Maths Fundi Study Guide – Grade 6
Sample Pages
Print ISBN: 978-1-7764054-2-8
Edition 2: July 2022
176 A4 pages
18 chapters
Study Guide Table of contents Grade 6
Content Area 1: Numbers, Operations and Relationships
Chapter 1 Whole Numbers
| 1.1 | Number Systems | |
| 1.1.1 | Roman Numerals | |
| 1.1.2 | Hindu-Arabic Number System | |
| 1.2 | Number Concept | |
| 1.2.1 | Place value | |
| 1.2.2 | Maths vocabulary and listing numbers | |
| 1.2.3 | Number lines | |
| 1.2.4 | Rounding off | |
| 1.2.5 | Compare and order | |
| 1.3 | Multiples, Factors and Prime Numbers | |
| 1.3.1 | Multiples and LCM | |
| 1.3.2 | Factors and HCF | |
| 1.3.3 | Prime and composite numbers and 1 | |
| 1.3.4 | Prime factorisation | |
| 1.4 | Exponents | |
| 1.4.1 | What are exponents? | |
| 1.4.2 | Squares and square roots | |
| 1.4.3 | Cubes | |
| 1.4.4 | Powers of 10 | |
| 1.4.5 | Powers of 2 | |
| 1.5 | Operations | |
| 1.5.1 | Laws for rearranging and grouping numbers | |
| 1.5.2 | Inverse operations | |
| 1.5.3 | Operations with 0 and 1 | |
| 1.5.4 | Using a calculator | |
| 1.5.5 | Divisibility rules | |
| 1.5.6 | Division and remainders | |
| 1.5.7 | Odds and evens in operations | |
| 1.5.8 | Strategies for mental calculations | |
| 1.5.9 | Traditional methods for basic operations | |
| 1.5.10 | Order of operations (BODMAS) | |
| 1.6 | Routine Word Problems | |
| 1.6.1 | Suggested setting out | |
| 1.6.2 | Examples | |
| Mixed Bag (Workbook only) |
Chapter 2 Common Fractions
| 2.1 | Basic Concepts |
| 2.1.1 | What is a fraction? |
| 2.1.2 | Numerator and denominator |
| 2.1.3 | Proper and improper; mixed numbers |
| 2.1.4 | Equivalent fractions (including simplifying) |
| 2.1.5 | Fractions on number lines |
| 2.1.6 | Lowest common denominator (LCD) |
| 2.1.7 | Compare and order fractions |
| 2.2 | Addition and Subtraction |
| 2.2.1 | Whole numbers and mixed numbers |
| 2.2.2 | Same denominator |
| 2.2.3 | Different denominators |
| 2.3 | Other Fraction Problems |
| 2.3.1 | Fraction of a whole number |
| 2.3.2 | Find fraction: one quantity of another |
| 2.3.3 | Find the whole amount |
| 2.4 | Multiplication |
| Mixed Bag (Workbook only) |
Chapter 3 Decimal Fractions
| 3.1 | Basic Concepts |
| 3.1.1 | Decimals and place value |
| 3.1.2 | Conversions: decimals common |
| 3.1.3 | Compare and order decimals |
| 3.1.4 | Decimals on number lines |
| 3.1.5 | Rounding off decimals |
| 3.2 | Operations with Decimals |
| 3.2.1 | Addition and subtraction |
| 3.2.2 | Multiplication |
| 3.2.3 | Division |
| 3.3 | Measurement Conversions |
| Mixed Bag (Workbook only) |
Chapter 4 Percentages
| 4.1 | Basic Concepts |
| 4.1.1 | Percentage as a fraction |
| 4.1.2 | Conversions: common decimal percentage |
| 4.2 | Calculations and Problems |
| 4.2.1 | Percentage of a whole number |
| 4.2.2 | Find percentage: one amount of another |
| 4.2.3 | Increased and decreased amounts |
| Mixed Bag (Workbook only) |
Chapter 5 Ratio and Rate
| 5.1 | Ratio |
| 5.1.1 | What is ratio? |
| 5.1.2 | Ratio tables |
| 5.1.3 | Simplifying ratios |
| 5.1.4 | Divide a quantity in a given ratio |
| 5.2 | Rate |
| 5.2.1 | What is rate? |
| 5.2.2 | Simplifying rates |
| 5.2.3 | Find an amount, given the rate |
| 5.2.4 | Compare rates |
| 5.2.5 | Direct and indirect proportion |
