Algebra

Linear Equations - Forming linear equations in two unknowns
Linear Equations - Forming linear equations in two unknowns (continued)

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

- Define a linear equation in two unknowns
- Form linear equations in two unknowns from real-life situations
- Show interest in using linear equations to model real-life problems

- Role-play shopping activities: one learner as shopkeeper, others as buyers; let price of one item be x and another be y
- Write two linear equations to represent amounts spent by different buyers
- Use a beam balance to form equations: two different masses x and y balance a known mass
- Discuss: simultaneous equations are a pair of linear equations with two unknowns

How do we form linear equations in two unknowns?

Smart Minds Mathematics Grade 8 pg. 95
- Shopping props
- Beam balance
- Digital resources
- Word problem cards

- Oral questions - Written assignments

Algebra

Linear Equations - Solving linear equations in two unknowns by the substitution method
Linear Equations - Solving linear equations in two unknowns by the substitution method (continued)

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

- Solve simultaneous equations in two unknowns using the substitution method
- Express one variable in terms of the other and substitute into the second equation
- Show confidence in applying the substitution method

- Apply the substitution method to solve more complex simultaneous equations
- Apply the substitution method to solve real-life problems
- Demonstrate accuracy when solving simultaneous equations

In groups, learners are guided to:
- Discuss and solve simultaneous equations: express x in terms of y from one equation and substitute into the other
- Solve for one variable then back-substitute to find the other
- Work through examples such as 2x−y=1, x−y=−1 step by step
- Discuss hints: (i) express x in terms of y, (ii) substitute, (iii) solve for y, (iv) back-substitute
- Solve simultaneous equations involving larger coefficients using substitution (e.g. 3x+5y=11 and x−2y=0)
- Solve real-life problems: ages of father and son, cost of pencils and erasers, cost of fruits
- Use IT tools or reference books to verify solutions

How do we solve linear equations in two unknowns using the substitution method?
How is the substitution method applied to solve real-life problems involving two unknowns?

Smart Minds Mathematics Grade 8 pg. 97
- Equation cards
- Digital resources
Smart Minds Mathematics Grade 8 pg. 97
- Word problem cards
- Calculators
- Digital resources

- Written assignments - Oral questions
- Written tests - Oral questions

Algebra

Linear Equations - Solving linear equations in two unknowns by the elimination method

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

- Solve simultaneous equations using the elimination method by adding or subtracting equations
- Reduce two unknowns to a single unknown by eliminating one variable
- Appreciate the elimination method as an alternative approach

In groups, learners are guided to:
- Make equation cards (e.g. 4x+2y=16 and 3x+2y=13) and subtract to eliminate y
- Discuss: to eliminate a variable, add or subtract a multiple of one equation from the other
- Solve examples where coefficients of one variable are already equal (e.g. 2x+5y=12 and 2x+3y=8)

How do we solve linear equations using the elimination method?

Smart Minds Mathematics Grade 8 pg. 100
- Equation cards
- Digital resources

- Written assignments - Oral questions

Algebra

Linear Equations - Solving linear equations in two unknowns by the elimination method

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

- Solve simultaneous equations using the elimination method by adding or subtracting equations
- Reduce two unknowns to a single unknown by eliminating one variable
- Appreciate the elimination method as an alternative approach

In groups, learners are guided to:
- Make equation cards (e.g. 4x+2y=16 and 3x+2y=13) and subtract to eliminate y
- Discuss: to eliminate a variable, add or subtract a multiple of one equation from the other
- Solve examples where coefficients of one variable are already equal (e.g. 2x+5y=12 and 2x+3y=8)

How do we solve linear equations using the elimination method?

Smart Minds Mathematics Grade 8 pg. 100
- Equation cards
- Digital resources

- Written assignments - Oral questions

Algebra

Linear Equations - Solving linear equations in two unknowns by the elimination method (continued)

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

- Apply the elimination method to equations requiring multiplication before elimination
- Solve real-life problems using the elimination method
- Show critical thinking when choosing steps in the elimination method

In groups, learners are guided to:
- Multiply one or both equations to make coefficients of one variable equal before eliminating
- Solve real-life problems: banknotes of different denominations, books of different prices, cost of petrol and diesel
- Compare substitution and elimination methods and discuss when each is more convenient

How do we choose the most efficient method to solve simultaneous equations?

