Measurements

Circles - Circumference of a circle
Circles - Length of an arc of a circle

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

- Work out the circumference of a circle using the formula C = πd or C = 2πr
- Apply the circumference formula to real-life situations involving circular objects
- Show integrity when drawing circles and working out their circumference

In groups, learners are guided to:
- Collect cylindrical objects (cups, pipes, tins) and wrap a string around each to measure circumference
- Measure the diameter using set squares and calculate C/d; observe it approximates π (≈ 3.142 or 22/7)
- Use the formula C = πd and C = 2πr to work out circumferences of given circles
- Discuss real-life examples: bicycle wheels, circular tanks, compact discs

How do we determine the circumference of a circle?

Smart Minds Mathematics Grade 8 pg. 104
- Cylindrical objects (cups, tins, pipes)
- String, ruler, set squares
- Digital resources
Smart Minds Mathematics Grade 8 pg. 107
- Manila paper, pair of compasses, scissors
- Ruler, protractor

- Oral questions - Written assignments

Measurements

Circles - Length of an arc (continued)
Circles - Perimeter of a sector of a circle
Circles - Perimeter of a sector (continued and application)
Area - Area of a circle

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

- Calculate arc length given angle and radius in different situations
- Find unknown values (radius or angle) given the arc length
- Show confidence when applying the arc length formula

In groups, learners are guided to:
- Complete tables relating angle subtended, circumference and arc length
- Calculate arc length when given radius and angle and find angle or radius when arc length is known
- Solve real-life problems: arc length of a clock hand sweep, arc of a circular path

What information is needed to calculate the length of an arc?

Smart Minds Mathematics Grade 8 pg. 107
- Mathematical tables
- Calculators
- Digital resources
Smart Minds Mathematics Grade 8 pg. 110
- Manila paper, pair of compasses, scissors
- Ruler, protractor
- Reference books
Smart Minds Mathematics Grade 8 pg. 114

- Written assignments - Oral questions

Measurements

Area - Area of a sector of a circle
Area - Surface area of cubes and cuboids
Area - Surface area of cylinders and triangular prisms

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

- Work out the area of a sector using A = (θ/360) × πr²
- Find unknown angle or radius given the area of a sector
- Show critical thinking when solving sector area problems

In groups, learners are guided to:
- Cut out a sector from a circle; relate area of sector to fraction of full circle area using angle/360
- Calculate areas of sectors given angle and radius
- Solve problems: area swept by a clock's minute hand, area swept by a windscreen wiper
- Find angle or radius when area of sector is given

How do we calculate the area of a sector of a circle?

Smart Minds Mathematics Grade 8 pg. 118
- Manila paper, pair of compasses, scissors
- Calculators
- Digital resources
Smart Minds Mathematics Grade 8 pg. 116
- Clay/cartons/plasticine
- Ruler
- Cylindrical objects, manila paper
- Digital resources (videos)

- Written assignments - Oral questions

Measurements

Area - Area of irregular shapes
Money - Principal and interest
Money - Simple interest

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

- Estimate the area of irregular shapes using a square grid
- Apply the square grid method to real-life contexts such as land estimation
- Recognise the use of area in real-life situations

In groups, learners are guided to:
- Trace an irregularly shaped object (leaf, palm of hand, foot) onto a unit square grid
- Count complete squares and half-squares; add to estimate total area
- Draw an irregular plot of land on a grid and estimate area in cm²; scale up to find actual area in hectares
- Use IT tools to explore estimation of irregular areas interactively

How do we estimate the area of irregular shapes?

Smart Minds Mathematics Grade 8 pg. 126
- Unit square grid paper
- Leaves/irregular objects
- Calculators
- Digital resources
Smart Minds Mathematics Grade 8 pg. 130
- Resource person (banker/SACCO officer)
- Reference books
Smart Minds Mathematics Grade 8 pg. 132

- Written assignments - Observation - Oral questions

Measurements

Money - Simple interest (continued)
Money - Compound interest

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

- Find principal, rate or time when other values are known
- Apply simple interest to varied real-life financial contexts
- Spend money responsibly on needs and leisure

In groups, learners are guided to:
- Rearrange SI formula to find P, R or T when the other values are given
- Solve problems: find principal given SI, rate and time; find rate given SI, principal and time
- Discuss real-life contexts: borrowing from SACCOs, saving in banks, mobile money apps
- Use calculators to verify solutions

How is simple interest used in everyday financial decisions?

