LIVING MATHS
A SEQUENTIAL COURSE FOR NON-UNIVERSITY BOUND STUDENTS
The following information pertains to the development and implementation of the Living Maths course. It is recommended teachers read through this information when making decisions as to how to implement the course.
WHY IMPLEMENT THE COURSE?
Previously courses for non-university bound students have consisted of a watered down version of academic courses or a theme based approach that treated objectives in an ad-hoc manner. It was found that these students saw little purpose in much of the content and it was often too difficult. Courses based on a thematic approach were often under-resourced and not sequential.
To solve these problems it was decided to develop a course for students not bound for university that was well resourced, well structured, well sequenced and provided the right type of learning experiences to both prepare students for life and to develop important essential concepts and skills. Hence, Living Maths was created.
WHICH STUDENTS IS IT FOR?
The material in the course is designed to provide about two years of learning experiences for students who are not intending to study university entrance mathematics courses in upper school. This may vary from about 70% of the year cohort in some schools to about 30% in others depending on the students' abilities and aspirations.
WHAT IS THE CONTENT BASED ON?
To initiate the planning of the content in the course we looked to these documents to form a basic structure. This has been embellished by the thoughts of the people involved in writing the materials and modified in places based on students' responses during the trial period.
HOW DOES THE COURSE RELATE TO THE OUTCOME STATEMENTS REQUIRED IN WESTERN AUSTRALIA?
Our content is what we believe these students are capable of achieving across each of the six strands; Working Mathematically, Space, Measurement, Chance and Data, Number and Algebra. The learning experiences are structured to both develop processes sequentially and to allow opportunities for mathematical thinking. Our planning takes into account the sequencing of concepts within each of the strands and integrates the strands throughout the course.
The course attempts to move this body of students from a level of development which averages about level 3 standard up to about level 5 standard. However, because we have designed this course to be used with classes of mixed ability we have provided a range of difficulty at each point of the course. This allows teachers to pick appropriate work for different classes and students.
THE STRUCTURE OF THE LIVING MATHS COURSE
The table below shows how the materials are intended to be sequenced although while trialling the material we have realised that for some classes it might also be appropriate to only cover books 1A to 3B over the two years. There is adequate material for this if the classes do not contain students from about the 40th to 60th percentile.
Part of the plan when writing these materials was to make them flexible enough to suit different teachers and different students so we would like to think that whatever structure people adopt it will work.
| AGE 14 | TERM 1 | Book 1A |
| TERM 2 | Book 1B | |
| TERM 3 | Book 2A | |
| TERM 4 | Book 2B | |
| AGE 15 | TERM 1 | Book 3A |
| TERM 2 | Book 3B | |
| TERM 3 | Book 4A | |
| TERM 4 | Book 4B |
THE DEVELOPMENT OF LEVEL OF DIFFICULTY:
Initial discussion on the type of course these students required to progress in their level of achievement suggested that they needed repetition of ideas over a long period of time. In keeping with this idea the Living Maths course enables students to study each content area four times over the two years. Each time there is revision of previous ideas followed by a progression into new concepts. To stop this being repetitive the texts alternate between two different sets of topics and use new contexts wherever possible when returning to content previously studied.
The diagram below shows how this development is intended to take place.
THE CONTENT TOPICS OF LIVING MATHS
A STRAND | B STRAND |
| 1. TIME | 14. DIRECTION |
| 2. TOPOLOGY | 15. PERCENTAGE |
| 3. NUMBER | 16. COORDINATES |
| 4. MEASUREMENT | 17. POWERS |
| 5. MONEY | 18. AREA |
| 6. NEGATIVE NUMBERS | 19. 3D SHAPES |
| 7. STATISTICS | 20. RATIO AND PROPORTION |
| 8. FRACTIONS | 21. VOLUME |
| 9. 2D SHAPES | 22. CHANCE |
| 10. AVERAGES | 23. RATES |
| 11. LENGTH | 24. TIME SERIES DATA |
| 12. MASS | 25. SCALE DRAWING |
| 13. ANGLE | 26. FORMULAE |
These twenty six topics evolved from the initial structuring of what we thought these students should learn. They have been modified, their names have been changed, and they have been resequenced as a result of further developments and trialling. There is an attempt to balance types of units between strands, and time has been spent trying to ensure prerequisite knowledge was available when needed. As they stand, they provide a framework on which to put together all of the different learning experiences included in the course.