Smart Minds Mathematics Grade 8 pg. 100
- Word problem cards
- Calculators
- Digital resources

- Written tests - Oral questions

Algebra

Linear Equations - Application of linear equations in two unknowns

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

- Apply linear equations in two unknowns to solve varied real-life problems
- Select the appropriate method (substitution or elimination) to solve simultaneous equations
- Recognise the use of linear equations in real life

- Solve mixed real-life problems forming and solving simultaneous equations using either method
- Visit a nearby shop (or role-play) to obtain prices of two items, form simultaneous equations and solve
- Watch videos involving linear equations in two unknowns using digital devices
- Share findings with other learners in class

Where do we apply linear equations in two unknowns in everyday life?

Smart Minds Mathematics Grade 8 pg. 100
- Calculators
- Digital resources (videos)
- Reference books

- Written tests - Oral questions - Observation

Algebra
Measurements

Linear Equations - Application of linear equations in two unknowns
Circles - Circumference of a circle

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

- Apply linear equations in two unknowns to solve varied real-life problems
- Select the appropriate method (substitution or elimination) to solve simultaneous equations
- Recognise the use of linear equations in real life

- 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

- Solve mixed real-life problems forming and solving simultaneous equations using either method
- Visit a nearby shop (or role-play) to obtain prices of two items, form simultaneous equations and solve
- Watch videos involving linear equations in two unknowns using digital devices
- Share findings with other learners in class
- 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

Where do we apply linear equations in two unknowns in everyday life?
How do we determine the circumference of a circle?

Smart Minds Mathematics Grade 8 pg. 100
- Calculators
- Digital resources (videos)
- Reference books
Smart Minds Mathematics Grade 8 pg. 104
- Cylindrical objects (cups, tins, pipes)
- String, ruler, set squares
- Digital resources

- Written tests - Oral questions - Observation
- Oral questions - Written assignments

Measurements

Circles - Length of an arc of a circle

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

- Identify major arc, minor arc and semicircle in a circle
- Work out the length of an arc using the formula l = (θ/360) × 2πr
- Appreciate the relationship between arc length and the circumference of a circle

In groups, learners are guided to:
- Draw a circle on manila paper, cut into equal parts and measure arc lengths
- Compare ratio of arc length to circumference with ratio of angle at centre to 360°; observe they are equal
- Use cut-outs (semicircle, quarter circle) to relate arc length to fraction of circumference
- Calculate arc lengths given radius and angle subtended at the centre

How do we calculate the length of an arc of a circle?

Smart Minds Mathematics Grade 8 pg. 107
- Manila paper, pair of compasses, scissors
- Ruler, protractor
- Digital resources

- Written assignments - Oral questions

Measurements

Circles - Length of an arc (continued)
Circles - Perimeter of a sector 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

- Written assignments - Oral questions

Measurements

Circles - Perimeter of a sector (continued and application)

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

- Solve problems involving perimeter of sectors in real-life contexts
- Find unknown radius or angle given the perimeter of a sector
- Promote use of circles in real-life situations

In groups, learners are guided to:
- Solve problems where perimeter of a sector is given and find radius or angle
- Discuss real-life uses of sectors: fan blades, pie charts, irrigation pivots
- Use IT tools to explore sectors of circles and verify calculations

How are sectors of circles used in real-life situations?

Smart Minds Mathematics Grade 8 pg. 110
- Calculators
- Digital resources
- Reference books

- Written tests - Oral questions

Measurements

Area - Area of a circle
Area - Area of a sector of a circle
Area - Surface area of cubes and cuboids

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

- Derive the formula for the area of a circle from a dissected circle activity
- Calculate the area of a circle in different situations
- Apply the area of a circle to real-life situations

- Work out the surface area of closed and open cubes in real-life situations
- Work out the surface area of closed and open cuboids in real-life situations
- Appreciate the application of surface area of cubes and cuboids in real life

In groups, learners are guided to:
- Draw a circle, divide into 16 equal sectors, rearrange into an approximate rectangle; derive A = πr²
- Calculate areas of circles given radius or diameter
- Solve real-life problems: grazing area for a tethered cow, area of a circular field, area of circular plots
- Study a cube: count faces (6), find area of each face; establish Surface area = 6l²
- Study a cuboid: identify 3 pairs of rectangular faces; establish Surface area = 2(lw + lh + wh)
- Model cubes and cuboids from clay or cartons and ask peers to find their surface areas
- Solve real-life problems: surface area of dice, cartons, building blocks, tanks

How do we use area in real-life situations?
How do we work out the surface area of cubes and cuboids?