Smart Minds Mathematics Grade 8 pg. 132
- Calculators
- Digital resources
Smart Minds Mathematics Grade 8 pg. 134
- Digital resources (videos)
- Resource person

- Written tests - Oral questions

Measurements

Money - Compound interest (continued)
Money - Appreciation and depreciation

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

- Work out compound interest and total amount for two and three year periods
- Apply compound interest to real-life savings and loan scenarios
- Show responsibility in financial decision making

In groups, learners are guided to:
- Calculate compound interest step by step for 2-year and 3-year problems
- Find total amount paid or received including compound interest
- Solve real-life problems: SACCO loans, bank savings accounts, cooperative society deposits
- Use calculators to carry out multi-step compound interest calculations

How do we calculate compound interest over multiple years?

Smart Minds Mathematics Grade 8 pg. 134
- Calculators
- Digital resources
Smart Minds Mathematics Grade 8 pg. 138
- Newspaper property pages

- Written tests - Oral questions

Measurements

Money - Depreciation
Money - Hire purchase

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

- Explain the meaning of depreciation and identify items that depreciate in value
- Work out depreciation per annum step by step up to three years
- Show critical thinking when comparing appreciation and depreciation

In groups, learners are guided to:
- Visit or compare prices of second-hand items (TV, car, motorcycle) with new prices; observe value loss
- Discuss: depreciation = decrease in value over time (vehicles, machinery, electronics) due to wear and tear
- Calculate depreciated value year by year: new value = old value − (old value × rate/100)
- Compare appreciation and depreciation side by side using examples

How does the value of assets depreciate over time?

Smart Minds Mathematics Grade 8 pg. 138
- Calculators
- Price lists / advertisements
- Digital resources
Smart Minds Mathematics Grade 8 pg. 144
- Shop catalogues / price lists

- Written assignments - Oral questions

Measurements
Geometry
Geometry
Geometry

Money - Hire purchase (continued and application)
Geometrical Constructions - Construction of lines and parallel lines
Geometrical Constructions - Construction of perpendicular lines
Geometrical Constructions - Proportional division of a line

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

- Calculate hire purchase price when it is expressed as a percentage more than the marked price
- Find monthly instalments, deposit or number of months from hire purchase terms
- Spend money responsibly by evaluating hire purchase vs cash options

In groups, learners are guided to:
- Solve problems where hire purchase price is a given % above marked price (e.g. 20% more)
- Calculate monthly instalment from: monthly instalments = (HP price − deposit) / number of months
- Complete a table of hire purchase values (price, deposit, monthly instalment, number of months)
- Discuss real-life consumer scenarios: buying a motorcycle, sofa set, water pump on hire purchase

How do we decide whether to buy on hire purchase or cash?

Smart Minds Mathematics Grade 8 pg. 144
- Calculators
- Digital resources
- Reference books
Smart Minds Mathematics Grade 8 pg. 148
- Pair of compasses, ruler, protractor
- Set squares
Smart Minds Mathematics Grade 8 pg. 153
- Pair of compasses, ruler, set square, protractor
Smart Minds Mathematics Grade 8 pg. 160
- Pair of compasses, ruler, set square

- Written tests - Oral questions

Geometry

Geometrical Constructions - Angle properties of polygons
Geometrical Constructions - Exterior angles in a polygon
Geometrical Constructions - Construction of regular polygons
Geometrical Constructions - Construction of irregular polygons (triangles)
Geometrical Constructions - Construction of other irregular polygons

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

- Identify the four types of triangles and state their angle properties
- Work out the sum of interior angles of quadrilaterals (rectangle, square, parallelogram, trapezium)
- Use the formula (n-2) × 180° to find the sum of interior angles of any polygon
- Show interest in geometric patterns in real life

In groups, learners are guided to:
- Trace triangles, rectangles, parallelograms and trapeziums; measure each interior angle using a protractor
- Establish sum of angles: triangle = 180°, quadrilateral = 360°
- Divide polygons into triangles; derive formula: sum of interior angles = (n−2) × 180°
- Solve problems: find missing angles in polygons; find number of sides given interior angle size

Where do we use polygons in real-life situations?