THE TYPES OF MATERIAL IN THE LIVING MATHS TEXTS
The table below shows the approximate number of learning activities provided in each book. It is obvious from this table that there is a wide range of types of learning experiences in all of the books. There are two ideas behind this. We want to ensure that everything a teacher might need is included in the book and we want to provide a surplus of material so that each teacher can develop a sequence of lessons to suit their students and their teaching style.
We also hoped to cover such diverse requirements as mathematical literacy, use of technology, and library skills. All of these items are programmed into the course at the appropriate time and place and are readily available to the teacher.
| 1A | 1B | 2A | 2B | 3A | 3B | 4A | 4B | |
| GRADED EXERCISES | 68 | 54 | 66 | 53 | 67 | 53 | 61 | 56 |
| PUZZLES | 7 | 10 | 12 | 12 | 7 | 12 | 10 | 10 |
| NEWSPAPER SEARCHES | 11 | 8 | 8 | 7 | 4 | 7 | 8 | 8 |
| PROJECTS | 3 | 3 | 6 | 4 | 4 | 5 | 4 | 4 |
| COMPUTING ACTIVITIES | 1 | 2 | 1 | 1 | 1 | 4 | 2 | 2 |
| GAMES | 3 | 2 | 1 | 2 | 1 | 1 | 2 | 2 |
| CROSSWORD PUZZLES | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| EXTENSION & ENRICHMENT | 3 | 3 | 5 | 6 | 5 | 7 | 3 | 7 |
| LIBRARY RESEARCH | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 2 |
| WORD SLEUTHS | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 |
| NUMBER FACT TABLES | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 |
SPECIFIC OBJECTIVES OF THE TOPICS IN LIVING MATHS
1. TIME
1.1 Tell the time and understand times expressed in terms of 12 hour and 24 hour clocks.
1.2 Choose and use appropriate techniques and tools to measure time.
1.3 Perform operations on time units.
1.4 Convert between time units.
1.5 Calculate the interval between two given times, and the finishing time, given the starting time and the duration.
1.6 Use a bus or train timetable.
2. TOPOLOGY
2.1 Describe, follow and record vertices, paths, regions and routes using networks.
3. NUMBER
3.1 Understand place value in numbers up to billions and five decimal places.
3.2 Possess confident recall of addition and multiplication facts up to 15 + 15 and
15 x 15 and the related subtraction and division facts.
3.3 Understand and make use of interrelationships of the kind:
13 x 8 = (10 x 8)+ (3 x 8).
3.4 Select the appropriate operation (addition, subtraction, etc.) for use in the solution of a variety of practical problems.
3.5 Appreciate the need for careful ordering of operations when using a calculator.
3.6 Understand and use the decimal system in practical situations and problems.
3.7 Describe the development of various counting and numeration systems.
3.8 Investigate and use number patterns and relationships.
3.9 Investigate and extend number sequences.
3.10 Round numbers up to four decimal places and millions.
4. MEASUREMENT
4.1 Have a 'feel' for the size of various units in relation to common objects within the students' experience.
4.2 Read scales, meters and dials of various types.
4.3 Understand the use of metric prefixes to unify measurements in a coherent way.
5. MONEY
5.1 Add and subtract decimals involving up to two decimal places in the context of measurement (including money).
5.2 Recognize coins and notes and know that 100c = $1. Handle money with confidence.
5.3 Carry out simple transactions, performing necessary calculations either mentally or on paper.
5.4 Add and subtract small sums of money without a calculator.
5.5 Multiply or divide a sum of money by a single digit without a calculator.
5.6 Perform more complex calculations involving money using any appropriate method.
5.7 Interpret the language of and deal with matters of personal finance.
6. NEGATIVE NUMBERS
6.1 Count, order, read and write positive and negative whole numbers and use them in context, e.g. what is the rise in temperature from -3°C to 10°C?
7. STATISTICS
7.1 Organize systematically the collection and tabulation of simple data.
7.2 Read and interpret simple graphs and charts and extract specific information from them; draw graphs by hand and using spreadsheet packages.
7.3 Extract information presented in tabular form.
8. FRACTIONS
8.1 Use the language and notation of simple fractions in appropriate context, e.g. half of a kilometre, two-thirds of the class.