Smart Minds Mathematics Grade 8 pg. 114
- Manila paper, pair of compasses, scissors
- Calculators
- Digital resources
Smart Minds Mathematics Grade 8 pg. 118
Smart Minds Mathematics Grade 8 pg. 116
- Clay/cartons/plasticine
- Ruler
- Digital resources

- Oral questions - Written assignments
- Written assignments - Oral questions

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

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

- Oral questions - Observation - Written assignments

Measurements

Money - Simple interest

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

- Calculate simple interest using the formula SI = (P × R × T) / 100
- Calculate the amount after simple interest in real-life situations
- Use calculators to carry out operations related to money

In groups, learners are guided to:
- Discuss the simple interest formula: SI = P × R/100 × T
- Note: rate per annum requires time in years; rate per month requires time in months
- Calculate simple interest and amount for varied principals, rates and time periods
- Complete a table of principal, rate, time, simple interest and amount
- Solve real-life problems: bank loans, SACCO deposits, mobile money lending

How do we calculate simple interest?

Smart Minds Mathematics Grade 8 pg. 132
- Calculators
- Digital resources
- Reference books

- Written assignments - Oral questions

Measurements

Money - Simple interest (continued)

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

- Written tests - Oral questions

Measurements

Money - Compound interest

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

- Distinguish between simple interest and compound interest
- Calculate compound interest per annum step by step up to three years
- Appreciate that compound interest grows faster than simple interest

In groups, learners are guided to:
- Invite resource person from a financial institution or watch a video on compound interest
- Discuss: in compound interest the interest earned is added to principal at end of each year; new principal earns interest next year
- Calculate compound interest year by year for up to 3 years using: Interest = P × R/100 × 1 year
- Compare compound interest with simple interest on the same principal

How is compound interest different from simple interest?

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

- Written assignments - 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 - 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

- 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:
- 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
- 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

How do we calculate compound interest over multiple years?
What causes the value of assets to appreciate over time?

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

- Written tests - Oral questions
- Written assignments - Oral questions

Measurements

Money - Depreciation

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

- Written assignments - Oral questions

Measurements

Money - Depreciation

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

- 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

Money - Hire purchase (continued and application)
Geometrical Constructions - Construction of lines and parallel lines

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

- Construct a line of given length using a ruler and pair of compasses
- Identify and describe properties of parallel lines
- Construct parallel lines using a protractor and ruler or a pair of compasses and ruler
- Show integrity in accurate geometric construction

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
- Construct lines of given lengths using ruler and pair of compasses
- Trace and extend given lines; observe that parallel lines never meet and are equal distance apart
- Construct a line parallel to a given line using a protractor and ruler
- Construct a line parallel to a given line using a pair of compasses and ruler only

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

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
- Digital resources

- Written tests - Oral questions
- Oral questions - Observation

Geometry

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:

- Construct a perpendicular line from a point to a given line
- Construct a perpendicular line through a given point on a line
- Construct a perpendicular bisector of a line segment
- Show responsibility when handling geometric instruments

In groups, learners are guided to:
- Construct a perpendicular from an external point to a line using a pair of compasses
- Construct a perpendicular through a point on a line using a pair of compasses
- Construct a perpendicular bisector by drawing arcs from each end of the line segment
- Use a set square and ruler to construct perpendicular lines
- Verify by measuring resulting right angles with a protractor

How do we construct perpendicular lines?

Smart Minds Mathematics Grade 8 pg. 153
- Pair of compasses, ruler, set square, protractor
- Digital resources
Smart Minds Mathematics Grade 8 pg. 160
- Pair of compasses, ruler, set square

- Written assignments - Oral questions

Geometry

Geometrical Constructions - Angle properties of 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

- Oral questions - Written assignments

Geometry

Geometrical Constructions - Exterior angles in a polygon

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

- Identify exterior angles in a polygon
- Establish that the sum of exterior angles of any polygon is 360°
- Apply angle properties to solve problems involving polygons
- Show curiosity in discovering angle relationships

In groups, learners are guided to:
- Trace a polygon and extend each side; identify and measure each exterior angle
- Sum the exterior angles and establish the result is always 360°
- Complete a table: number of sides, sum of interior angles, sum of exterior angles for polygons from 3 to 6 sides
- Find missing angles in polygons using interior and exterior angle relationships

How do interior and exterior angles of polygons relate?