| Mixed Bag (Workbook only) |
Content Area 2: Patterns, Functions and Algebra
Chapter 6 Algebra
| 6.1 | Introduction to Algebra |
| 6.2 | Substitution into Expressions |
| 6.3 | Solve Equations |
| 6.3.1 | Methods |
| 6.3.2 | Unknown on one side of the equation |
| 6.3.3 | Unknown on both sides of the equation |
| 6.4 | Write Equations for Problems |
| Mixed Bag (Workbook only) |
Chapter 7 Patterns and Sequences
| 7.1 | Vocabulary |
| 7.2 | Ways of Expressing Patterns |
| 7.3 | Number Patterns |
| 7.3.1 | Add or subtract the same number |
| • Single operation patterns | |
| • Two operation patterns | |
| 7.3.2 | Multiply or divide by the same number |
| 7.3.3 | Term to term changes not identical |
| • Square numbers | |
| • Triangular numbers | |
| 7.3.4 | More complex patterns |
| Mixed Bag (Workbook only) |
Content Area 3: Geometry (Space and Shape)
Chapter 8 Geometry – Lines and Angles
| 8.1 | Lines |
| 8.2 | Angles |
| 8.2.1 | What is an angle? |
| 8.2.2 | Naming angles |
| 8.2.3 | Compare sizes of angles |
| 8.2.4 | Classification of angles |
Chapter 9 Geometry of 2D Shapes
| 9.1 | What are 2D Shapes? |
| 9.2 | Circles |
| 9.3 | Polygons |
| 9.3.1 | Properties of polygons |
| 9.3.2 | Classification: number of sides |
| 9.4 | Symmetry in 2D Shapes |
| 9.5 | Quadrilaterals |
| 9.5.1 | Classification: sides and angles |
| 9.5.2 | Comparing quadrilaterals |
| 9.6 | Triangles |
| 9.6.1 | Three angles of a triangle |
| 9.6.2 | Classification: sides and angles |
| Mixed Bag (Workbook only) |
Chapter 10 Transformation of 2D Shapes
| 10.1 | Position using Co-ordinates |
| 10.2 | Transformations |
| 10.2.1 | What is a transformation? |
| 10.2.2 | Translations |
| 10.2.3 | Reflections |
| 10.2.4 | Rotations |
| 10.2.5 | Enlargements and reductions |
| 10.3 | Tessellations |
| Mixed Bag (Workbook only) |
Chapter 11 Geometry of 3D Objects
| 11.1 | Three-Dimensional Objects |
| 11.1.1 | Types of 3D objects |
| 11.1.2 | Parts 3D objects: faces, edges, vertices |
| 11.2 | Polyhedra: Prisms and Pyramids |
| 11.3 | Nets and Naming of 3D Objects |
| 11.4 | Polyhedra: Faces, Edges, Vertices |
| 11.5 | Plans and Views of 3D Objects |
| Mixed Bag (Workbook only) |
Content Area 4: Measurement
Chapter 12 Time
| 12.1 | History of Time |
| 12.1.1 | Calendars: years, months and days |
| 12.1.2 | Instruments to measure time of day |
| 12.2 | Units of Time |
| 12.3 | Calendars |
| 12.4 | Telling Time |
| 12.4.1 | Analogue and digital instruments |
| 12.4.2 | 12-hour time |
| 12.4.3 | 24-hour time |
| 12.4.4 | Conversions: 12-hour 24-hour |
| 12.4.5 | Working with seconds |
| 12.5 | Calculations with Time |
| 12.5.1 | Time conversions |
| 12.5.2 | Operations |
| 12.5.3 | Time intervals (period of time) |
| 12.6 | Time Zones |
| 12.6.1 | About time zones |
| 12.6.2 | Time zone calculations |
| 12.7 | Moon Phases |
| Mixed Bag (Workbook only) |
Chapter 13 Measurement – Temperature, Length, Mass, Capacity
| 13.1 | Introduction to Measurement |
| 13.2 | Temperature |
| 13.3 | Metric Conversions |
| 13.4 | Length |
| 13.4.1 | What is length? |
| 13.4.2 | Measuring instruments for length |
| 13.4.3 | Units of length and conversions |
| 13.4.4 | Real life examples of length |
| 13.5 | Mass |
| 13.5.1 | What is mass? |
| 13.5.2 | Measuring instruments for mass |