8.2 Add and subtract fractions with denominators 2, 4 or 8 in the context of measurement.
8.3 Know the decimal equivalent of 1/4, 1/2, 3/4, 1/10, 1/100, and also that 1/3 is about 0.33.
8.4 Convert fractions to decimals with the help of a calculator.
9. TWO DIMENSIONAL SHAPES
9.1 Recognize and name simple plane figures.
9.2 Understand and use terms such as side, diagonal, perimeter, area, angle.
9.3 Understand and use terms relating to the circle: centre, radius, diameter, circumference, chord.
9.4 Draw a simple plane figure to given specifications.
9.5 Use translations, rotations and reflections and the relationships between them.
10. AVERAGES
10.1 Understand the differences among the various measures of average and the purpose for which each is used.
10.2 Summarise and interpret data using visual representations and measures of location and spread.
11. LENGTH
11.1 Measure length using appropriate metric units.
11.2 Understand the relationships among millimetres, centimetres, metres and kilometres.
11.3 Have a 'feel' for the size of these units in relation to common objects within the students' experience.
11.4 Find the perimeter of planar figures.
11.5 Understand and use the fact that the circumference of a circle = ¶ x diameter; know that is a little more than 3.
11.6 Add and subtract decimals involving up to two decimal places in the context of measurement .
11.7 Choose and use appropriate techniques and tools to measure length.
12. MASS
12.1 Measure weight using appropriate metric units.
12.2 Understand the relationships among grams, kilograms and tonnes.
12.3 Have a 'feel' for the size of these units in relation to common objects within the students' experience.
12.4 Add and subtract decimals involving up to two decimal places in the context of measurement.
12.5 Choose and use appropriate techniques and tools to measure mass.
13. ANGLE
13.1 Measure angles in degrees.
13.2 Identify angle types.
13.3 Understand bearings and the ways in which they are measured.
13.4 Choose and use appropriate techniques and tools to measure angles.
14. DIRECTION
14.1 Identify vertical, horizontal and oblique objects.
14.2 Understand the relationships parallelism and perpendicularity.
14.3 Understand the directions clockwise and anticlockwise.
15. PERCENTAGE
15.1 Calculate a percentage of a sum of money.
15.2 Increase or decrease a sum of money by a given percentage.
15.3 Appreciate the use made of percentages in everyday life.
16. COORDINATES
16.1 Understand the Cartesian coordinate system.
16.2 The use of coordinates to locate areas (as on a street map) and points (as on an ordnance survey map).
16.3 Follow and give directions on a map.
16.4 Determine distances on a map using a scale.
16.5 Interpret contour maps.
16.6 Draw and interpret scattergraphs.
17. POWERS
17.1 Understand and use powers of numbers.
17.2 Use scientific notation to represent small and large numbers.
18. AREA
18.1 Find the area of planar figures.
18.2 Choose and use appropriate techniques and tools to measure area.
19. THREE DIMENSIONAL SHAPES
19.1 Recognize and name common solid shapes: cube, rectangular block, sphere, cylinder, cone, pyramid.
19.2 Be able to visualize and understand simple mechanical movement, including the working of simple linkages.
19.3 Use translations, rotations and reflections and the relationships between them.
20. RATIO AND PROPORTION
20.1 Understand the use of ratio as applied to such things as mixtures, e.g. 4 parts sand to 1 part cement, and recipes, e.g. work out the quantities required for six people from a recipe which serves four.
20.2 Understand informally simple ideas of direct and inverse proportion.
21. VOLUME
21.1 Find the volume of a rectangular solid.
21.2 Find the volume of solids using formulae.
21.3 Measure capacity, using appropriate metric units.
21.4 Understand the relationships among millilitres, litres and kilolitres. Know that 1 litre is equivalent to 1000 cubic centimetres. Convert between units.
21.5 Have a 'feel' for the size of these units in relation to common objects within the students' experience.
21.6 Understand the relationship between volume and capacity.
21.7 Choose and use appropriate techniques and tools to measure capacity and volume.
22. CHANCE
22.1 Appreciate basic ideas of randomness and variability.
22.2 Know the meaning of probability and odds in simple cases.
23. RATES
23.1 Understand and use simple rates, e.g. dollars per hour, kilometres per 100 litres.
23.2 Solve simple problems involving time, distance and speed.
23.3 Understand and use the derived measures of density, speed and other rates.
24. TIME SERIES DATA
24.1 Draw inferences and construct and evaluate arguments based on sample data.
24.2 Draw freehand sketches of and interpret graphs which model real phenomena qualitatively.
24.3 Use graphs to model real situations and make predictions including those based on interpolation, extrapolation, slope and critical points.
