Measurements

Area - Surface area of cylinders and triangular prisms

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

- Work out the surface area of closed, open and hollow cylinders
- Determine the surface area of a triangular prism
- Use IT tools and other materials to learn more about surface area

In groups, learners are guided to:
- Collect a cylindrical object, wrap paper around curved surface; open and measure to show curved surface area = 2πrh
- Derive: closed cylinder = 2πr² + 2πrh; open cylinder = πr² + 2πrh; hollow cylinder = 2πrh
- Identify faces of a triangular prism (2 triangles + 3 rectangles) and find total surface area
- Watch videos on surface area of cubes, cuboids, cylinders and prisms
- Solve real-life problems: cylindrical tins, pipes, metal rods, wedge-shaped pieces of wood

How do we calculate the surface area of cylinders and triangular prisms?

Smart Minds Mathematics Grade 8 pg. 116
- Cylindrical objects, manila paper
- Calculators
- Digital resources (videos)

- Written assignments - Oral questions

Measurements

Area - Area of irregular shapes

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

- Written assignments - Observation - Oral questions

Measurements

Money - Principal and interest
Money - Simple interest

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

- Identify principal and interest in real-life financial situations
- Calculate interest given principal and amount in different situations
- Show interest in consumer awareness and financial responsibility

In groups, learners are guided to:
- Visit or invite a resource person from a financial institution to discuss services, deposits, loans and interest
- Discuss meanings of: principal (money deposited or borrowed), interest (additional charge or earnings), amount (principal + interest)
- Calculate interest and principal from given real-life statements (bank deposits, SACCO loans)
- Write a report and share findings with classmates

What is interest in money?

Smart Minds Mathematics Grade 8 pg. 130
- Resource person (banker/SACCO officer)
- Digital resources
- Reference books
Smart Minds Mathematics Grade 8 pg. 132
- Calculators

- Oral questions - Observation - Written assignments

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)

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

- Written tests - Oral questions

Measurements

Money - Appreciation and depreciation
Money - Depreciation

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

- Explain the meaning of appreciation and identify items that appreciate in value
- Work out appreciation per annum step by step up to three years
- Make informed decisions on goods worth investing in

In groups, learners are guided to:
- Discuss: appreciation = increase in value over time (land, gold, currency); initial value = principal
- Calculate appreciated value year by year: new value = old value + (old value × rate/100)
- Solve problems: commercial plots, buildings, batteries over 2–3 years
- Identify and discuss items in the local environment that appreciate in value

What causes the value of assets to appreciate over time?

Smart Minds Mathematics Grade 8 pg. 138
- Calculators
- Newspaper property pages
- Digital resources
- Price lists / advertisements

- Written assignments - Oral questions

Measurements

Money - Hire purchase

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

- Explain the meaning of hire purchase and compare it with cash purchase
- Work out hire purchase price given deposit and monthly instalments
- Recognise why hire purchase price is higher than cash price

In groups, learners are guided to:
- Visit a shop or study a catalogue; enquire about cash price and hire purchase price of items
- Record: deposit, monthly instalment, number of months for different items
- Establish: hire purchase price = deposit + total monthly instalments
- Compare hire purchase price with cash price; discuss why people prefer hire purchase despite higher cost
- Solve problems: find hire purchase price, monthly instalment, deposit or number of months

How do we pay for goods on hire purchase?

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

- Written assignments - Oral questions - Observation

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

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

- Oral questions - Written assignments

Geometry

Geometrical Constructions - Construction of irregular polygons (triangles)
Geometrical Constructions - Construction of other irregular polygons
Geometrical Constructions - Construction of a circumscribed circle

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

- Construct a triangle given the lengths of three sides (SSS)
- Construct a triangle given two angles and the length of one side (AAS)
- Construct a triangle given two sides and the included angle (SAS)
- Show accuracy in geometric construction

In groups, learners are guided to:
- Construct triangle ABC given three side lengths: draw AB, use arcs from A and B to locate C
- Construct a triangle given two angles and one side: draw base, construct angles at each end and extend until sides meet
- Construct a triangle given two sides and included angle: draw one side, construct angle, mark second side length
- Measure constructed triangles to verify accuracy

How do we construct triangles given different information?

Smart Minds Mathematics Grade 8 pg. 179
- Pair of compasses, ruler, protractor
- Digital resources
Smart Minds Mathematics Grade 8 pg. 183
- Digital resources (videos)
Smart Minds Mathematics Grade 8 pg. 190

- Written assignments - Oral questions

Geometry

Geometrical Constructions - Construction of an inscribed circle

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

- Bisect angles of a triangle using a pair of compasses
- Locate the incentre as the intersection of angle bisectors
- Draw a circle touching all three sides of a triangle
- Admire geometric patterns created using circles and triangles

In groups, learners are guided to:
- Construct a triangle from given dimensions
- Bisect any two angles; let bisectors meet at O (incentre)
- Drop a perpendicular from O to one side; use this length as radius
- Draw the inscribed circle touching all three sides; measure and record the radius
- Use IT devices to create patterns using circles touching sides of polygons

How do we construct a circle touching the three sides of a triangle?

