Measurements

Area - Applications of triangular prisms

By the end of the lesson, the learner should be able to:

- Discuss real-life objects in the shape of triangular prisms
- Calculate surface areas of dust pans, tents, and goal posts
- Show interest in applying prism knowledge

In groups, learners are guided to:
- Calculate surface area of rabbit hutches
- Work out surface area of tents and dust pans
- Solve problems involving wedges
- Calculate surface area of handball goal posts covered with nets

Where do we find triangular prisms in real life?

- Master Mathematics Grade 8, pg. 102
- Real-life problem cards
- Prism models
- Calculators

- Written assignments - Problem-solving - Presentations

Measurements

Area - Area of irregular shapes using square grids
Area - Estimating areas of maps and other irregular shapes
Money - Interest and principal

By the end of the lesson, the learner should be able to:

- Explain the method for estimating area of irregular shapes
- Estimate areas by counting full and partial squares
- Show patience in counting and estimating

In groups, learners are guided to:
- Select graph paper and trace leaf outlines
- Count number of full squares enclosed
- Count partial squares and divide by 2
- Add full squares to half of partial squares

How do we estimate areas of irregular shapes?

- Master Mathematics Grade 8, pg. 103
- Graph paper
- Square grids
- Leaves
- Pencils
- Master Mathematics Grade 8, pg. 105
- Maps
- Tracing paper
- Calculators
- Master Mathematics Grade 8, pg. 107
- Sample loan documents
- Financial scenario cards

- Practical activities - Written exercises - Observation

Measurements

Money - Calculating simple interest
Money - Applications of simple interest
Money - Compound interest calculation step by step

By the end of the lesson, the learner should be able to:

- Explain simple interest as money charged only on principal
- Calculate simple interest using formula: S.I = P × R × T / 100
- Show accuracy in simple interest calculations

In groups, learners are guided to:
- Discuss Mr. Murithi's loan scenario
- Calculate total amount paid and interest
- Express interest as percentage
- Practice using formula with different values

How do we calculate simple interest?

- Master Mathematics Grade 8, pg. 109
- Calculators
- Formula charts
- Loan scenario cards
- Master Mathematics Grade 8, pg. 110
- Real-life problem cards
- Bank documents (samples)
- Master Mathematics Grade 8, pg. 112
- Step-by-step charts
- Comparison worksheets

- Written tests - Problem-solving - Class activities

Measurements

Money - Working out appreciation per annum
Money - Working out depreciation per annum
Money - Hire purchase

By the end of the lesson, the learner should be able to:

- Define appreciation as gain in value of a commodity
- Calculate appreciation using compound interest method
- Show understanding that appreciation is calculated like compound interest

In groups, learners are guided to:
- Discuss meaning of appreciation in relation to monetary value
- List items that appreciate in value
- Calculate appreciation of land value year by year
- Apply appreciation formula to various scenarios

What items appreciate in value and why?

- Master Mathematics Grade 8, pg. 115
- Calculators
- Appreciation scenario cards
- Charts
- Master Mathematics Grade 8, pg. 116
- Depreciation charts
- Real-life examples
- Master Mathematics Grade 8, pg. 117
- Hire purchase documents
- Price comparison charts

- Written exercises - Problem-solving - Oral questions

Measurements
4.0: Geometry
4.0: Geometry
4.0: Geometry
4.0: Geometry
4.0: Geometry

Money - Visiting financial institutions and using IT for shopping
4.1: Geometrical Constructions - Constructing parallel lines using ruler and compasses
4.1: Geometrical Constructions - Constructing parallel lines using set square and ruler
4.1: Geometrical Constructions - Constructing perpendicular bisector of a line
4.1: Geometrical Constructions - Constructing perpendicular from a point to a line using compasses
4.1: Geometrical Constructions - Constructing perpendicular using set square and ruler

By the end of the lesson, the learner should be able to:

- Discuss information gathered from financial institutions
- Use IT to access online shopping platforms and identify terms of sale
- Spend money responsibly on needs and leisure

In groups, learners are guided to:
- Visit or invite resource persons from banks and SACCOs
- Gather information about interest rates offered on deposits
- Use IT to access online shopping platforms
- Discuss terms of sale for consumer awareness and protection

How do we make informed financial decisions?