25. SCALE DRAWING
25.1 Appreciate the concept of scale in geometrical drawings and maps.
25.2 Use similarity and Pythagoras' theorem for indirect measurement in two and three dimensions.
26. FORMULAE
26.1 Substitute numbers in a simple formula expressed in words, and evaluate the answer.
26.2 Understand the use of variables in formulae.
26.3 Use formulae to find values.
CONTENTS OF THE TOPICS IN LIVING MATHS
| TOPIC | AREA | BOOK 1A | BOOK 2A | BOOK 3A | BOOK 4A | |
| 1 | Time | Units of time and conversions | Seconds, minutes, hours and days (whole number conversions only) | Seconds, minutes, hours and days (conversions with fractions and decimals) | Weeks, fortnights, months, years, decades and centuries (whole number conversions only) | Weeks, fortnights, months, years, decades and centuries (conversions with fractions and decimals) |
| Choose appropriate units of time | Choose from seconds, minutes, hours and days for a given situation | Comparing units of time given different units (seconds, minutes, hours and days) | Choose from weeks, fortnights, months, years, decades and centuries for a given situation | Comparing units of time given different units (weeks, fortnights, months, years, decades and centuries) | ||
| Tell time in 12 and 24 hour format | Conversions of 12 to 24 hour time | Setting alarm clocks | Setting ovens | Setting videos and TV programming | ||
| Reading clocks, stopwatches and calendars | Reading clocks Drawing clock faces to given times | Reading calendars Stopwatches | Reading calendars World Time Zones | Australian Time Zones | ||
| Time calculations | Addition and subtraction (no carrying) Elapsed times | Multiplication and division (no carrying) | Addition and subtraction (with carrying) Elapsed times | Multiplication and division (with carrying) Elapsed times | ||
| Bus and Train Timetables | Reading timetables | Reading timetables | Reading timetables | Reading timetables | ||
| 2 | Topology | Networks | Vertices and paths | Vertices and paths Regions Euler's Rule | Routes Shortest routes | Vertices, regions and paths Shortest route Shortest connection |
| 3 | Number | Number Facts | To 10 | To 12 | To 12 | To 15 |
| Place Value (inc. Numbers Words) | Up to thousands Three decimal places | Up to millions Three Decimal places | Up to millions Four Decimal places | Up to billions Five decimal places | ||
| Choosing operations | One stage | One or two stages | One to three stages | One to four stages | ||
| Number Sequences | Linear (Positives only) | Linear (+ & -) Quadratic (+ & -) | Linear Quadratic Exponential (r > 1) | Linear Quadratic Exponential | ||
| Rule of Order | BMDAS One level of brackets Up to 3 operations | BIMDAS Two levels of brackets Indices only Power 2 Up to 4 operations | BIMDAS Brackets to include vinculums - up to two levels Other powers to be included Up to 5 operations | BIMDAS Up to three levels of brackets including vinculums Indices to include roots Up to 6 operations | ||
| Number Patterns | Number Patterns | Number Patterns | Number Patterns | Number Patterns | ||
| Distributive Property | Distributive property (addition only) | Distributive property (addition and subtraction) | ||||
| Counting Systems | Hindu Arabic | Japanese | Roman | Binary | ||
| Rounding | Nearest 1, 10, 100, 1000 One decimal place | Nearest 1, 10, 100, 1000 Up to 2 decimal places | Nearest 1, 10, 100, 1000, ... Up to 5 decimal places Rounding money | |||
| 4 | Measurement | Measurement | Metric system Common units Reading scales, meters and dials | Drawing scales Reading scales, meters and dials | Comparison with Imperial system | Reading scales Metric units Conversions Imperial units |
| 5 | Money | Coins and notes | Money conversion | Money conversion | Money conversion | Money conversion |
| Add and subtract money | Money calculations Rounding | Money calculations Rounding | Money calculations Rounding | Money calculations Rounding | ||
| Money transactions | Choosing operations - one stage | Choosing operations - one stage | Choosing operations - one and two stage | Choosing operations - one and two stage | ||
| 'Mental' money computations | Mental computations (two amounts) Estimation | Mental computations (two amounts) Estimation | Mental computations (two or three amounts) | Mental computations (two to four amounts) | ||
| Calculations and Personal Finance | Change Money rates Shopping Pay rates | Foreign currency and exchange rates Earning an income Banking | Foreign currency Earning an income, time cards and taxation Hire purchase Budgeting Cheque accounts | Hire purchase Buying a car Cheque accounts Costs of living Earning an income | ||