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

- 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

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

- Oral questions - Written assignments

Geometry

Coordinates and Graphs - Table of values for linear equations

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

- Generate a table of values for a given linear equation
- Calculate y values by substituting x values into a linear equation
- Show accuracy when constructing tables of values

In groups, learners are guided to:
- Substitute selected x values into a linear equation to find corresponding y values
- Record results in a table of values
- Generate tables of values for equations such as x + y = 6, 2x + y = 8, y = 2x + 3
- Discuss patterns observed in the table of values

How do we generate a table of values for a linear equation?

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

- Written assignments - Oral questions

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)

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

- Written assignments - Oral questions

Geometry

Coordinates and Graphs - Solving simultaneous linear equations graphically
Coordinates and Graphs - Simultaneous equations graphically (application)

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

- Draw two linear graphs on the same Cartesian plane
- Identify the point of intersection as the solution to simultaneous equations
- Apply graphical solutions to real-life problems

In groups, learners are guided to:
- Draw tables of values for two simultaneous equations
- Plot both graphs on the same Cartesian plane using the same scale
- Identify point of intersection P; read coordinates as the solution (x, y)
- Verify solution by substituting back into both original equations

How do we solve simultaneous equations graphically?

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

- Written assignments - Oral questions

Geometry

Coordinates and Graphs - Review and consolidation
Scale Drawing - Representing length to a given scale

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

- Apply skills of plotting, drawing linear graphs and solving simultaneous equations graphically
- Connect graphical solutions to algebraic solutions
- Use IT or other resources to further explore graphs

In groups, learners are guided to:
- Solve mixed problems: plot points, draw linear graphs, solve simultaneous equations graphically
- Compare graphical and algebraic solutions to simultaneous equations; discuss accuracy
- Use IT graphing tools to explore further examples and verify results

How do we use linear graphs in real life?

Smart Minds Mathematics Grade 8 pg. 198
- Graph books/grid paper
- Calculators
- Digital resources
Smart Minds Mathematics Grade 8 pg. 211
- Tape measure / metre rule
- Ruler

- Written tests - Oral questions - Observation

Geometry

Scale Drawing - Converting actual length to scale length

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

- Convert actual length to scale length using a given scale
- Apply the conversion to real-life contexts involving distances and land
- Show accuracy when converting lengths

In groups, learners are guided to:
- Discuss: divide actual length by the second number of the scale to get drawing length
- Convert actual lengths to scale lengths for various scales (1 cm represents 3 km, 1 cm represents 50 000 cm)
- Convert actual lengths in km to cm before dividing where necessary
- Solve problems involving road lengths, river lengths and field dimensions

How do we convert actual lengths to scale lengths?

Smart Minds Mathematics Grade 8 pg. 214
- Ruler
- Calculators
- Digital resources

- Written assignments - Oral questions

Geometry

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

- Written assignments - Oral questions

Geometry

Scale Drawing - Linear scale in ratio form
Scale Drawing - Converting linear scales between forms

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

- Interpret a linear scale expressed in ratio form
- Write a linear scale in ratio form given drawing and actual lengths
- Show confidence in reading and writing scales in ratio form

In groups, learners are guided to:
- Read and interpret ratio scales: 1:5 000 means 1 cm represents 5 000 cm
- Convert ratio scale to units: 1:700 000 = 1 cm represents 7 km
- Given drawing length and actual length, convert actual length to same units as drawing length and express as ratio
- Complete tables converting ratio scales to centimetres, metres and kilometres

How do we interpret and write scales in ratio form?

Smart Minds Mathematics Grade 8 pg. 221
- Ruler
- Calculators
- Digital resources
Smart Minds Mathematics Grade 8 pg. 224
- Digital resources (map scale calculator)

- Written assignments - Oral questions

Geometry

Scale Drawing - Making scale drawings

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

- Choose an appropriate scale for a given set of dimensions
- Calculate drawing dimensions from actual dimensions using the chosen scale
- Make an accurate scale drawing of a shape or plot of land

In groups, learners are guided to:
- Discuss how to choose a scale: the drawing must fit comfortably in the available space
- Calculate drawing dimensions by dividing actual dimensions by the scale factor
- Make scale drawings of rectangular plots, rooms, and irregular land shapes
- Measure distances and angles on completed scale drawings and interpret in context

Where do we use scale drawing in real-life situations?