Smart Minds Mathematics Grade 8 pg. 164
- Protractor, ruler
- Polygon cut-outs
- Digital resources
Smart Minds Mathematics Grade 8 pg. 171
- Polygon cards
Smart Minds Mathematics Grade 8 pg. 173
- Pair of compasses, ruler, protractor
Smart Minds Mathematics Grade 8 pg. 179
Smart Minds Mathematics Grade 8 pg. 183
- Digital resources (videos)

- Oral questions - Written assignments

Geometry

Geometrical Constructions - Construction of a circumscribed circle
Geometrical Constructions - Construction of an inscribed circle

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

- Construct perpendicular bisectors of sides of a triangle
- Locate the circumcentre as the intersection of perpendicular bisectors
- Draw a circle passing through all three vertices of a triangle
- Show accuracy in construction and measurement

In groups, learners are guided to:
- Construct a triangle from given dimensions
- Construct perpendicular bisectors of any two sides; identify meeting point O as circumcentre
- Use O as centre and radius OK (vertex to centre) to draw the circumscribed circle
- Measure and record the radius; verify circle passes through all three vertices

How do we construct a circle passing through the three vertices of a triangle?

Smart Minds Mathematics Grade 8 pg. 190
- Pair of compasses, ruler, protractor
- Digital resources
Smart Minds Mathematics Grade 8 pg. 193

- Written assignments - Oral questions

Geometry

Geometrical Constructions - Circumscribed and inscribed circles (practice)
Geometrical Constructions - Review and application

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

- Construct circumscribed and inscribed circles for varied triangles
- Compare the sizes of circumscribed and inscribed circles of the same triangle
- Apply construction skills to solve problems

In groups, learners are guided to:
- Practise constructing circumscribed and inscribed circles for different types of triangles (equilateral, right-angled, scalene)
- Compare radii; discuss which circle is larger and why
- Watch videos on construction software; use IT to create geometric patterns using circles and polygons

How are circumscribed and inscribed circles applied in real-life situations?

Smart Minds Mathematics Grade 8 pg. 190
- Pair of compasses, ruler, protractor
- Digital resources (videos)
Smart Minds Mathematics Grade 8 pg. 148
- Digital resources

- Written assignments - Oral questions

Geometry

Coordinates and Graphs - Drawing and labelling a Cartesian plane
Coordinates and Graphs - Identifying and plotting points on the Cartesian plane
Coordinates and Graphs - Table of values for linear equations

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

- Draw and label a Cartesian plane with x-axis and y-axis
- Identify and read coordinates of points on the Cartesian plane in the form (x, y)
- Appreciate the Cartesian plane as a tool for locating points

In groups, learners are guided to:
- Draw two perpendicular number lines meeting at the origin; label x-axis (horizontal) and y-axis (vertical)
- Label equal intervals on both axes including negative values
- Discuss: coordinates are written as (x, y); x is horizontal distance, y is vertical distance from origin
- Identify coordinates of marked points on a given Cartesian plane

How do we plot coordinates on a Cartesian plane?

Smart Minds Mathematics Grade 8 pg. 198
- Graph books/grid paper
- Ruler
- Digital resources
Smart Minds Mathematics Grade 8 pg. 199
Smart Minds Mathematics Grade 8 pg. 203
- Calculators

- Oral questions - Written assignments

Geometry

Coordinates and Graphs - Determining appropriate scale for linear graphs
Coordinates and Graphs - Drawing linear graphs on a Cartesian plane

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

- Determine an appropriate scale for plotting a linear graph on the Cartesian plane
- Set up a Cartesian plane with a chosen scale that accommodates all values in the table
- Appreciate the importance of choosing an appropriate scale

In groups, learners are guided to:
- Examine the range of x and y values in a table; determine scale so all points fit in the graph space
- Choose a scale for x-axis and y-axis separately (e.g. 1 cm represents 1 unit or 2 units)
- Set up the Cartesian plane with the chosen scale and label both axes
- Discuss: a poor scale choice wastes space or squashes the graph

Why is choosing an appropriate scale important when drawing a linear graph?