- Master Mathematics Grade 8, pg. 118
- Digital devices
- Internet access
- Financial institution brochures
- Guest speakers
- MASTER Mathematics Grade 8 Learner's Book pg. 119
- Ruler
- Pair of compasses
- Pencil
- Plain paper
- Set square
- Drawing paper
- Protractor

- Portfolio assessment - Presentations - Reflection journals - Self-assessment

4.0: Geometry

4.1: Geometrical Constructions - Proportional division of a line
4.1: Geometrical Constructions - Sum of interior angles of polygons
4.1: Geometrical Constructions - Exterior angles of polygons
4.1: Geometrical Constructions - Constructing regular triangles
4.1: Geometrical Constructions - Constructing regular quadrilaterals (squares)

By the end of the lesson, the learner should be able to:

- State the method of dividing a line proportionally
- Apply the method of proportional division to divide lines into equal parts
- Demonstrate accuracy in geometric constructions

In groups, learners are guided to:
- Draw line of given length
- Draw auxiliary line at suitable angle
- Mark equal intervals along auxiliary line using compasses
- Join last point to end of original line
- Draw parallel lines through other points
- Verify equal divisions on original line

How can we divide a line without measuring its length?

- MASTER Mathematics Grade 8 Learner's Book pg. 119
- Ruler
- Pair of compasses
- Set square
- Pencil
- Protractor
- Calculator
- Chart showing polygon properties
- Plain paper

- Observation - Practical tasks - Written tests

4.0: Geometry

4.1: Geometrical Constructions - Constructing regular pentagons
4.1: Geometrical Constructions - Constructing regular hexagons and circles
4.2: Coordinates and Graphs - Drawing labelled Cartesian plane

By the end of the lesson, the learner should be able to:

- Recall that interior angle of regular pentagon is 108°
- Construct regular pentagon using ruler and protractor
- Show patience in multi-step constructions

In groups, learners are guided to:
- Draw line of given length
- Measure specified interior angle at one end
- Mark point along the line at given distance
- Repeat process at each new vertex
- Join last vertex to starting point to complete pentagon
- Verify all sides and angles are equal

Why is each interior angle of a regular pentagon 108°?

- MASTER Mathematics Grade 8 Learner's Book pg. 119
- Ruler
- Protractor
- Pencil
- Calculator
- Pair of compasses
- MASTER Mathematics Grade 8 Learner's Book pg. 147
- Graph paper
- Digital resources

- Observation - Practical construction - Written tests

4.0: Geometry

4.2: Coordinates and Graphs - Drawing Cartesian plane with different scales
4.2: Coordinates and Graphs - Identifying points on Cartesian plane
4.2: Coordinates and Graphs - Plotting points on Cartesian plane

By the end of the lesson, the learner should be able to:

- Explain the concept of scale in graphs
- Draw Cartesian plane with specified scales on both axes
- Demonstrate accuracy in scaling

In groups, learners are guided to:
- Draw Cartesian plane with various scales
- Practice with different unit representations
- Label axes correctly with chosen scale
- Discuss when to use different scales
- Compare graphs with different scales

How does scale affect the appearance of a graph?

- MASTER Mathematics Grade 8 Learner's Book pg. 147
- Graph paper
- Ruler
- Pencil
- Calculator
- Worksheet with points
- List of coordinates

- Observation - Practical tasks - Written tests

4.0: Geometry

4.2: Coordinates and Graphs - Reading coordinates from graphs
4.2: Coordinates and Graphs - Generating table of values from linear equations
4.2: Coordinates and Graphs - Completing tables for linear equations

By the end of the lesson, the learner should be able to:

- Identify coordinates of plotted points on graphs
- Read coordinates from all four quadrants correctly
- Show accuracy in coordinate reading

In groups, learners are guided to:
- Examine graph with plotted points
- Write down coordinates of labeled points
- Identify points on x-axis and y-axis
- Match given coordinates to labeled points on graph
- Practice with various coordinate positions

What special coordinates do points on the axes have?

