

NATIONAL 5 

MATHEMATICS CONTENT 

no content 

DW Time-01 


sP24 

Smartboard file, 

Standard Grade/Int 1 

Item Banks 

AW sJ25 option 1 

DW Time-03 

AW sJ25 option 2 

DW Time-03 

Past Int 1/Standard 

Grade questions 

AW sK28 

- Page 16 -



DIRECTION AND SCALE 

Areas for Development: 

3 rd /4 th level CfE Direction/Scale/Enlargement outcomes: 

Having investigated navigation in the world, I can apply my I can apply my understanding of scale 

understanding of bearings and scale to interpret maps and when enlarging or reducing pictures and 

plans and create accurate plans, and scale drawings of shapes, using different methods, 

routes and journeys. MTH 3-17b 

including technology. MTH 3-17c 


I can apply my understanding of the 

properties of similar figures to solve problems 

involving length and area. MTH 4-17b 

By the end of the topic, pupils should be able to: Notes on approaches and activities for learning RESOURCES 

Use an 8 point compass rose. 

Give directions for a route or journey. 

Follow paths described by instructions such as: 

Straight ahead, second on left, first on right 

(if appropriate) Logo or turtle 

Giving directions to others 

Investigate scale drawings, maps and plans of the school and its 

local area, and who uses them. 

Use a scale drawing or map to calculate real life distance 

Create simple scale drawings based on a simple sketch of a 

perimeter 

Understand and measure 3 figure bearings 

Convert the eight compass points into bearings 

Enlarge a simple shape on squared paper by a scale factor of 2, 

3 or ½ 

Follow or give more complicated directions (e.g. from a street 

map) involving three or more steps 

“Never Eat Shredded Wheat” 

“Naughty Elephants Squirt Water” 

Practical Split class into groups; each group has to choose 

somewhere in the school and give accurate directions from 

maths classroom to that place (move around school). Groups 

then swap directions and try to follow them. Class discussion 

on good and bad ways of phrasing instructions (literacy). 

Use plan of classrooms in school or maps of local area to 

describe journeys from one classroom to another 

Look at a variety of scale drawings, maps, etc. 

Where the scale is expressed in the form 

1cm = 1m, 1cm = 2m, 1cm = 10m, 1cm = 5m 

Measure perimeter of classroom, then Quad, Bite Site, 

(challenge) outside of Astro – and then draw them to scale 

Class need to understand the words “to” and “from” in the 

context of bearings 

e.g. old Access 3 questions 

World Tour 

worksheet – crosscurricular 

Geography; atlases 

 

 

Electronic LOGO 

ICT Services 

have a “turtle” 

that can be lent 

to schools 

Maps of classrooms 

(on Intranet) 

Class set of 

orienteering 

compasses (Base) 

Electronic school 

map (on server) 

See MD for street 

maps of local 

communities 

- Page 17 -


Use a fractional scale factor to enlarge or reduce linear non 

rectangular shape 

Use a given scale drawing or map to calculate real life distance 

Create simple scale drawings including an angle or a threefigure 

bearing 

Enlarge or reduce a shape that may include some basic 

diagonal lines by a scale factor of 2, 3 or ½ 

Revise pentagon content 


No content at dodecagon (covered in shape, and proportion topics) 




Similar shapes – length, area, volume Use bearings 

with trigonometry 

Where the scale may be expressed in the form of (e.g.) 1:100, 

as well as 1cm=___ 

Do not spend more than one lesson on this! 

As at pentagon, though scale factors should be extended to 

include any fraction, such as ¼, ½, 3 / 2 

M1 to check group 

work activity from S1 

Fast Track 

Check resources 

- Page 18 -



COORDINATES AND SYMMETRY 

Areas for Development: come back to idea of distance formula after basic Pythagoras? 

3 rd /4 th level CfE Coordinates and Symmetry outcomes: 

I can use my knowledge of the coordinate 

system to plot and describe the location of a 

point on a grid. MTH 2-18a / MTH 3-18a 

I can illustrate the lines of symmetry for a range 

of 2D shapes and apply my understanding to 

create and complete symmetrical pictures and 

patterns. MTH 2-19a / MTH 3-19a 

I can plot and describe the position of a 

point on a 4-quadrant coordinate grid. 

MTH 4-18a 

I can apply my understanding of the 4-quadrant 

coordinate system to move, and describe the 

transformation of, a point or shape on a grid. MTH 4-18b 

Having investigated patterns in the environment, I can use appropriate mathematical vocabulary to 

discuss the rotational properties of shapes, pictures and patterns and can apply my understanding 

when completing or creating designs. MTH 4-19a 


S1 Symmetry and Coordinates Experience (Christmas Symmetry and Coordinates) 

By the end of the topic, pupils should have experienced: Notes on approaches and activities RESOURCES 

Read and plot coordinates 

Complete the missing half of a simple symmetrical shape or pattern on a 

squared grid 

Create a snowflake and discuss rotational symmetry 

Do a coordinate shape activity 

One quadrant diagram 

One quadrant diagram 

Four quadrant diagram 

At circle level, lines of symmetry would be 

horizontal or vertical; and there may be no 

diagonal lines in the diagram. 

At triangle or pentagon level, diagonal lines of 

symmetry should be introduced; and diagrams 

themselves would contain diagonal lines. 

S2 Symmetry and Coordinates Outcomes: “rigorous not reindeer!” 



learning 

Read and plot positive coordinates on a Cartesian diagram. Coordinate bingo, Billy Bug and similar games. 

Coordinate pictures, Treasure maps 

Investigate other ways of recording position e.g. map grid 

references, cinema seat plans, airline seating 

Play battleships, and similar games. 