Smart Minds Mathematics Grade 8 pg. 227
- Ruler, protractor, pair of compasses
- Graph books/grid paper
- Digital resources

- Written assignments - Observation

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

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)

- Oral questions - Observation

Geometry

Common Solids - Edges, vertices and faces of common solids
Common Solids - Sketching nets of solids

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

- Count and record edges, vertices and faces of common solids
- Classify solids by their faces, edges and vertices
- Show responsibility when handling solid models

In groups, learners are guided to:
- Collect or make models of cube, cuboid, square-based pyramid, triangular pyramid, cone, cylinder and sphere
- Count faces, vertices and edges for each; record in a table
- Discuss: a cube has 6 faces, 12 edges, 8 vertices; a cone has 1 face, 0 edges, 1 vertex (apex)
- Sort solids by number of faces and discuss patterns

How do we classify common solids?

Smart Minds Mathematics Grade 8 pg. 233
- Solid models (clay/cartons)
- Digital resources
Smart Minds Mathematics Grade 8 pg. 234
- Manila paper, scissors, pair of compasses
- Ruler

- Oral questions - Written assignments

Geometry

Common Solids - Nets of cylinders, pyramids and cones
Common Solids - Surface area of cubes and cuboids from nets

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

- Sketch nets of closed and open cylinders
- Sketch nets of square-based pyramids and cones
- Identify the solid formed by a given net

In groups, learners are guided to:
- Sketch net of closed cylinder (2 circles + rectangle); open cylinder (1 circle + rectangle)
- Sketch net of square-based pyramid (1 square + 4 triangles); triangular prism (2 triangles + 3 rectangles)
- Sketch net of cone (circle + sector); note: curved surface opens to a sector
- Draw a given net on thick paper, fold and paste to identify the resulting solid

How do we sketch and use nets of common solids?

Smart Minds Mathematics Grade 8 pg. 234
- Manila paper, scissors, pair of compasses
- Ruler, protractor
- Digital resources
Smart Minds Mathematics Grade 8 pg. 239
- Graph books/squared paper
- Ruler
- Calculators

- Written assignments - Observation

Geometry

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 closed and open cylinders
- Use nets to calculate the surface area of triangular prisms
- Show accuracy in calculating surface area from nets

In groups, learners are guided to:
- Draw net of closed cylinder (2 circles + rectangle); calculate area of each part; find sum
- Surface area of closed cylinder = 2πr² + πdh; open cylinder = πr² + πdh
- Draw net of triangular prism (2 triangles + 3 rectangles); calculate area of each face and sum
- Solve real-life problems: cylindrical tins, metallic rods, wedge-shaped objects

How do we find the surface area of cylinders and prisms from their nets?

Smart Minds Mathematics Grade 8 pg. 239
- Graph books/squared paper
- 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

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 - Distance between two points (continued)

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

- Calculate the distance between two points on the surface of a triangular prism
- Solve more complex surface distance problems on various solids
- Demonstrate confidence when applying Pythagoras' theorem on nets

In groups, learners are guided to:
- Open a triangular prism into its net; identify the right-angled triangle formed between the two points
- Use Pythagoras' theorem to calculate required distances step by step
- Solve problems where the path passes through more than one face
- Verify answers by measuring on physical models

What information do we need to find the distance between two points on a solid's surface?

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

- 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)

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

- Written tests - Oral questions

Geometry

Coordinates and Graphs - Review and application
Scale Drawing - Converting linear scales (practice)

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

- Apply all Cartesian plane and graph skills to varied problems
- Connect plotting, linear graphs and simultaneous equations as an integrated topic
- Use IT tools to further explore coordinates and graphs

In groups, learners are guided to:
- Solve mixed problems: identify coordinates of points, generate tables of values, draw linear graphs, solve simultaneous equations graphically
- Discuss real-life uses: reading maps, interpreting distance-time graphs, solving business cost problems
- Use IT graphing tools to create and explore linear graphs interactively

How do we use linear graphs in real life?

Smart Minds Mathematics Grade 8 pg. 198
- Graph books/grid paper
- Digital resources
Smart Minds Mathematics Grade 8 pg. 224
- Ruler, calculators
- Digital resources (map scale calculator)

- Written tests - Oral questions - Observation

Geometry

Scale Drawing - Making scale drawings (introduction)

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

- Choose an appropriate scale for given actual dimensions
- Calculate drawing dimensions from actual measurements
- Begin making accurate scale drawings on graph paper

In groups, learners are guided to:
- Discuss how to test whether a scale is appropriate: multiply drawing length by scale factor; check result fits on paper
- For each given scenario, calculate drawing dimensions from actual dimensions
- Begin scale drawings of rectangular plots and rooms; use ruler and protractor for accuracy

What makes a scale appropriate for a particular drawing?