| 6 | Negative Numbers | Positive and negative numbers | Understanding positive and negative numbers Count, order and read numbers | Understanding positive and negative numbers Problems in context | Understanding positive and negative numbers Problems in context | Understanding positive and negative numbers Problems in context |
| 7 | Statistics | Data collection | Collection of data | Collection of data | Collection of data | Collection of data |
| Representing data - graphs | Reading tables | Histograms, line graphs | Circle/Pie graphs | Multiple column graphs Divided bar graphs | ||
| Representing data - tables | Construct and interpret tables - two columns | Tables involving class intervals | Tables - construction and interpretation involving multiple columns | Tables - construction and interpretation involving multiple columns and continuous data | ||
| 8 | Fractions | Understanding fractions | Understand the notation and meaning of simple fractions | Know decimal equivalents for fractions with denominators 2,3, 4, 5, 10 and 100 | Conversions of fractions to decimals with a calculator Equivalent fractions | |
| Fraction operations | Add simple fractions Complete questions of the type ¾ of $60 | Add simple fractions | Add and subtract fractions with simple numerators | Add and subtract fractions Further questions of the type ¾ of $60 | ||
| 9 | 2D Shapes | Polygons | Square, rectangle and triangle Label parts of shapes | Parallelogram, rhombus, kite and trapezium Label parts of shapes | Pentagon, hexagon and octagon Properties of polygons Angles in polygons Label parts of shapes | Compound shapes Label parts of shapes |
| Circles | Parts of a circle | Labelling circle parts | Sector, segment, quadrant | Labelling circle parts | ||
| Drawing plane figures | Draw squares, rectangles, triangles and circles to given dimensions | Draw parallelograms, rhombi, kites, trapeziums and circles to given dimensions | Compass drawings | Draw complex figures | ||
| Transformations | Translations of squares, rectangles and triangles | Reflections of shapes from books 1 and 2 | Rotations of shapes from books 1, 2 and 3 | Combinations of transformations | ||
| 10 | Averages | Mean, mode, median and range | Understand and calculate these measures | Understand and calculate these measures | Understand and calculate these measures | Understand and calculate these measures Combined means Missing values |
| Graphical representation | Dot frequency diagrams Frequency tables | Averages from column graphs Stem and leaf plots | Averages from graphs | |||
| 11 | Length | Length | Units of length Imperial length units Estimating lengths | Measuring lengths Estimation of length Use of units and conversions | Estimation of length Use of units | Conversions of lengths |
| Perimeter | Perimeter of plane figures | Circumference of circles | Perimeter of compound shapes | Perimeter of compound shapes | ||
| 12 | Mass | Understanding mass and mass units | Units of mass Conversions Choosing units Operations with mass | Conversions Operations with mass Imperial measures | Conversions Scales and meters | Units and conversions Operations with mass Mass and weight |
| 13 | Angle | Angles | Understanding angles Angle measurement Estimating angle sizes Drawing angles Angle types | Drawing and measuring angles Angles in triangles Drawing triangles Scale drawings | Drawing figures including angles Scale drawing with angles | Drawing figures including angles Reflex angles Scale drawing with angles |
| Bearings | True bearings Common directions - N, S, E, W, NE, SE, SW and NW | Angles and bearings Bearing from one location to another | Bearings to locate objects Diagrams showing bearings | Bearings to locate objects Relative bearings Diagrams showing bearings Angles and directional bearings | ||
| TOPIC | AREA | BOOK 1B | BOOK 2B | BOOK 3B | BOOK 4B | |
| 14 | Direction | Understanding directions | Horizontal, vertical and oblique in 2D Clockwise and anti-clockwise | Parallel and perpendicular in 2D Clockwise and anti-clockwise | Horizontal, vertical and oblique in 3D | Parallel and perpendicular in 3D |
| 15 | Percentage | Understanding percentage | Fundamentals of percentage Percentage calculations | Percentage calculations | Percentage calculations | Percentage calculations |
| Applications | Commission Discount Sales Tax | Commission Sales Tax Simple Interest Inflation and percentage increase Depreciation and percentage decrease | VAT Simple Interest Compound Interest Inflation and percentage increase Depreciation and percentage decrease | Simple Interest Compound Interest Reducible Interest Inflation and percentage increase Depreciation and percentage decrease | ||
| 16 | Coordinates | Locate and draw points | 1st quadrant | 1st and 2nd quadrant | All quadrants | All quadrants Latitude and longitude |