Smart Minds Mathematics Grade 8 pg. 204
- Graph books/grid paper
- Ruler
- Digital resources
Smart Minds Mathematics Grade 8 pg. 205

- Oral questions - Written assignments

Geometry

Coordinates and Graphs - Drawing linear graphs (practice)
Coordinates and Graphs - Solving simultaneous linear equations graphically

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

- Draw a variety of linear graphs including those with negative gradients
- Read off specific values from a drawn linear graph
- Reflect on the use of graphs in real life

In groups, learners are guided to:
- Draw linear graphs for equations involving negative coefficients such as y = −2x + 3 and 2x − y = 4
- Read values from drawn graphs: given x find y, given y find x
- Discuss real-life uses of linear graphs: distance-time graphs, cost graphs, conversion charts
- Use IT graphing tools to create and compare linear graphs

How are linear graphs used in real-life situations?

Smart Minds Mathematics Grade 8 pg. 205
- Graph books/grid paper
- Ruler
- Digital resources
Smart Minds Mathematics Grade 8 pg. 208

- Written assignments - Oral questions

Geometry

Coordinates and Graphs - Simultaneous equations graphically (application)
Coordinates and Graphs - Review and consolidation

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

- Form and solve simultaneous equations from real-life word problems graphically
- Interpret the intersection point in context
- Show critical thinking when applying graphical methods

In groups, learners are guided to:
- Form simultaneous equations from real-life problems (fruits in baskets, items bought at a market, animals in a park)
- Draw tables of values for both equations and plot on the same Cartesian plane
- Read the intersection point and interpret in context (e.g. cost of each item)
- Use IT graphing tools to verify graphical solutions

Where do we use simultaneous equations in real life?

Smart Minds Mathematics Grade 8 pg. 208
- Graph books/grid paper
- Calculators
- Digital resources
Smart Minds Mathematics Grade 8 pg. 198

- Written tests - Oral questions

Geometry

Scale Drawing - Representing length to a given scale
Scale Drawing - Converting actual length to scale length

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

- Explain the concept of scale drawing as a reduced or enlarged representation
- Represent the length of objects from the environment to a given scale
- Show responsibility when measuring and representing objects to scale

In groups, learners are guided to:
- Measure lengths of objects in the classroom (blackboard, desk, window) using a tape measure
- Represent each length using a given scale (e.g. 1 cm represents 1 m)
- Record actual length and drawing length in a table
- Discuss: scale drawing allows large objects to be represented on paper; drawing length is always stated first in the scale

How do we determine scales in real life?

Smart Minds Mathematics Grade 8 pg. 211
- Tape measure / metre rule
- Ruler
- Digital resources
Smart Minds Mathematics Grade 8 pg. 214
- Calculators

- Oral questions - Observation

Geometry

Scale Drawing - Converting scale length to actual length
Scale Drawing - Linear scale in statement form
Scale Drawing - Linear scale in ratio form

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

- Convert scale length to actual length using a given scale
- Express actual lengths in appropriate units (m or km)
- Apply conversions to map and plan reading

In groups, learners are guided to:
- Measure scale lengths on diagrams using a ruler
- Multiply scale length by the scale factor to get actual length
- Convert actual length to appropriate units (cm → m → km)
- Solve problems: find actual dimensions of plots, roads and rivers from scale drawings

How do we find actual lengths from scale drawings?

Smart Minds Mathematics Grade 8 pg. 216
- Ruler
- Calculators
- Maps or scale diagrams
Smart Minds Mathematics Grade 8 pg. 218
- Digital resources
Smart Minds Mathematics Grade 8 pg. 221

- Written assignments - Oral questions

Geometry

Scale Drawing - Converting linear scales between forms
Scale Drawing - Making scale drawings

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

- Convert a linear scale from statement form to ratio form
- Convert a linear scale from ratio form to statement form
- Apply conversions to real-life map contexts

In groups, learners are guided to:
- Convert statement form to ratio form: change actual length to same units as drawing length, then express as 1:n
- Convert ratio form to statement form: interpret 1:n as "1 cm represents n cm" then express in appropriate units
- Use online map scale calculator to practise conversions
- Discuss: maps use ratio form (e.g. 1:50 000) while builders may use statement form

How do we convert scales between statement and ratio form?