Complete a symmetrical shape 

Find lines of symmetry of shapes, including those with no line 

symmetry 

Non-routine questions e.g. Foundation past papers, reallife 

examples of plans e.g. cinema seat plans, online 

seat bookings and create questions based on these 

Students may benefit from practice at accurately copying 

shapes first 

Christmas 

symmetry 

pictures 

Christmas 

coordinate 

pictures 

RESOURCES 

Maths Pack 1 – 

Coordinates 

Active maths worksheet 

pQ29/Q30 

Primary Games 1 – Billy 

Bug 

Continue and complete a basic tiling pattern where some shapes 

are already drawn in place 

Pupils can investigate shapes that do or do not tile 

- Page 19 - 

DTL activities, old MIA 

worksheets



Find the 4 th corner of a quadrilateral (that lies parallel to the axes) 

given two or three other corners (1 quadrant grids) 

Translating shapes on a 1-quadrant grid along the x and/or y-axis. 

Give coordinates of a point or corners of a shape reflected in a 

horizontal or vertical line of symmetry on a one-quadrant grid 

Completing a symmetrical with horizontal, vertical or basic diagonal 

lines of symmetry 

Find lines of symmetry of more complex shapes, including those 

with no line symmetry 

Identify the order of rotational symmetry of a shape 

One quadrant grids only. S2 classes repeating triangle 

may benefit from seeing a four quadrant diagram if 

appropriate. 

Students may benefit from practice at accurately copying 

shapes first 

Active Worksheets 

pQ30/Q31/Q32 

Maths Pack 1 - 

Coordinates 

Active Worksheets sN1, 

sN2, sN3, sQ11/Q17 

Continue and complete a tiling pattern where some shapes are 

already drawn in place 


Solve problems involving completion of a described shape across at least 3 quadrants 

(AVU) 

rotational symmetry with straightforward linear shapes 

Find the 4 th corner of a quadrilateral in the first quadrant (lying 

parallel to the axis) given two or three other corners 

Translating shapes on a 4-quadrant grid along the x and/or y-axis. 

Give coordinates of a point or corners of a shape reflected in a 

horizontal or vertical line of symmetry (including the axes) on a 

four-quadrant grid 

DTL activities, old MIA 

worksheets 


3d coordinates including skeleton diagrams 

Vectors and components in 2d and 3d 

Maths Pack 1 - 

Coordinates 


Primary Q17/Q18 

Identify the midpoint of two points in the first quadrant with a 

diagram 

Identify the order of rotational symmetry of a shape 

Rotate a basic shape (e.g. right angled triangle) 90° or 180° 

clockwise or anticlockwise about a given turning point 

Pupils should be familiar with the different possible 

language e.g. “quarter turn symmetry” or “rotational 

symmetry of order 4” 

- Page 20 -



Build upon the key skills of pentagon: 

Find the 4 th corner of a quadrilateral spread across quadrants 

(that may not lie parallel to the axes) given two or three other 

corners 

Identify the midpoint of two points with or without a diagram 

Rotate shapes 90° or 180° clockwise or anticlockwise about the 

origin 

Identify the transformation when shown the original shape and the 

transformed shape (one step transformations only) 

Complete a straightforward diagram to give it half or quarter turn 

symmetry 

Use the midpoint formula to find the midpoint of two coordinates 

(Not in exam) 

Introduce the 3d coordinate grid and z-axis 

Write down the coordinates of vertices of 3d shapes or endpoints of 

a directed line segment on a 3d coordinate diagram 

Revision of 3d coordinates from decagon 

Introduce concept of directed line segments in 2d and 3d 

Introduce concept of vectors as something that has both direction 

and magnitude 

Discuss the horizontal and vertical components of a directed line 

segment in 2d., using column vector notation 

Discuss adding 2d and 3d vectors by adding their horizontal and 

vertical components 

Not involving a formula 

See points being plotted on Autograph 

e.g. a cuboid or cube 

i.e. explain difference between what a (2d or 3d) 

coordinate and a vector are. Introduce using 2d, then 

move on to 3d. 

e.g. forces 

i, j and k are Higher and are not required at National 5 

e.g. two forces acting on one object, add the horizontal 

and vertical components to obtain the overall force 

Int 1 and General Item 

Bank Questions 

Autograph 

Worksheet (M5) 

- Page 21 -



MONEY 

Areas for Development: numeracy across learning group to look at 3 rd /4 th level outcomes in their own subjects and record this 

in whole school numeracy plan 

3 rd /4 th level CfE Money outcomes: 

When considering how to spend my 

money, I can source, compare and 

contrast different contracts and 

services, discuss their advantages 

and disadvantages, and explain 

which offer best value to me. MNU 

3-09a 

I can budget effectively, 

making use of technology 

and other methods, to 

manage money and plan 

for future expenses. MNU 

3-09b 

I can discuss and illustrate the 

facts I need to consider when 

determining what I can afford, 

in order to manage credit and 

debt and lead a responsible 

lifestyle. MNU 4-09a 


I can source information 

on earnings and 

deductions and use it 

when making 

calculations to 

determine net income. 

MNU 4-09b 

I can research, compare 

and contrast a range of 

personal finance products 

and, after making 

calculations, explain my 

preferred choices. MNU 4- 

09c 

By the end of the topic, pupils should be able to: Notes on approaches and activities for learning RESOURCES 

S1 Christmas money task 

Christmas money task (Christmas S1): 

pupils will be asked to work with a budget to buy presents. 

There are three versions of this task in existence. The specific requirements 

of this task should be matched to what pupils hav e experienced with 

fractions, decimals and percentages in NUNP by this point in S1 

S2 Maths in a Social Context 

Rationale: The emphasis on this topic should be about getting pupils to apply their knowledge of number in financial contexts. A focus on interpreting the 

question and applying knowledge of number to solve problems is key and one that needs to be developed. Class should work through the smartboard files 

appropriate to their level. The main approach should be discussion based, exploring the issues that the questions bring up and the vocabulary (i.e. per 

annum) around finance, pupils should use mini-whiteboards and gathering answers. The files are not an exhaustive list and teachers are encouraged to 

add further materials. The idea of best buy is one that is important in financial planning and should, from two for one offers to units cost to identifying the 

best contracts, it is central to good financial sense. 