Smart Minds Mathematics Grade 8 pg. 227
- Ruler, graph paper
- Calculators

- Oral questions - Written assignments

Geometry

Scale Drawing - Making scale drawings of irregular shapes
Scale Drawing - Scale Drawing review and consolidation

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

- Written assignments - Observation

Geometry

Common Solids - Surface area of triangular prisms from nets
Common Solids - Surface distances on solids (further practice)

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

- Draw the net of a triangular prism
- Calculate the surface area of a triangular prism from its net
- Apply surface area of triangular prisms to real-life problems

In groups, learners are guided to:
- Draw net of a triangular prism (2 triangles + 3 rectangles); identify equal faces
- Calculate area of each triangular and rectangular face separately; find total surface area
- Solve real-life problems: wedge-shaped pieces of wood, rooftop models, tent structures
- Use nets drawn on squared paper to calculate surface area accurately

How do we find the surface area of a triangular prism from its net?

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 - Ethnomath project and final review

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

- Connect knowledge of common solids to cultural and real-world applications
- Apply all Common Solids skills in a review activity
- Promote the use of common solids in real-life situations

In groups, learners are guided to:
- Carry out ethnomath project: research and discuss how pots, granaries and other cultural objects reflect solid shapes
- Solve a mixed review of Common Solids: identify solids, sketch nets, calculate surface area, find surface distances, relate to models
- Share completed models and discuss how common solids appear in architecture, engineering and everyday life

How do we use common solids in real life and cultural contexts?

Smart Minds Mathematics Grade 8 pg. 259
- Clay/plasticine
- Digital resources
- Reference books

- Written tests - Observation - 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

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

- Oral questions - Written assignments

Data Handling and Probability

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

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

- Read and interpret line graphs including travel graphs
- Calculate speed from a travel graph
- Show critical thinking when reading and interpreting line graphs

In groups, learners are guided to:
- Study given line graphs: identify scale on each axis, read off values for given inputs
- Interpret a travel graph: find distance at a given time, find time for a given distance, identify rest periods (horizontal line segments)
- Calculate speed = distance ÷ time from segments of a travel graph
- Compare line graphs and discuss trends (increasing, decreasing, constant)

How do we interpret information from a line graph?

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

- Written assignments - Oral questions

Data Handling and Probability

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:

- Calculate the mean of a set of discrete data using Mean = sum of values ÷ number of values
- Find a missing value when the mean is given
- Apply the mean to real-life data sets such as health and academic records

In groups, learners are guided to:
- Discuss: mean = sum of all values ÷ number of values
- Calculate mean for given data sets: test scores, temperatures, blood sugar levels, number of pins in packets
- Find a missing value when mean and other values are known: rearrange formula to get missing value
- Solve multi-step mean problems: corrected mean when an error is discovered; number needed to reach a target mean

How do we determine the mean of data?

Smart Minds Mathematics Grade 8 pg. 280
- Calculators
- Digital resources
- Reference books
Smart Minds Mathematics Grade 8 pg. 283

- Written assignments - 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

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

- Oral questions - Observation - Written assignments

Data Handling and Probability

Probability - Experimental probability
Probability - Expressing experimental probability as fractions

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

- Define experimental probability and write it as: P(event) = number of occurrences ÷ total number of trials
- Calculate experimental probability from results of chance experiments
- Show accuracy when recording and computing experimental probabilities

In groups, learners are guided to:
- Spin a colour wheel 50 times; record occurrences of each colour in a table
- Calculate experimental probability of each colour: occurrences ÷ total spins
- Flip a coin 20 times; calculate experimental probability of getting a head and of getting a tail
- Toss a die 20 times; calculate experimental probability of each face
- Draw coloured balls from a bag; calculate probability of each colour from the experiment

How do we calculate experimental probability?

Smart Minds Mathematics Grade 8 pg. 290
- Colour wheels, coins, dice
- Coloured balls in a bag
- Calculators
Smart Minds Mathematics Grade 8 pg. 293
- Coins, dice, coloured balls
- Digital resources

- Written assignments - Oral questions

Data Handling and Probability

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 as a decimal
- Express experimental probability as a percentage
- Convert probability between fraction, decimal and percentage forms

In groups, learners are guided to:
- Toss a die 100 times; record occurrences of each outcome; express each probability as a fraction, then as a decimal, then as a percentage
- Convert probability fractions to decimals (divide numerator by denominator) and percentages (multiply decimal by 100)
- Solve problems: defective bottles probability as decimal; favourite breakfast choice as percentage
- Verify: sum of all probabilities for all outcomes = 1 (or 100%)

How do we express probability as a decimal or percentage?

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

- Written assignments - Oral questions