Smart Minds Mathematics Grade 8 pg. 224
- Ruler
- Calculators
- Digital resources (map scale calculator)
Smart Minds Mathematics Grade 8 pg. 227
- Ruler, protractor, pair of compasses
- Graph books/grid paper
- Digital resources

- Written assignments - Oral questions

Geometry

Scale Drawing - Making scale drawings (continued and application)
Scale Drawing - Review and consolidation

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

- Make scale drawings of real-life objects and spaces such as school compounds and classrooms
- Determine actual area and perimeter from a scale drawing
- Appreciate the application of scale drawing in architecture and maps

In groups, learners are guided to:
- Measure the classroom and make a scale drawing at 1:100
- Draw a scale drawing of an irregular plot; find actual perimeter and area from the drawing
- Use ICT to display maps and use zoom functions to demonstrate how scale changes
- Use maps to locate places and measure distances using the map scale

How do architects and map makers use scale drawings?

Smart Minds Mathematics Grade 8 pg. 227
- Tape measure
- Ruler, graph paper
- Digital resources (maps, ICT)
Smart Minds Mathematics Grade 8 pg. 211
- Ruler, calculators
- Maps
- Digital resources

- Written tests - Observation - Oral questions

Geometry

Common Solids - Identifying common solids from the environment
Common Solids - Edges, vertices and faces of common solids

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

- Identify and name common solids from the environment (cube, cuboid, cylinder, cone, pyramid, sphere, prism)
- Describe properties that distinguish one solid from another
- Show curiosity in exploring solids in the environment

In groups, learners are guided to:
- Collect real objects that represent common solids (tins, boxes, balls, ice cream cones, bricks)
- Sort and name each collected solid; draw its shape in exercise book
- Discuss features: cones have an apex; pyramids have a polygonal base and triangular faces; spheres have no edges or vertices
- Watch videos on common solids using digital devices

What are common solids?

Smart Minds Mathematics Grade 8 pg. 231
- Collected solid objects
- Digital resources (videos)
Smart Minds Mathematics Grade 8 pg. 233
- Solid models (clay/cartons)
- Digital resources

- Oral questions - Observation

Geometry

Common Solids - Sketching nets of solids
Common Solids - Nets of cylinders, pyramids and cones

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

- Define a net as the flat shape obtained when a solid is opened and laid flat
- Sketch nets of cubes, cuboids, cylinders and triangular pyramids
- Make solids from drawn nets

In groups, learners are guided to:
- Cut open hollow solids (boxes, tins) and lay flat; observe the net formed
- Sketch nets of: triangular pyramid (4 triangles), square pyramid (1 square + 4 triangles), cube (6 squares), cuboid (6 rectangles)
- Draw nets on squared paper, cut out and fold to verify they form the correct solid
- Note: a closed cylinder's net = 2 circles + rectangle; rectangle length = circumference of circle

What is the net of a solid?

Smart Minds Mathematics Grade 8 pg. 234
- Manila paper, scissors, pair of compasses
- Ruler
- Digital resources
- Ruler, protractor

- Oral questions - Written assignments - Observation

Geometry

Common Solids - Surface area of cubes and cuboids from nets
Common Solids - Surface area of cylinders and triangular prisms from nets

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

- Use nets to calculate the surface area of cubes
- Use nets to calculate the surface area of closed and open cuboids
- Appreciate the use of nets in calculating surface area

In groups, learners are guided to:
- Draw net of a cube; count 6 equal squares; multiply area of one square by 6 for surface area
- Draw net of closed cuboid; identify 3 pairs of equal rectangles; sum all six areas for surface area
- Draw net of open cuboid; identify 5 rectangles; sum their areas
- Solve real-life problems: surface area of dice, cartons, rooms

How do we use nets to calculate the surface area of solids?