- MASTER Mathematics Grade 8 Learner's Book pg. 147
- Graph paper with plotted points
- Ruler
- Pencil
- Practice worksheets
- Graph paper
- Calculator
- Exercise book

- Observation - Written tests - Oral questions

4.0: Geometry

4.2: Coordinates and Graphs - Determining appropriate scale for graphs
4.2: Coordinates and Graphs - Drawing line graphs from tables
4.2: Coordinates and Graphs - Drawing graphs for various linear equations

By the end of the lesson, the learner should be able to:

- List factors to consider when choosing scales
- Choose suitable scales for given data ranges
- Show judgment in scale selection

In groups, learners are guided to:
- Examine table with range of values
- Consider graph paper size
- Calculate range of values
- Select scale that accommodates all values
- Ensure efficient use of graph space

How do we choose a scale that makes best use of graph paper?

- MASTER Mathematics Grade 8 Learner's Book pg. 147
- Graph paper
- Ruler
- Calculator
- Data tables
- Pencil
- Set of equations

- Observation - Practical tasks - Problem-solving

4.0: Geometry

4.2: Coordinates and Graphs - Introduction to simultaneous equations graphically
4.2: Coordinates and Graphs - Solving simultaneous linear equations graphically
4.2: Coordinates and Graphs - Practice solving simultaneous equations with different forms

By the end of the lesson, the learner should be able to:

- Define simultaneous equations
- Identify point of intersection of two lines as solution
- Show interest in graphical methods

In groups, learners are guided to:
- Solve simultaneous equations algebraically
- Draw graphs of both equations on same axes
- Identify where lines intersect
- Read coordinates of intersection point
- Compare graphical solution to algebraic solution

How can graphs help us solve two equations together?

- MASTER Mathematics Grade 8 Learner's Book pg. 147
- Graph paper
- Ruler
- Calculator
- Number cards
- Pencil
- Scientific calculator

- Observation - Oral questions - Written assignments

4.0: Geometry

4.2: Coordinates and Graphs - Applying simultaneous equations to real-life problems
4.3: Scale Drawing - Representation of length to given scale
4.3: Scale Drawing - Converting actual length to scale length

By the end of the lesson, the learner should be able to:

- State real-life situations involving simultaneous equations
- Formulate and solve simultaneous equations from word problems graphically
- Appreciate practical applications of mathematics

In groups, learners are guided to:
- Formulate equations from shopping scenarios
- Set up equations from pricing problems
- Solve using graphical method
- Interpret solutions in context
- Discuss other real-life applications

How do simultaneous equations help solve everyday problems?

- MASTER Mathematics Grade 8 Learner's Book pg. 147
- Graph paper
- Ruler
- Calculator
- Real-life problem cards
- MASTER Mathematics Grade 8 Learner's Book pg. 160
- Tape measure
- Pencil
- Drawing paper
- Conversion tables

- Observation - Problem-solving - Oral questions

4.0: Geometry

4.3: Scale Drawing - Converting scale length to actual length
4.3: Scale Drawing - Interpreting linear scales in statement form
4.3: Scale Drawing - Writing linear scales in statement form

By the end of the lesson, the learner should be able to:

- Explain the process of converting scale to actual measurements
- Convert scale measurements to actual measurements accurately
- Show systematic calculation approach

In groups, learners are guided to:
- Measure lengths on scale diagrams
- Use given scales to find actual lengths
- Calculate actual distances
- Work with different unit conversions
- Practice reverse calculations

How do we find real dimensions from scale drawings?

- MASTER Mathematics Grade 8 Learner's Book pg. 160
- Ruler
- Calculator
- Scale drawings
- Pencil
- Maps with linear scales
- Sample plans
- Linear scale examples
- Drawing paper

- Observation - Written tests - Practical tasks

4.0: Geometry

4.3: Scale Drawing - Interpreting linear scales in ratio form
4.3: Scale Drawing - Writing linear scales in ratio form
4.3: Scale Drawing - Converting scale from statement to ratio form

By the end of the lesson, the learner should be able to:

- Define ratio form of scales
- Convert measurements to same units and express scales as ratios
- Show understanding of proportional relationships

In groups, learners are guided to:
- Convert scales ensuring same units
- Express scales as ratios
- Practice unit conversions before writing ratios
- Work with various scales
- Understand ratios have no units

What does a scale ratio tell us about a drawing?