Know vocabulary: income, expenditure, savings, budget 

Calculate income and expenditure in basic everyday 

contexts 

Compare two or more products and identify the best buy 

Make a basic budget 

Make a basic savings plan 

Tills/shops, counting out change (in NUNP) 

e.g. a shopping list. 

e.g. when told monthly household income and 

expenditure, calculate what they have left over 

e.g. when told weekly pocket money and a desired 

purchase, work out how many weeks they will need 

to save for 

Link to NUNP choosing the sum and understanding 

money as a decimal 

- Page 22 -

[Note: to meet the National 3 assessment standards, pupils 

must have covered NUNP triangle percentages to attempt 

this outcome] 

Know vocabulary: income, expenditure, savings, budget, 

gross pay, net pay, deductions, tax, VAT, bonus 

Calculate income and expenditure for a household or 

workplace 



e.g. work out net pay given gross pay and 

deductions. Work out total income for a household. 

Work out bonuses and deduct tax. Basic numbers, 

questions may have 2 or 3 simple steps. 

Circle, Triangle, Pentagon, 

Octagon files: Resources\0 S1 

S2 S3 (3rd 4th 

level)\Money\S2-3 Money in 

Social Context 2012. 

Best Buy Chocolate Bar also 

for level Pentagon or Octagon. 

Compare two or more products and identify the best buy 

when at least one product has a percentage discount 

applied 

Make a basic budget 

Make a basic savings plan 

Tills for lower triangle sets 

Apply fractions/decimals/percentages to a range of 

financial topics e.g. commission, interest, HP, wages, best 

buy, currencies, comparing financial products 

Same as pentagon 

e.g. when given (or after calculating) net monthly 

pay and monthly expenditure, identify how much 

money is left over 

e.g. given (or after calculating) what is left over 

each month, calculate how many weeks/months 

someone would need to save for to buy a desired 

item 

Link to NUNP choosing the sum and understanding 

money as a decimal; and add/subtract decimals. 

Link to literacy 

All examples matched appropriate to 3 rd level and 

pentagon number 

- Page 23 -



PERIMETER, AREA AND VOLUME 


3 rd /4 th level CfE Perimeter Area Volume outcomes: 

I can solve practical 

problems by applying my 

knowledge of measure, 

choosing the appropriate 

units and degree of 

accuracy for the task and 

using a formula to calculate 

area or volume when 

required. MNU 3-11a 

Having investigated different 

routes to a solution, I can 

find the area of compound 

2D shapes and the volume 

of compound 3D objects, 

applying my knowledge to 

solve practical 

problems.MTH 3-11b 

Having investigated the 

relationships between the 

radius, diameter, 

circumference and area of a 

circle, I can apply my 

knowledge to solve related 

problems. MTH 4-16b 



Perimeters: 

simple straight-sided shapes, all lengths given 

Areas: 

Straight sided shapes by counting squares and half squares 

Curved sided shapes by considering full squares and part squares 

Rectangles with cm² grid showing; leading to multiplying instead of counting 

Volume 

Units for volumes: ml/l as well as cm³/m³ etc, and remind class of the links 

between these covered in the measurement topic 

Of objects by counting cubes 

Of cuboids by counting cm cubes 

Perimeters: 

Simple straight sided shapes where some sides are not marked (e.g. regular 

polygons or symmetrical shapes where they know which sides are the same, or 

composite rectangles/squares where one length may need calculating) 

Basic problem solving questions in real-life context involving proportion, linked 

to perimeter and cost of materials 

Find a missing length in a square, rectangle or triangle when given the 

perimeter 

Areas, briefly with counting squares, then leading to a formula (but only if class 

have done triangle algebra, otherwise use this topic to introduce and teach the 

Through investigating real 

life problems involving the 

surface area of simple 3D 

shapes, I can explore ways 

to make the most efficient 

use of materials and carry 

out the necessary 

calculations to solve related 

problems. MTH 4-11b 

Notes on approaches and 

activities for learning 

using rule by words and not using formula 

discuss with class where they have come 

across word volume in science and what it 

means 

not leading to multiplying at this level, but 

will at triangle 

e.g, ribbon costs 30p a cm, how much will 

it cost to go around the outside of this 

shape? Fences around fields etc. 

I have explored with others 

the practicalities of the use 

of 3D objects in everyday 

life and can solve problems 

involving the volume of a 

prism, using a formula to 

make related calculations 

when required. MTH 4-11c 

RESOURCES 

SMARTBOARD 

problems 

Questions from SHM 

and TJ etc 


pP13, sP11/19/13/21 

plastic interlocking 

multilink cubes 

SMARTBOARD 

problems 

Questions from SHM 

and TJ etc 

- Page 24 -



concept of a formula): 

Rectangles and squares using A=LB (or A=L×B if needed) 

Basic examples of working out the other dimension where the area and one 

length are given (informal methods, not rearranging formula) 

Basic problem solving questions in real-life context involving proportion, linked 

to area and cost of materials. 

Right-angled triangles as half a rectangle, leading to formula. At triangle level, 

the formula should be A=½LB (explained as “half OF length times breadth”; 

and not “½ × length times breadth”), not A=½BH and definitely not A=LB/2. 

Basic problem solving giving answer as a sentence: e.g. “which of these two 

fields is bigger and by how much?” 

(do not use the term “squaring” when 

doing squares) 

e.g. carpet costs £5 per m², how much will 

it cost to carpet this room? [room is a 

rectangle]; painting a wall, turf for a 

garden etc. 

*** DEPARTMENTAL POLICY agreed 

9/3/12 *** 

At triangle level, we use A = ½ LB to avoid 

confusing them by using “length” and 

“breadth” in one formula and “base” and 

“height” in the other 

Volumes (discuss with class where they have come across this word in science, 

and what it means to them): 

Units for volumes: ml/l as well as cm³/m³ etc, and remind class of the links 

between these covered in the measurement topic 

Cuboids, first by counting squares, leading to formula V=LBH (or V=L×B×H if 

needed). 