| 13.5.3 | Units of mass and conversions |
| 13.5.4 | Real life examples of mass |
| 13.6 | Capacity |
| 13.6.1 | What is capacity? |
| 13.6.2 | Measuring instruments for capacity |
| 13.6.3 | Units of capacity and conversions |
| 13.6.4 | Real life examples of capacity |
| Mixed Bag (Workbook only) |
Chapter 14 Perimeter and Area of 2D Shapes
| 14.1 | Perimeter |
| 14.1.1 | What is perimeter? |
| 14.1.2 | Perimeter of irregular shapes |
| 14.1.3 | Perimeter of regular shapes, including squares |
| 14.1.4 | Perimeter of rectangles |
| 14.2 | Area |
| 14.2.1 | What is area? |
| 14.2.2 | Units of measurement for area |
| 14.2.3 | Area of irregular shapes |
| 14.2.4 | Area of squares |
| 14.2.5 | Area of rectangles |
| 14.3 | Relationship: Perimeter and Area |
| 14.3.1 | Same perimeter, different areas |
| 14.3.2 | Same area, different perimeters |
| Mixed Bag (Workbook only) |
Chapter 15 Volume and Surface Area of 3D Objects
| 15.1 | Volume |
| 15.1.1 | What is volume? |
| 15.1.2 | Using cubes to measure volume |
| 15.1.3 | Units of measurement for volume |
| 15.1.4 | Volume of rectangular prisms (cuboids) |
| 15.1.5 | Volume of cubes |
| 15.1.6 | Relationship: volume and capacity |
| 15.2 | Surface Area |
| 15.2.1 | What is surface area? |
| 15.2.2 | Surface area of cubes |
| 15.2.3 | Surface area of rectangular prisms |
| Mixed Bag (Workbook only) |
Content Area 5: Data Handling
Chapter 16 Data Handling
| 16.1 | What are Data and Statistics? |
| 16.2 | Collecting Data |
| 16.3 | Recording Data |
| 16.4 | Organising and Summarising Data |
| 16.5 | Presenting Data: Graphs and Charts |
| 16.6 | Types of Graphs |
| 16.6.1 | Picture graphs / pictographs / pictograms |
| 16.6.2 | Column graphs |
| 16.6.3 | Pie / circle / sector graphs |
| 16.6.4 | Line graphs |
| 16.7 | Drawing Graphs: Common Errors |
| 16.8 | Analysing Data |
| 16.8.1 | Range |
| 16.8.2 | Averages (mean, median, mode) |
| Mixed Bag (Workbook only) | |
| Assignments (Workbook only) |
Chapter 17 Probability
| 17.1 | Introduction to Probability |
| 17.1.1 | What is probability? |
| 17.1.2 | Probability scale |
| 17.1.3 | Vocabulary and how to show probability |
| 17.2 | Finding Probability |
| 17.2.1 | All results (outcomes) equally likely |
| 17.2.2 | All results (outcomes) not equally likely |
| 17.3 | Tools for organising results |
| 17.3.1 | Two-way tables |
| 17.3.2 | Tree diagrams |
| 17.4 | No Replacement: Decreasing Outcomes |
| Mixed Bag (Workbook only) |
All Content Areas: Problem Solving
Chapter 18 Problem Solving
| 18.1 | Important for Teachers |
| 18.2 | Some Habits of Mind |
| 18.3 | Some Strategies |
| 18.3.1 | Get rid of unnecessary information |
| 18.3.2 | Make it simple |
| 18.3.3 | Be a drama queen / king (Act it out) |
| 18.3.4 | Make a model |
| 18.3.5 | Draw a diagram |
| 18.3.6 | Draw up organised lists |
| 18.3.7 | Use a table |
| 18.3.8 | Find a pattern |
| 18.3.9 | Work backwards |
| 18.3.10 | ‘Goldilocks’ method (Guess and improve) |
| 18.4 | Some Useful Methods |
| 18.4.1 | Bar modelling |
| 18.4.2 | Number combinations |
| 18.4.3 | How many shapes? |
| 18.4.4 | Adding consecutive numbers |
| 18.4.5 | Two-way tables |
| 18.4.6 | Venn diagrams |
| 18.4.7 | Last digits |
| 18.4.8 | Mystic rose |
| 18.4.9 | Networks |
| 18.5 | Think outside the Box |