- MASTER Mathematics Grade 8 Learner's Book pg. 160
- Ruler
- Calculator
- Conversion charts
- Pencil
- Conversion tables
- Practice worksheets
- Unit conversion chart

- Observation - Problem-solving - Oral questions

4.0: Geometry

4.3: Scale Drawing - Converting scale from ratio to statement form
4.3: Scale Drawing - Making scale drawings with calculations
4.3: Scale Drawing - Scale drawings with distance calculations

By the end of the lesson, the learner should be able to:

- Explain the process of converting ratio to statement form
- Convert ratio form scales to statement form using appropriate units
- Demonstrate understanding of both forms

In groups, learners are guided to:
- Convert ratio scales to statement form
- Determine appropriate units for actual measurements
- Express scales clearly in words
- Practice with various ratio scales
- Choose suitable units for statements

How do we choose appropriate units in statement form?

- MASTER Mathematics Grade 8 Learner's Book pg. 160
- Atlas
- Calculator
- Ruler
- Pencil
- Drawing paper
- Pair of compasses
- Graph paper

- Observation - Problem-solving - Oral questions

4.0: Geometry

4.3: Scale Drawing - Using maps and demonstrating scale
4.3: Scale Drawing - Application problems with scale
4.3: Scale Drawing - Using ICT for scale and maps

By the end of the lesson, the learner should be able to:

- Identify scales on actual maps
- Read scales from maps and measure distances accurately
- Appreciate real-world applications of scale

In groups, learners are guided to:
- Examine maps in atlas
- Identify and read map scales
- Measure distances between locations
- Calculate actual distances using scale
- Compare different maps with different scales
- Discuss map features

How does scale choice affect what we can show on a map?

- MASTER Mathematics Grade 8 Learner's Book pg. 160
- Atlas
- Maps
- Ruler
- Calculator
- Digital resources
- Problem cards
- Reference materials
- Digital devices (tablets/computers)
- Internet access
- Digital mapping software
- Projector

- Observation - Practical measurement - Oral questions

4.0: Geometry

4.4: Common Solids - Identifying common solids from environment
4.4: Common Solids - Properties of solids (faces, edges, vertices)
4.4: Common Solids - Sketching nets of cubes

By the end of the lesson, the learner should be able to:

- Name common solids: cubes, cuboids, cylinders, pyramids and cones
- Classify solids by their properties
- Show awareness of geometric shapes in environment

In groups, learners are guided to:
- Collect objects from environment
- Group objects by shape categories
- Identify properties of each solid type
- Discuss examples in daily life
- Create display of classified solids

Where do we see these solids in our daily lives?

- MASTER Mathematics Grade 8 Learner's Book pg. 176
- Collection of solid objects
- Models of solids
- Pictures of buildings
- Digital images
- Ruler
- Labels
- Worksheet
- Model cubes
- Scissors/razor blade
- Pencil
- Plain paper

- Observation - Practical classification - Oral questions

4.0: Geometry

4.4: Common Solids - Sketching nets of cuboids
4.4: Common Solids - Sketching nets of cylinders
4.4: Common Solids - Sketching nets of pyramids

By the end of the lesson, the learner should be able to:

- Identify faces of cuboids
- Sketch nets of closed and open cuboids
- Show accuracy in net construction

In groups, learners are guided to:
- Label cuboid vertices
- Cut along specified edges
- Spread faces on flat surface
- Sketch net with all faces for closed cuboid
- Sketch net with appropriate faces for open cuboid
- Identify pairs of equal faces

How does the net of a cuboid differ from that of a cube?