Basic problem solving involving capacity (e.g. “how many of these boxes can 

you fill using 500ml of juice?”) 

Basic problem solving giving answer as a sentence: e.g. “which of these two 

cartons is bigger and by how much?” 


Volume of cube and cuboid 

Area of parallelogram, kite, trapezium (as composite triangles) 

Area of rectangle and square 

Draw nets and calculate surface area of a prism 

Perimeter of straight sided shape Volume of triangular prism, cylinder, other prisms given area of 

Circumference/area of circle 

base 

e.g. the volume of a drinks carton is 

3×2×7. How many cartons could you fill 

from 420ml of juice? 

Investigation using 

cubes (M1) 


Arc length/sector area 

Volumes of spheres, cones, 

pyramid 

Area of a triangle with ½absinC 

- Page 25 -



Perimeters: 

Find the missing side and then calculate perimeter in more complex shapes 

More complex problem solving: 

o Find a missing length in a composite shape when given the perimeter 

o Find a missing length in a symmetrical shape (e.g. isosceles triangle) 

when more than one side is missing. 

Areas using formulae (link to NUAP work) 

Reinforce the formula A=LB for area of a rectangle and A=L² for area of a 

square (but only if squaring has been taught in NUNP). 

Triangles: revise right-angled triangles, adapting the formula learnt at triangle 

level, to become A=½BH 

Area of any triangle when given base and perpendicular height. 

Compound shapes involving two or more rectangles or a rectangle and a rightangled 

triangle; including some basic examples involving subtraction. 

Volume (discuss with class where they have come across this word in science, and 

what it means to them): 

Units for volumes; remind class of link between ml/l as well as cm³/m³ etc. 

Reinforce the formula V=LBH for volume of a cuboid 

Volume of basic compound shapes made of two or more cuboids where all 

lengths are marked 

Circles: 

Briefly revise link between diameter and radius 

Calculate circumference (not area) when given diameter or radius using 

formula, basic examples. 

More complex problem solving mixing perimeter, area and volume and different 

shapes solving: 

Mixing all examples previously encountered including choosing the formula 

(could extend to basic semicircles, cubes etc) 

Generalisations – come up with a formula for perimeters of very basic shapes 

e.g. perimeter of a rectangle, perimeter of a regular pentagon (link to NUAP) 

Area of rectangles or triangles or volume of cuboids when the dimensions have 

been given in different units (e.g. 2m × 50cm) 

More complex problem solving giving answer as a sentence: e.g. “which of 

these two cartons is bigger? Explain your answer” or “this carton needs to hold 

200ml of juice. Is it big enough? Explain your answer” or “which of these 

cartons is better value?” 

Composite area with some missing lengths, if appropriate to the class 

At pentagon level, all lengths would 

normally be given. Compound shapes 

would usually not include any missing 

lengths unless class were ready for it. 

Introduce pi initially through a practical 

activity 

Basic examples 

Link to NUAP work – e.g. write a formula 

to express the link between diameter and 

radius 

- Page 26 -



Formulae: 

Reinforce NUAP work on creating formula for perimeter/area/volume of a shape 

where one or more dimensions are letters. 

Circles: 

Calculate area and circumference of any circle. 

Areas: 

Area of composite shapes including: 

o Shapes involving semicircles 

o Kites, parallelograms, trapeziums by splitting into triangles and using 

formula for area of a triangle. 

o case where one or more length may need to be calculated first 

o Surface areas of a basic triangular prism or cuboid when shown its net. 

Volumes: 

given the volume and two of the dimensions of a cuboid, calculate the third 

dimension. 

Calculate volume of any prism when told its cross-section area using formula 

V=Ah (not V=AL, as standard cuboid and cylinder formulae use ‘h’ for height) 

Calculate volume of a cylinder or triangular prism, using appropriate formulae. 

Problem solving: 

More complex problem solving – see pentagon examples for ideas of 

questions; but use more complex shapes. 

Questions of the form (e.g.) how many 2×3×10 cuboid cartons can be filled 

from 1.5 litres of juice. Answer may be a decimal and class have to interpret 

this. 

Surface area of a triangular prism or cuboid when not shown its net. 

Areas: 

Area of any triangle using ½ ab sin C – routine examples only 

Volumes: 

Volumes of spheres, cones, pyramids – routine examples only, plus basic 

composite shapes only 

Circles: 

Arc length and area of any sector – routine examples only 

Able classes could be extended to surface 

area of other shapes such as pyramids or 

cylinders, but this is optional 

*** DEPARTMENTAL POLICY agreed 

9/3/12 *** 

Intermediate 1 and 

General item bank 


General and 

Intermediate 1 with 

Applications item bank 

Old Intermediate 2 

NABs Unit 1 Outcome 

5 

- Page 27 -



Beyond decagon: 

Areas and Perimeters: 

Problem solving: 

Area of composite shapes using ½ ab sin C 

Areas of segments of sectors of circles (i.e. sector area minus triangle area) 

Problem solving questions involving arc length and area. 

Calculate the angle, given the sector area or arc length. 

Volumes: 

Volumes of composite shapes involving spheres, cylinders, cones, 

Volumes of prisms where the cross-sectional area requires use of ½ ab sin C 

or area of a sector of a circle 

Going backwards with all volume formulae 

Problem solving/non routine questions involving volume. 

Class should know the difference between 

a question asking for the arc length, and a 

question asking for the perimeter of a 

shape. 


credit Item Bank 

questions 

- Page 28 -



SHAPE AND TRIGONOMETRY 


3 rd /4 th level CfE Shape outcomes: 

Having investigated a range of methods, I can accurately draw 2D shapes 

using appropriate mathematical instruments and methods. MTH 3-16a 

(this is the only 3 rd level outcome that we have decided not to cover in maths due to time 

restrictions. Pupils will have some experience from CDT and Art of drawing accurate 

diagrams – agreed as a department 23/4/12 ) 

Cross Curricular Links (whole school numeracy record): to be inserted here – see note above about CDT/Art 

I have explored the relationships that exist between the 

sides, or sides and angles, in right-angled triangles and can 

select and use an appropriate strategy to solve related 

problems, interpreting my answer for the context. MTH 4-16a 

By the end of the topic, pupils should 

be able to: 

Notes on approaches and activities for learning RESOURCES 

S1 Shape Course (3 rd level Shape) 

For all classes: 

Teachers should bear in mind that all pupils (even the weakest) are likely to have done the lowest level work repeatedly in Primary school. This is 

why the work is at one level – so that all classes can get a new experience with shape rather than making the lowest classes repeat the basics. 