Smart Minds Mathematics Grade 8 pg. 239
- Graph books/squared paper
- Ruler
- Calculators
- Ruler, calculators
- Digital resources

- Written assignments - Oral questions

Geometry

Common Solids - Surface area of pyramids and cones from nets
Common Solids - Distance between two points on the surface of a solid
Common Solids - Distance between two points (continued)

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

- Use nets to calculate the surface area of square-based pyramids
- Use nets to calculate the surface area of cones
- Apply surface area calculations to real-life problems

In groups, learners are guided to:
- Draw net of square-based pyramid (square + 4 triangles); calculate area of base and each triangular face; sum all areas
- Draw net of cone (circle + sector); calculate area of circle = πr²; area of sector = (θ/360)πl²; find sum
- Solve problems: surface area of tent models combining cube and pyramid, gift boxes, display cones

How do we calculate the surface area of pyramids and cones from nets?

Smart Minds Mathematics Grade 8 pg. 239
- Graph books/squared paper
- Ruler, calculators
- Digital resources
Smart Minds Mathematics Grade 8 pg. 254
- Card/manila paper, scissors

- Written assignments - Oral questions

Geometry

Common Solids - Making models of hollow and compact solids
Common Solids - Making models (continued) and review

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

- Make models of hollow solids (cube, cuboid, cylinder, pyramid, cone) using locally available materials
- Make compact solid models using clay or plasticine
- Promote the use of common solids in real-life situations

In groups, learners are guided to:
- Use thick paper, cartons or manila paper to construct nets and fold into hollow solid models
- Use clay or plasticine to make compact solid models of cubes, cuboids and cylinders
- Carry out an ethnomath project: discuss how pots were moulded and decorated in African culture
- Use IT devices to watch videos on making models of common solids
- Display and discuss completed models with the class

How do we use common solids in real life?

Smart Minds Mathematics Grade 8 pg. 259
- Clay/plasticine
- Manila paper, cartons, scissors
- Digital resources (videos)
- Manila paper, ruler
- Digital resources

- Observation - Oral questions - Project work

Geometry

Coordinates and Graphs - Simultaneous equations (real-life problem 2)
Coordinates and Graphs - Simultaneous equations (real-life problem 3)

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

- Draw tables of values and graphs for a pair of simultaneous equations from a word problem
- Read and interpret the solution from the point of intersection
- Show confidence in using graphical methods

In groups, learners are guided to:
- Form and solve simultaneous equations from market/shopping scenarios (books and pencils, cows and goats, plates and spoons)
- Draw tables of values for both equations; plot on same Cartesian plane
- Read intersection point; write solution and interpret in context
- Verify by substituting back into both equations

How do we use graphs to solve real-life problems involving two unknowns?

Smart Minds Mathematics Grade 8 pg. 208
- Graph books/grid paper
- Calculators
- Digital resources

- Written assignments - Oral questions

Geometry

Coordinates and Graphs - Simultaneous equations (practice and consolidation)
Coordinates and Graphs - Review and application

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

- Solve a variety of simultaneous equation pairs graphically
- Select an appropriate scale to display both graphs clearly
- Use IT graphing tools to confirm graphical solutions

In groups, learners are guided to:
- Solve at least four pairs of simultaneous equations graphically including those with negative values
- Choose appropriate scales independently for each set of equations
- Use IT graphing tools to draw the graphs and verify intersection points

When is the graphical method preferred for solving simultaneous equations?

Smart Minds Mathematics Grade 8 pg. 208
- Graph books/grid paper
- Digital resources
Smart Minds Mathematics Grade 8 pg. 198

- Written tests - Oral questions

Geometry

Scale Drawing - Converting linear scales (practice)
Scale Drawing - Making scale drawings (introduction)

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

- Convert a variety of scales between statement and ratio form fluently
- Solve problems requiring identification and use of scales on plans and maps
- Show critical thinking when selecting and converting scales

In groups, learners are guided to:
- Convert multiple scales in both directions (statement → ratio, ratio → statement) using varied units
- Use an online map scale calculator to practice conversions
- Solve problems: identify scale from drawing and actual length; express in both forms
- Discuss how architects and surveyors use both forms of scale in their work

How do engineers and map makers use both forms of scale?