| Bivariate Data | Two points | More than two points | Scattergraphs | Scattergraphs Line of best fit | ||
| Maps | Grid references | Six figure grid references Scales Contour maps | Six figure grid references Scales Contour maps | Six figure grid references Scales Bus routes | ||
| 17 | Powers | Understanding and using powers | Squares and square roots Cubes and cube roots | Powers of integers | Scientific notation | Scientific notation |
| 18 | Area | Areas of planar figures | Concept of area Units of area Estimating areas Areas of squares, rectangles and triangles | Estimating area Areas of squares, rectangles, triangles, parallelograms and circles Area by dissection | Areas of squares, rectangles, triangles, parallelograms and circles Area by dissection Conversions of units of area | Areas of squares, rectangles, triangles, parallelograms and circles Area by dissection and subtraction Conversions of units of area Perimeter/Area relationships |
| 19 | 3D Shapes | Common solid shapes | Cubes and rectangular prisms - Nets - Euler's rule - Cross-sections - Drawing - Relationships of parts | Other prisms - Nets - Euler's rule - Cross-sections - Drawing - Relationships of parts | Pyramids - Nets - Euler's rule - Cross-sections - Drawing - Relationships of parts | Polyhedra - Nets - Euler's rule - Cross-sections - Drawing - Relationships of parts |
| Mechanical movement | Circular motion Pulleys and belts | Circular motion Pulleys and belts | Circular motion Gears and ratios | Circular motion Pulleys and belts Gears, cogs and ratios | ||
| Transformations | Translations | Dilations | Reflections | Rotations | ||
| 20 | Ratio and Proportion | Understanding and calculations | Unitary method Direct proportion only Ratio | Unitary method Direct and inverse proportion | Ratio method Direct proportion | Ratio method Direct and inverse proportion |
| 21 | Volume | Volumes of solids | Concept of volume Units of volume and capacity Conversions | Volume of rectangular prisms Conversions Volume and capacity relationships | Volume of prisms Conversions Volume and capacity relationships Volumes of cylinders and cones | Volume of spheres Units of volume and capacity Conversions Volume and capacity relationships Inverse calculations |
| 22 | Chance | Understanding chance | Chance Randomness Outcomes | Chance Randomness Outcomes | Chance Randomness Outcomes | Chance Randomness Outcomes |
| Probability and Odds | Simple probability | Tree diagrams and sample spaces Probability from a sample space | Odds Simulations | Probability from tree diagrams Relative frequency | ||
| 23 | Rates | Understanding and using rates | Concept of a rate Examples of rates Direct calculations | Further examples of rates Inverse and direct calculations | Car rates Further calculations Comparative rates Speed = Distance/Time | Derived quantities Density, frequency, pressure and acceleration |
| 24 | Time Series Data | Interpreting graphs | Distance time graphs | Graphs relating two variables | Graphs relating two variables Drawing graphs relating two variables | Graphs relating two variables Drawing graphs relating two variables |
| Line Graphs | Draw and interpret line graphs | Draw and interpret line graphs | Draw and interpret line graphs Trends Extrapolation and interpolation | Draw and interpret line graphs Trends Extrapolation and interpolation | ||
| 25 | Scale Drawing | Similar figures | Grid enlargements | Projection method | Scale factors Distortions | Enlargements and reductions by percentage |
| Scale drawings | Reading scale drawings | Reading scale drawings | Reading scale drawings | Reading scale drawings | ||
| Scales on Maps | Measure and convert using scales | Using scales to calculate distances | Using scales to calculate distances | Using scales to calculate distances | ||
| House Plans | Finding measurements from house plans | Finding measurements from house plans Calculating areas | Finding measurements from house plans Rooms and furniture sizes | Finding measurements from house plans Rooms and furniture sizes | ||
| Pythagoras | Finding hypotenuse | Finding short sides | Finding sides including decimal approximations | Finding sizes in three dimensions | ||
| 26 | Formulae | Use and understanding of formulae | Substitution into formulae (words) - one variable Meaning of common algebraic notation | Substitution into formulae (words) - several variables Meaning of common algebraic notation Substitution into algebraic formulae | Substitution into multiple variable algebraic formulae | Substitution into more complex formulae Inverse problems |
If you wish to find out more about the Living Maths series please contact Mark at OTRNet by clicking the link here: mark@otrnet.com.au.