In this topic, the experience is more important than mastery of every aspect of shape. This topic should be visited briefly and not in depth. 

Discuss and identify a range of 2d [with 

progression into hexagons, pentagons etc] and 3d 

shapes. 

When naming shapes, class should discuss number of sides, 

corners, faces etc. At the top levels, classes should use the words 

faces, vertices, edges and diagonals as specified at National 4. 

Smartboard file – 

Naming Shapes 

Use nets to make 3d shapes. 

Know the: 

types of triangles – isosceles, equilateral, 

scalene and right-angled. 

words diameter, radius, centre and 

circumference for circles. (word diameter is 

used in science in discussions on planets – 

make sure this link is made) 

Activities for identifying/describing objects: 

one pupil describes shape orally in terms of its properties. Rest 

identify the shape. 

Design “Wanted” poster for a shape describing only properties 

(CL) 

Group work tasks: Robbie’s Shape, Tammy’s Shape… (in base) 

Dragging and sorting activities (Venn diagram style) 

 

 

Smartboard file – Nets 

Net templates in folder 

(DW) 

Smartboard file – 

Sorting shapes 

Class discussion on how/where different shapes 

are used e.g. circles/sphere roll; triangles for 

strength. 

Investigate shapes found in the environment – look outdoors at 

buildings, constructions, playground equipment, etc. and discuss why 

shapes are used in a particular way. 

Look at a range of photographs of constructions throughout the 

world, Discuss the shapes in these buildings, why they have been 

used (aesthetic, practical, etc.) 

 

Smartboard file of 

photographs 

- Page 29 -



S2/S3 Shape Course (Trigonometry) Pentagon and above only; S2 and after only 


Pythagoras given measurements or coordinates 

Trigonometry to find angle or side 

Face, vertex, edge 

Draw nets 

Basic Pythagoras: 

Discover Pythagoras rule (as a rule in words) 

Find the hypotenuse only in right-angled triangles 

Draw nets of cuboids, cubes and triangular prisms when shown a basic 3d sketch 

Draw nets of cuboids, cubes, triangular prisms, pyramids and cylinders when shown 

a basic 3d sketch. 


Sine and cosine rules for side and angle 

BEARINGS with trig 

Pythagoras – converse and 3d; and in circles 

Apply properties of triangles, quadrilaterals, circles, polygons 

Pentagon classes will NOT use a 

formula for Pythagoras 

Check General past 

paper questions 

Use Pythagoras to find hypotenuse or shorter side in a right-angled triangle 

Use sin, cos and tan to find an angle in a right-angled triangle when given two sides 

Use sin, cos and tan to find a length in a right-angled triangle when given a side and 

an angle 

Use Pythagoras and sin/cos/tan in context 

Briefly revise sin, cos and tan to find lengths and angles in right-angled triangles, 

including the case where the unknown is in the denominator 

Use the sine rule formula and cosine rule formula to find lengths in basic examples 

Use cosine rule for angles formula in basic examples 

Beyond decagon: 

Do not use the formula for Pythagoras: 

just teach class to square, add/take 

away, square root 

*** DEPARTMENTAL POLICY agreed 23/4/12 *** 

Excluding the case where the unknown 

is in the denominator 

Context should include revision of 

bearings 


General mixed triangle 

item bank questions 

We are just looking for pupils to be able to make calculations with 

straightforward examples. There should be a heavy link to NUAP 

formulae here. Problem solving and choosing the formula would 

not be required 

More complex Pythagoras problems: 

Apply the converse of Pythagoras 

Use Pythagoras in a 3d situation 

Use Pythagoras in circle questions 

Be able to choose between sine and cosine rule formulae to find both angles and 

lengths, including in context 

Context must include bearings; and 

more complex polygons 

Use questions requiring more than one rule 

Exam standard questions requiring the use of properties of 2d shapes 

- Page 30 - 


Credit Item Bank 

Questions



Areas for Development: 

MEASUREMENT 

3 rd /4 th level CfE Measurement outcomes: 

I can solve practical problems by applying my Having investigated the practical impact of 

knowledge of measure, choosing the 

inaccuracy and error, I can use my knowledge of 

appropriate units and degree of accuracy for tolerance when choosing the required degree of 

the task. MNU 3-11a 

accuracy to make real life calculations. MNU 4-01a 

Cross Curricular Links (whole school numeracy record): CDT 


Discuss and investigate concepts of length, weight and volume 


learning 

I can apply my knowledge and understanding of 

measure to everyday problems and tasks and 

appreciate the practical importance of accuracy 

when making calculations. MNU 4-11a 

RESOURCES 

Teaching Measures 

Equivalences: 100cm=1 metre, 10mm=1cm, 1000g = 1kg, 

1000ml = 1litre, 1ml = 1cm³ 

Changing between units, whole numbers only. 

Reading ruler scales to nearest whole number; draw lines of a given 

length 

Estimate then measure: 

* length of classroom objects in millimetres, and/or centimetres 

* lengths around the school in metres. 

Class discussion on sensible estimates for: 

weights of everyday objects 

heights of everyday objects 

volumes of everyday objects 

Equivalences for length: 100cm=1 metre, 10mm=1 centimetre, 

1000m=1 kilometre, 1000mm=1 metre 

Other equivalences: 1000g=1 kilogram, 1000ml=1 litre, 

1ml = 1cm³, 1 litre = 1000cm³ 

Change between units, 

Change mixed units (e.g. m and cm, l and ml) to (e.g.) cm/ml only 

(i.e. no decimals) e.g. 1m 3cm = 103cm 

Triangle continued on next page 

Whole numbers only, no decimals. 