- MASTER Mathematics Grade 8 Learner's Book pg. 176
- Model cuboids
- Scissors/razor blade
- Ruler
- Pencil
- Grid paper
- Model cylinders
- Pair of compasses
- Model pyramids
- Drawing paper

- Observation - Practical tasks - Written tests

4.0: Geometry

4.4: Common Solids - Sketching nets of cones
4.4: Common Solids - Matching solids to nets and vice versa
4.4: Common Solids - Surface area of cubes from nets

By the end of the lesson, the learner should be able to:

- Identify components of cone nets
- Sketch nets of cones showing sector shape
- Appreciate relationship between arc and circumference

In groups, learners are guided to:
- Cut base from cone
- Cut curved surface along slant height
- Observe curved surface forms sector
- Note relationship between arc length and base circumference
- Sketch net showing circle and sector
- Label components

Why does the cone's curved surface form a sector?

- MASTER Mathematics Grade 8 Learner's Book pg. 176
- Model cones
- Scissors/razor blade
- Protractor
- Pair of compasses
- Pencil
- Various nets
- Model solids
- Ruler
- Matching cards
- Model cubes
- Calculator
- Net templates

- Observation - Practical construction - Written assignments

4.0: Geometry

4.4: Common Solids - Surface area of cuboids from nets
4.4: Common Solids - Surface area of cylinders from nets
4.4: Common Solids - Surface area of pyramids from nets

By the end of the lesson, the learner should be able to:

- State the formula for surface area of cuboid
- Calculate total surface area of cuboid from nets
- Show organized calculation method

In groups, learners are guided to:
- Draw net of cuboid with given dimensions
- Calculate areas of different faces
- Identify pairs of equal faces
- Add all areas to find total
- Practice with various dimensions
- Verify calculations

Why do we calculate surface area in pairs for cuboids?

- MASTER Mathematics Grade 8 Learner's Book pg. 176
- Model cuboids
- Ruler
- Calculator
- Grid paper
- Pencil
- Model cylinders
- Pair of compasses
- Formula chart
- Model pyramids
- Net templates

- Observation - Written assignments - Practical calculations

4.0: Geometry

4.4: Common Solids - Surface area of cones and distance on surfaces
4.4: Common Solids - Making models of hollow solids (cubes and cuboids)
4.4: Common Solids - Making models of cylinders, cones and pyramids

By the end of the lesson, the learner should be able to:

- State formula for surface area of cone
- Calculate surface area of cone from net and determine shortest distances on solid surfaces
- Show advanced spatial reasoning

In groups, learners are guided to:
- Identify cone net components
- Calculate circular base area
- Calculate sector area using given angle
- Find total surface area
- Open cuboid into net to find paths between points
- Measure distances along net surface

How does opening a solid help find distances on its surface?

- MASTER Mathematics Grade 8 Learner's Book pg. 176
- Model cones and cuboids
- Protractor
- Calculator
- String
- Scissors
- Manila paper
- Ruler
- Pencil
- Glue/paste
- Colored markers
- Pair of compasses
- Glue

- Observation - Problem-solving - Practical tasks

4.0: Geometry
5.0: Data Handling and Probability
5.0: Data Handling and Probability
5.0: Data Handling and Probability
5.0: Data Handling and Probability

4.4: Common Solids - Using IT devices and drawing technology
5.1: Data Presentation and Interpretation - Collecting data and drawing bar graphs
5.1: Data Presentation and Interpretation - Drawing bar graphs with suitable scale
5.1: Data Presentation and Interpretation - Interpreting bar graphs
5.1: Data Presentation and Interpretation - Drawing line graphs

By the end of the lesson, the learner should be able to:

- Identify technology tools for learning about solids
- Use technology to explore and draw solids and nets
- Appreciate technology in mathematics learning

In groups, learners are guided to:
- Watch educational videos about solids
- Use software to draw 3D shapes
- Explore rotating solids digitally
- Practice drawing nets using technology
- Use apps to visualize net folding
- Share digital creations

How does technology enhance our understanding of 3D shapes?