Smart Minds Mathematics Grade 8 pg. 224
- Ruler, calculators
- Digital resources (map scale calculator)
Smart Minds Mathematics Grade 8 pg. 227
- Ruler, graph paper
- Calculators

- Written assignments - Oral questions

Geometry

Scale Drawing - Making scale drawings of irregular shapes
Scale Drawing - Scale Drawing review and consolidation
Common Solids - Surface area of triangular prisms from nets

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

- Make accurate scale drawings of irregular polygonal shapes
- Use a scale drawing to determine actual area and perimeter
- Appreciate scale drawing as a tool in land surveying

In groups, learners are guided to:
- Make scale drawings of irregular plots of land given side lengths and angles
- Measure the scale drawing to find actual perimeter and area using the scale
- Discuss how surveyors use scale drawings to represent plots of land
- Visit school grounds with tape measure; produce a scale drawing of an area

How do surveyors use scale drawings to represent pieces of land?

Smart Minds Mathematics Grade 8 pg. 227
- Ruler, protractor, tape measure
- Graph paper
- Digital resources
Smart Minds Mathematics Grade 8 pg. 211
- Ruler, calculators
- Maps
Smart Minds Mathematics Grade 8 pg. 239
- Graph books/squared paper

- Written assignments - Observation

Geometry

Common Solids - Surface distances on solids (further practice)
Common Solids - Ethnomath project and final review

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

- Solve further problems involving distance between two points on various solids
- Correctly identify which faces the path crosses when finding surface distances
- Demonstrate systematic problem-solving skills

In groups, learners are guided to:
- Solve surface distance problems on cuboids where the path passes through two faces
- Solve problems on cylinders: unroll curved surface into a rectangle and use Pythagoras
- Solve mixed surface distance problems; verify by measuring on physical models
- Discuss: always open the solid into a net first; the straight-line distance on the net is the shortest surface path

What is the strategy for finding the shortest path between two points on a solid?

Smart Minds Mathematics Grade 8 pg. 254
- Card/manila paper, scissors
- Ruler, calculators
- Digital resources
Smart Minds Mathematics Grade 8 pg. 259
- Clay/plasticine
- Reference books

- Written tests - Oral questions

Geometry

Common Solids - Nets and surface area (consolidation)
Common Solids - Making compact solid models

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

- Draw nets of mixed solid types from memory
- Use nets to calculate surface area for a variety of solids
- Show creativity when drawing and using nets

In groups, learners are guided to:
- Draw nets of cube, cuboid, cylinder, cone and pyramid from memory without reference
- Calculate surface area of each using the drawn net
- Peer-assess each other's nets for correctness and completeness
- Use IT to trace or draw nets of solids interactively

How do nets help us understand and calculate the surface area of solids?

Smart Minds Mathematics Grade 8 pg. 234
- Graph books/squared paper
- Ruler, calculators
- Digital resources
Smart Minds Mathematics Grade 8 pg. 259
- Clay/plasticine
- Ruler

- Written assignments - Oral questions

Data Handling and Probability

Data Presentation and Interpretation - Drawing bar graphs
Data Presentation and Interpretation - Drawing bar graphs (continued)
Data Presentation and Interpretation - Interpreting bar graphs
Data Presentation and Interpretation - Drawing line graphs
Data Presentation and Interpretation - Interpreting line graphs

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

- Collect data from real-life situations and organise it in a table
- Choose an appropriate scale and draw a bar graph to represent data
- Show interest in collecting and representing data from their environment

In groups, learners are guided to:
- Collect data from classmates on favourite sports, colours or shoe sizes; record in a frequency table
- Discuss and choose an appropriate scale for the vertical axis; use 1 cm per day on horizontal axis
- Draw a bar graph with labelled axes, a title and uniform bar widths
- Discuss: the tallest bar represents the highest frequency and the shortest represents the lowest

What are the different ways of representing data?