Class should be introduced to millilitres through the 

concept of 1cm³ holding 1ml of water; and should be 

introduced to grams through the concept that 1ml of 

water weighs 1 gram. 

Pupils should be encouraged to choose an 

appropriate measuring instrument, to choose the 

most appropriate units, and to decide on an 

appropriate degree of accuracy. 

Class should be reminded that millilitres were 

originally introduced through the concept of 1cm³ 

holding 1ml of water; and that 1ml of water weighs 1 

gram. 

Whole numbers and basic halves (e.g. 2½m, 4½kg) 

and “point fives” e.g. 2.5cm, 4.5m [for some classes 

this may be the first time they have worked with 1d.p. 

in maths] 

Measurement equipment 

in Base. Trundle wheels 

from PE. 

DW Measure-02 

Teaching Measures (and 


worksheets 

- Page 31 -



Read ruler scales to 1 decimal place 

Identify appropriate units and devices for measuring length, weight, 

volume, area, temperature 

Class discussion on making sensible estimates (including choosing 

sensible units) for: 

Long distances in miles/kilometres (using 1km≈½ mile) 

Heights of people (3 feet ≈ 1 metre), buildings, hills, mountains 

etc 

Capacity of everyday objects 

Weights of everyday objects, including very large objects 

Temperature in different places under certain weather conditions 


Units to measure length, weight, volume, temperature 

Use measuring instruments, read scales 

Interpret results of measurement: length, time, weight, volume, 

temperature 

Know all equivalences from triangle, plus 1000kg=1 tonne, 

1000cm³=1 litre 

Changing between all units, emphasising decimals. 

Changing between mixed units (e.g. m&cm to cm or to m (with a 

point)) 

e.g. 2.04kg = 2kg___g 

e.g. write 1m 3cm as a decimal, write 10l 5ml as a decimal 

Class discussion about estimating measurements, including 

choosing units 

Non-routine questions, discussing methods, e.g. questions where 

units are mixed (e.g. one length in cm, the other in mm) 

Pupils should be aware that people in measuring jobs 

only use millimetres 

(measurement of temperature will also be covered 

under NUNP (integers)) 

Class discussions are likely to also touch upon 

commonly used imperial measurements (e.g. feet 

and inches for height; stone for weight). An in depth 

treatment would not be required, but pupils should 

know their existence. 

 

 

Interrelationships between units 

use vocabulary associated with measurement to 

make comparisons for length, weight, volume 

and temperature 

*** NUNP: remember a pentagon class SHOULD 

know that 2.4 = 2.40 (but not 2.04); but will NOT 

necessarily know how to multiply or divide decimals 

by 10, 100 etc. as this is late in pentagon NUNP. 

Therefore a pentagon class should not use rote rules 

(e.g. “just divide by 100”) when decimals are 

involved; but instead should use methods like “there 

are 1000g in a kg. Thousandths need three decimal 

places, so 2 kg 5 g = 2.005kg) 

See triangle section for what needs to be covered 

Possible resources include banks of level D/E 

(roughly) 5-14 measurement questions 

worksheets) 



worksheets) 

Who Wants to Be a 

Millionaire PowerPoints 


CONTENT 

None 

DW Measure-02 and 

Measure-03 



worksheets) 

AW P23a 

- Page 32 -



Convert between all units previously encountered 

All the below content is designed to be covered in 1½ lessons ± 

½ lesson (see what we did there?) 

Discuss the idea that in real life we cannot always obtain the “exact” 

measurement and that we have to choose a degree of accuracy 

Discussion on choosing the correct units, and choosing the correct 

degree of accuracy. 

Activity: investigate tolerance. 

Class measure various items (e.g. width of a protractor in mm, width 

of a desk in cm, length of jotter in mm). Discuss range of values 

measured by class and how this can be expressed. 

Take the minimum and maximum values and calculate the 

circumference of protractor; area of desk etc; and show how 

tolerance errors are compounded by multiplication. 

Understand the meaning of ± notation in the context of 

measurement; 

Identifying maximum and minimum values. Identify which values are 

possible and which are not. 

Be aware of the range of possible “real” values of a given rounded 

measurement 

e.g. road distances. Is it exactly 40 miles from 

Edinburgh to Glasgow? Do you get exactly 500g of 

cornflakes in a box? Other examples e.g. weight of 

food, Smarties in box. 

e.g. when measuring the length of the corridor, 

should we use mm, cm, m, km? Should we measure 

to nearest mm? nearest cm? nearest 10cm? 

nearest m? Introduce idea of tolerance. 

Distinction between measuring wrongly and tolerance 

of a “correct” measurement 

e.g. the temperature is allowed to be 40°C ± 2 

e.g. the height of a box is 1.5m ± 0.1m 

Pupils must understand that the tolerance shows a 

range of numbers (i.e. the temperature is between 

38 and 42, not either 38 or 42) 

e.g. in the example above, could the temperature be 

39°, could it be 45°? Write five values that the height 

of the box in the second example could take 

e.g. the length of a pencil is 12.7cm (1d.p.) Identify 

the maximum and minimum possible lengths of the 

pencil (12.75cm and 12.65cm).. 

e.g. The Great Wall of China is 6700km long to the 

nearest hundred km. What is the maximum possible 

length? 

See Octagon Tolerance 

Whiteboard file (MD) 

Apply knowledge of tolerance to solve problems 



- Page 33 -



PROBABILITY AND RISK 


3 rd /4 th level CfE Probability outcomes: 

I can find the probability of a simple event happening and explain why the 

consequences of the event, as well as its probability, should be considered 

when making choices.MNU 3-22a 



Work with the vocabulary of probability (e.g. certain, likely, unlikely, impossible, 

possible, good chance, fifty-fifty) to describe probability of a given outcome 

By applying my understanding of probability, I can determine how many 

times I expect an event to occur, and use this information to make 

predictions, risk assessment, informed choices and decisions. MNU 4-22a 

Notes on approaches and 

activities for learning 

Class discussions 

Make posters 

RESOURCES 

Poster template (M5) 

Identify events which are “likely but not certain” and “unlikely but not impossible” 

and how these differ from events that are impossible or certain. 