- MASTER Mathematics Grade 8 Learner's Book pg. 176
- Computers/tablets
- Internet access
- GeoGebra software
- Projector
- 3D modeling apps
- MASTER Mathematics Grade 8 Learner's Book pg. 197
- Ruler
- Graph paper
- Pencil
- Data collection sheets
- Calculator
- Data tables
- Sample bar graphs
- Question sheets

- Observation - Digital portfolio - Oral presentation - Peer evaluation

5.0: Data Handling and Probability

5.1: Data Presentation and Interpretation - Interpreting line graphs
5.1: Data Presentation and Interpretation - Identifying mode of discrete data
5.1: Data Presentation and Interpretation - Calculating mean of discrete data
5.1: Data Presentation and Interpretation - Working out averages from different sets
5.1: Data Presentation and Interpretation - Determining median of discrete data

By the end of the lesson, the learner should be able to:

- Explain how to read values from line graphs
- Interpret line graphs to extract information
- Show analytical skills in reading trends

In groups, learners are guided to:
- Read values at specific points on graph
- Identify highest and lowest values
- Determine trends from line graphs
- Calculate totals from graph data
- Answer questions based on line graphs
- Discuss patterns observed

How do line graphs help us see changes over time?

- MASTER Mathematics Grade 8 Learner's Book pg. 197
- Sample line graphs
- Ruler
- Pencil
- Question sheets
- Number cards
- Exercise books
- Data sets
- Calculator
- Problem cards

- Observation - Written tests - Problem-solving

5.0: Data Handling and Probability

5.1: Data Presentation and Interpretation - Using IT for data presentation and calculations
5.2: Probability - Identifying events involving chance in real life
5.2: Probability - Discussing likely and unlikely events

By the end of the lesson, the learner should be able to:

- Identify IT tools for creating graphs
- Use technology to create bar graphs and line graphs and calculate mean, mode and median
- Appreciate technology in data handling

In groups, learners are guided to:
- Use spreadsheet software to enter data
- Create bar graphs using software
- Create line graphs using software
- Use formulas to calculate mean
- Use functions to find mode and median
- Compare manual and digital methods
- Present findings digitally

How does technology make data presentation and analysis easier?

- MASTER Mathematics Grade 8 Learner's Book pg. 197
- Computers/tablets
- Spreadsheet software
- Internet access
- Projector
- Data sets
- MASTER Mathematics Grade 8 Learner's Book pg. 210
- Pictures of chance events
- Pencil
- Chart paper
- Real-life scenario cards
- Likelihood scale chart
- Event cards
- Exercise books

- Observation - Digital portfolio - Practical demonstration - Peer evaluation

5.0: Data Handling and Probability

5.2: Probability - Performing chance experiments
5.2: Probability - Writing experimental probability outcomes
5.2: Probability - Expressing probability outcomes as fractions

By the end of the lesson, the learner should be able to:

- Define chance experiment
- Perform chance experiments such as flipping coins, tossing dice, and drawing objects
- Show interest in hands-on probability activities

In groups, learners are guided to:
- Obtain coins and flip them
- Toss dice and record outcomes
- Draw colored balls or beads from bags
- Use spinners and record results
- Record outcomes from experiments
- Compare results with other groups
- Discuss patterns observed

What are the possible outcomes when we perform chance experiments?

- MASTER Mathematics Grade 8 Learner's Book pg. 210
- Coins
- Dice
- Colored balls/beads
- Bags
- Spinners
- Recording sheets
- Number cards
- Pencil
- Exercise books
- Calculator

- Observation - Practical tasks - Oral questions

5.0: Data Handling and Probability

5.2: Probability - Expressing probability as decimals and percentages
5.2: Probability - Using IT to play probability games
5.2: Probability - Using IT to play probability games

By the end of the lesson, the learner should be able to:

- Explain the relationship between probability in fractions, decimals and percentages
- Convert probability from fractions to decimals and percentages
- Demonstrate proficiency in probability conversions

In groups, learners are guided to:
- Convert probability fractions to decimals
- Convert probability fractions to percentages
- Understand that probability in decimals cannot exceed 1
- Understand that probability in percentages cannot exceed 100%
- Calculate complementary probabilities
- Solve problems in different forms
- Apply probability in real contexts

Why is probability sometimes expressed as decimals or percentages?

- MASTER Mathematics Grade 8 Learner's Book pg. 210
- Calculator
- Pencil
- Exercise books
- Conversion charts
- Computers/tablets
- Internet access
- Probability apps/software
- Projector
- Recording sheets

- Observation - Written tests - Problem-solving