Smart Minds Mathematics Grade 8 pg. 261
- Graph books/grid paper, ruler
- Collected class data
- Digital resources
- Calculators
Smart Minds Mathematics Grade 8 pg. 264
- Printed bar graph charts
- Newspapers/reports
Smart Minds Mathematics Grade 8 pg. 269
Smart Minds Mathematics Grade 8 pg. 273
- Printed line graph charts

- Oral questions - Written assignments

Data Handling and Probability

Data Presentation and Interpretation - Interpreting line graphs (continued)
Data Presentation and Interpretation - Mode of discrete data
Data Presentation and Interpretation - Mean of discrete data
Data Presentation and Interpretation - Median of discrete data

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

- Solve multi-step problems from line graphs including total sales comparisons
- Draw and interpret line graphs for real-life data from the environment
- Recognise use of line graphs in science, business and everyday life

In groups, learners are guided to:
- Solve problems from given line graphs: total distance in a journey, how much more was sold in first half vs second half of a year
- Collect environmental data (rainfall records, temperature over days) and represent on a line graph
- Discuss: line graphs are used in weather stations, hospitals (patient monitoring), businesses (sales trends)
- Use IT to display and explore line graphs from online datasets

How are line graphs used in real-life contexts such as science and business?

Smart Minds Mathematics Grade 8 pg. 273
- Graph books/grid paper, ruler
- Calculators
- Digital resources
Smart Minds Mathematics Grade 8 pg. 278
- Fruit cards/tally charts
Smart Minds Mathematics Grade 8 pg. 280
- Reference books
Smart Minds Mathematics Grade 8 pg. 283

- Written tests - Oral questions

Data Handling and Probability

Data Presentation and Interpretation - Review and application
Probability - Identifying events involving chance

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

- Apply all data presentation and interpretation skills to real-life situations
- Use IT to create graphs and calculate measures of central tendency
- Recognise the use of data representation and interpretation in real life

In groups, learners are guided to:
- Collect data from a class survey (shoe sizes, heights, favourite activities); draw bar graph and line graph
- Calculate mean, mode and median for the collected data set
- Use IT (spreadsheet) to create bar and line graphs and calculate averages
- Discuss real-life uses: hospitals use mean temperature; businesses use mode for stock planning; journalists use median income

How do we use data representation and interpretation in real life?

Smart Minds Mathematics Grade 8 pg. 261
- Graph books/grid paper, ruler
- Calculators
- Digital resources
Smart Minds Mathematics Grade 8 pg. 285
- Chance word cards
- Coins, dice

- Written tests - Oral questions - Observation

Data Handling and Probability

Probability - Chance experiments
Probability - Experimental probability

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

- Perform chance experiments involving spinning a colour wheel, flipping a coin and tossing a die
- Predict outcomes and compare predictions with actual results
- Show interest in chance experiments and their outcomes

In groups, learners are guided to:
- Make a colour wheel with equal and unequal colour sections; spin and record colour obtained each time
- Discuss: colour with largest section has highest likelihood of occurring
- Flip a coin multiple times; record heads and tails using a tally chart; compare results with prediction
- Toss a die; record each outcome; observe that each face has an equal chance of appearing
- Draw coloured balls from a bag one at a time; identify which colour is most/least likely

How do we carry out chance experiments?

Smart Minds Mathematics Grade 8 pg. 287
- Colour wheels, coins, dice
- Coloured balls in a bag
- Digital resources
Smart Minds Mathematics Grade 8 pg. 290
- Calculators

- Oral questions - Observation - Written assignments

Data Handling and Probability

Probability - Expressing experimental probability as fractions
Probability - Expressing experimental probability as a decimal or percentage
Probability - Experimental probability (extended practice)
Probability - Review and application

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

- Express experimental probability outcomes as fractions in their simplest form
- Find unknown probability outcomes given the probability of the complementary event
- Show confidence when working with probability fractions

In groups, learners are guided to:
- Express experimental probabilities from coin flipping, die tossing and ball drawing as fractions in simplest form
- Use the relationship: P(tail) = 1 − P(head) to find complementary probabilities
- Calculate probability from real-life data: days of rainfall per month, defective bottles from a sample, injured players in a school team
- Solve problems: given P(head) = 0.3 = 3/10, find P(tail) as a fraction

How do we express experimental probability as a fraction?

Smart Minds Mathematics Grade 8 pg. 293
- Coins, dice, coloured balls
- Calculators
- Digital resources
Smart Minds Mathematics Grade 8 pg. 294
- Dice, coins
Smart Minds Mathematics Grade 8 pg. 290
- Coins, dice
Smart Minds Mathematics Grade 8 pg. 285

- Written assignments - Oral questions