Use 50-50 probabilities to estimate roughly how often an event will occur. 

Understand that this is a best guess and not an exact answer. 

Know the word probability, and be able to identify events which might have a 

probability of 0, 1 or ½ 

Draw arrows on a number line from 0 to 1 to identify probabilities of different 

events 

Class discussion on which events have 50-50 probability and which do not e.g. 

chance of it snowing tomorrow, raining tomorrow, tossing a coin, rolling a six on 

a die. Use terms like “more likely than 50-50”, “a lot more likely than 50-50”, 

“less likely than 50-50” etc, leading into numerical equivalents (e.g. 0.3, 0.9, one 

in six etc) 

Estimate how often an event with equal probabilities will occur (e.g. rolling a dice 

– how many 6s in 30 throws? Spinning a fair spinner – how many of a particular 

number in 100 goes?). Understand that this is a best guess and not an exact 

answer. 


 

Calculate probability 

an event happening 

Interpret probability in context of risk 

Flipping coins – collating data in groups; 

compare group totals and class total. 

What would you expect to happen if a coin 

was flipped 1000 or 10,000 times? 

Class likely to think in “black and white” and 

to want to always use 0, 1 or ½. 

Get class to realise that 50-50 means “we 

wouldn’t be surprised either way whether or 

not it happened”; so events that we think 

are likely to happen do not have a 50-50 

chance. 

Rolling a dice – collating data in groups; 

compare group totals and class total. 

What would you expect to happen if a dice 

was rolled 1000 or 10,000 times? 

recognise patterns and trends and use these to state the probability of 

make predictions and use these predictions to make decisions 

Probability strategy 

Games (Rat Race, 

Horse Race) (M5) 


Probability strategy 

Games (Rat Race, 

Horse Race) (M5) 

Collaborative Activities 

in folder (see M4!) 

NATIONAL 5 

MATHEMATICS CONTENT 

None 

- Page 34 -



Know the word probability, and be able to suggest events which might have a 

probability of 0, 1, ½, close to 0 but not 0, close to 1 but not 1, a bit less than 

0.5, a bit more than 0.5 etc 

Draw arrows on a number line from 0 to 1 to identify probabilities of different 

events 

Be able to write probability as a fraction – basic examples 

Use probabilities to estimate how often an event may occur 

PROBABILITY, PREDICTIONS AND RISK 

Discuss tables of risks of events taking place (e.g. risk of dying on the road 

is 1 in 85, getting four balls in lottery is 1 in 206 – see Smartboard file) – 

which is more or less likely? Are the statistics what pupils would expect? 

Real-life scenarios involving probability. Pupils have to make a decision and 

justify it in sentences and describe a possible risk of their decision. 

Be able to write probability as a fraction from a real life situation, which may be 

given in words, in a table or in a frequency table 

Use probabilities to estimate how often an event may occur, giving reasons in 

a sentence: use Whiteboard Worksheet R1 or R11 (http://www.activemaths.co.uk/whiteboard/3prob/prob3a.html) 

to identify the mystery spinner. 

Class have to write which spinner they think it is and to write at least two 

reasons why in a sentence 

PROBABILITY, PREDICTIONS AND RISK 

Discuss tables of risks of events taking place (e.g. risk of dying on the road 

is 1 in 85, getting four balls in lottery is 1 in 206 – see Smartboard file) – 

which is more or less likely? Are the statistics what pupils would expect? 

Real-life scenarios involving probability. Pupils have to make a decision and 

justify it in sentences and describe a possible risk of their decision. 



Number line could be drawn on mini 

whiteboards and events labelled A, B, C etc 

could be displayed on Smartboard 

Class should have seen the P(…) notation 

as part of teaching 

e.g. given a spinner which may have equal 

or unequal probabilities, identify the 

probability of each event coming up. If 

spinner is spun 100, 1000, 10000 times 

how many times would you expect to get a 

2? Or a 5? Or a 10? 


Millionaire/voting handset quiz to get 

opinions and discuss as class 

Pentagon risk worksheet (G6) 

Use class discussion. Can you always 

identify the mystery spinner? Discuss the 

idea that probability is what is likely to 

happen, not what WILL happen, and that 

sometimes you might get an “unusual” 

result. Discuss the idea of fewer spins 

making it harder to tell; more spins making 

it easier 


Millionaire/voting handset quiz to get 

opinions and discuss as class 

Octagon risk worksheet (G6) 


Putting events on 

number lines – see M5 


Smartboard file, 

textbook exercises (be 

selective) 

Excellent tool to open 

up a discussion on 

probability and 

frequency: Whiteboard 

Worksheets 

R1/R11/R12 – plus 

others 

Which Spinner group 

work cards task (M7) 

(for an able pentagon 

class) 

Past Int 1 exam 

questions, Smartboard 

files 

Whiteboard 

Worksheets 

R1/R11/R12 

Which Spinner group 

work cards task (M7) 

- Page 35 -



MATHEMATICS – ITS IMPACT ON THE WORLD, PAST, PRESENT AND FUTURE 

Areas for Development: review S3 Planet Maths after first run through in Sept 2012 

3rd/4th level CfE Mathematics – it’s impact on the world outcomes: 

I have worked with others to research a famous mathematician and I have discussed the importance of mathematics in the real world, investigated 

the work they are known for, or investigated a mathematical topic, the mathematical skills required for different career paths and delivered, with 

and have prepared and delivered a short presentation. MTH 3-12a others, a presentation on how mathematics can be applied in the workplace. MTH 

4-12a 


S1 Planet Maths 3rd level 

ALL CLASSES WILL: 

In groups of 2-3, pupils will be asked to: 

collect and research information using books and the 

internet on a given topic. 

Organise their information into their own words and 

present their findings in the form of a PowerPoint 

presentation. 

Give a 2-3 minute presentation in front of the whole class 

where all members will be asked to contribute. 

Pupils will complete an evaluation sheet to evaluate 

themselves, the work of their group, and the presentations of 

other groups in their class 

S3 Planet Maths 4th level 

ALL CLASSES WILL: 

In groups of 2-3, pupils will be asked to: 

collect and research information using books and the 

internet on a given topic. 

Organise their information into their own words and 

present their findings in the form of a PowerPoint 

presentation. 

Give a 2-3 minute presentation in front of the whole class 

where all members will be asked to contribute. 

Pupils will complete an evaluation sheet to evaluate 

themselves, the work of their group, and the presentations of 

other groups in their class 

Topics will be chosen from: 

Numbers in sport. 

Numbers in food. 


Zero 

Famous Mathematicians and the work they are known for 

Topics could include: 

Famous Mathematicians and the work they are known for. 

Pi 

Zero 

Infinity 

The theme is “How is maths used in real life jobs?” 

See Triangle 


Graphs and Charts 

Shape Graphs and Charts 

Area and Perimeter 

Money 

Topics could include: 

Pythagoras 

Trigonometry 

Graphs and Charts 

Statistics 

- Page 36 - 

Planet Maths 

documentation 

Smart Notebook file 

Evaluation sheet 

Planet Maths 

documentation 

Smart Notebook file 

Evaluation sheet



PROBLEM SOLVING (LAST WEEK OF EACH YEAR) 

Areas for Development: all resources and content needs developing – next year’s development plan 

3 rd /4 th level outcomes: 

I can use a variety of methods to solve number problems in familiar contexts, 

clearly communicating my processes and solutions.MNU 3-03a 


Having recognised similarities between new problems and problems I 

have solved before, I can carry out the necessary calculations to solve 

problems set in unfamiliar contexts. MNU 4-03a 

By the end of the topic, pupils should 

be able to: 

Notes on approaches and activities for learning 

RESOURCES 

NATIONAL 4 AND NATIONAL 5 MATHEMATICS CONTENT 

Interpret a situation where maths can be used and identify a valid 

strategy 

Same week as reading day 

 

 

Choosing the operation 

Reasoning, making and explaining decisions 

 

 

Explain a solution and/or relate to context 

Explaining decisions as a result of calculation 

Not included in course planners for now until 

work is developed – did not do this in 2012-3. 

Was supposed to be for all classes in last 

week 

Some of the old 

problem solving 5-14 

materials like using 

logic? 

 

Using logic 

To be worthwhile all activities would have to be directly relevant to preparing 

pupils to be able tot understand, interpret or communicate their responses to 

Nat4/Nat5 exam/Higher exam questions 

- Page 37 -

3 rd /4 th level outcomes: 

I can show how quantities that are related can be increased or decreased 

proportionally and apply this to solve problems in everyday contexts. 

MNU 3-08a 



PROPORTION 


Using proportion, I can calculate the change in one quantity caused by a 

change in a related quantity and solve real life problems. MNU 4-08a 


Given a unit amount and quantity, calculate total amount in 

context (e.g. prices, weights, lengths, volumes) 

Given total amount and quantity, calculate unit amount 

Given total amount and quantity, calculate unit amount and then 

calculate total amount for a different quantity in context (e.g. 

prices, weights, lengths, volumes, speeds, currencies) 


Calculate ratio and direct proportion 

Calculate rates – miles per hour, text per month 

Given total amount and quantity, calculate total amount for a 

different quantity in context (e.g. prices, weights, lengths, 

volumes, speeds, currencies) 

Calculate rates 

Introduce concept of ratio in real life examples 

Introduce idea of equivalences of ratios 

Use equivalent ratios to solve direct proportion problems 

Calculate and compare rates 


learning 

Must link in to NUNP. Emphasis should be on 

distinguishing between multiplying and dividing 

At triangle level, calculations will be done in two steps 

e.g. 7 pencils cost 84p. 

a) Find the cost of one pencil 

b) What will 11 pencils cost? 


Similar triangles 

Area/volume of similar shapes 

At pentagon level, this will be done in one step 

e.g. 7 pencils cost 84p, what will 11 pencils cost? 

e.g. miles per hour, texts per month, pence per gram, 

kilometres per litre 

e.g. ratio of males:females; 2 parts water, 1 part milk; a 

cake being made out of flour, sugar and butter in the ratio 

2:3:5 

Brief. Link to NUNP fraction work. 

e.g. a cake is made out of flour, sugar and butter in the 

ratio 2:3:5. How much sugar and butter will be needed for 

100g of flour? A map is drawn to a scale 1:300. How 

long in real life is 20cm? 

e.g. calculate area painted per minute for two different 

painters; or fat per 100g for two foods; or price per text for 

two contracts and write a sentence comparing. 

- Page 38 - 

RESOURCES 

Access 3 “money working 

out bills” 

spreadsheet/worksheet 

(M5) 

MIA 2+ 

Intermediate 1 item bank

Briefly revise concept of enlargement and reduction and scale 

factor 

Introduce concept of similarity, and the idea that a scale factor 

can be a decimal or fraction 



Apply scale factors to shapes through calculation 

Calculate scale factor when shown diagrams of two similar 

shapes 

e.g. the three sides of a triangle are 3cm, 4cm, 5cm. 

Enlarge this using a scale factor of ¾ or 1.6 using a 

calculator (just writing down lengths, not drawing) 

Use formula for scale factor (i.e. scale factor = new 

length/old length). Pupils should know that an 

enlargement has a scale factor > 1 and a reduction has a 

scale factor between 0 and 1 

Discover by investigation that when length is increased by a 

scale factor s, area increases by factor s² and volume increases 

by factor s³ 

Credit Item Bank 

Questions 

Use area/volume properties of similar shapes to solve problems 

in exam style questions 

- Page 39 -

New S1-S3 CfE Course Plan - Newbattle Community High School

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