Smart Minds Mathematics Grade 8 pg. 171
- Protractor, ruler
- Polygon cards
- Digital resources

- Written assignments - Oral questions

Geometry

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:

- Construct an equilateral triangle and a square using a pair of compasses and ruler
- Construct a regular pentagon using a protractor and ruler
- Construct a regular hexagon using a pair of compasses and ruler
- Admire geometric patterns in objects in real life

- Construct a rectangle using a pair of compasses and ruler
- Construct a rhombus and parallelogram using a pair of compasses and ruler
- Construct an irregular pentagon
- Appreciate the use of geometric constructions in design and architecture

In groups, learners are guided to:
- Construct equilateral triangle ABC: draw AB, use A and B as centres with equal radius to locate C
- Construct square ABCD: draw AB, construct perpendicular at A, mark D; use B and D as centres to locate C
- Construct regular pentagon: draw AB, use interior angle 108° at each vertex with equal side lengths
- Construct regular hexagon using a circle: mark points 3 cm apart around circumference with compasses
- Construct rectangle ABCD: draw AB, construct perpendicular at A and B, mark off equal widths
- Construct a rhombus: draw one side, use equal radius arcs to locate other vertices
- Construct a parallelogram: draw two sides with included angle, complete using parallel lines
- Construct an irregular pentagon from given dimensions
- Visit or watch videos on construction sites where geometric shapes are applied

How do we construct regular polygons?
Where do we use polygons in real-life situations?

Smart Minds Mathematics Grade 8 pg. 173
- Pair of compasses, ruler, protractor
- Digital resources
Smart Minds Mathematics Grade 8 pg. 179
Smart Minds Mathematics Grade 8 pg. 183
- Pair of compasses, ruler, protractor
- Digital resources (videos)

- Written assignments - Observation

Geometry

Geometrical Constructions - Construction of a circumscribed 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

- 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)

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)

- Written assignments - Oral questions

Geometry

Geometrical Constructions - Review and application

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

- Apply construction skills to solve problems involving parallel lines, perpendicular lines, polygons and circles
- Select appropriate construction tools and methods for a given task
- Admire geometric patterns in objects and substances in real life

In groups, learners are guided to:
- Solve mixed construction problems involving parallel lines, perpendicular bisectors, proportional division, regular and irregular polygons, and circles
- Discuss where geometric constructions appear in architecture, art, nature and design
- Use IT construction software to verify constructions and create geometric patterns

How do we use geometric constructions in real-life situations?

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

- Written tests - Observation - Oral questions

Geometry

Coordinates and Graphs - Drawing and labelling a 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

- Oral questions - Written assignments

Geometry

Coordinates and Graphs - Identifying and plotting points on the Cartesian plane

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

- Identify points in all four quadrants on the Cartesian plane
- Plot given points on the Cartesian plane accurately
- Show confidence in working with coordinates

In groups, learners are guided to:
- Locate and write coordinates of given points in all four quadrants
- Plot points given as ordered pairs on the Cartesian plane including positive and negative coordinates
- Draw geometric shapes (triangles, rectangles, circles) by plotting and joining given vertices on the Cartesian plane
- Use IT graphing tools to plot and verify points

How do we identify and plot points on a Cartesian plane?

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

- Written assignments - Oral questions

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 - Table of values for linear equations
Coordinates and Graphs - Determining appropriate scale for linear graphs

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

- 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:
- 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
- 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

How do we generate a table of values for a linear equation?
Why is choosing an appropriate scale important when drawing a linear graph?

Smart Minds Mathematics Grade 8 pg. 203
- Graph books/grid paper
- Calculators
- Digital resources
Smart Minds Mathematics Grade 8 pg. 204
- Graph books/grid paper
- Ruler
- Digital resources

- Written assignments - Oral questions
- Oral questions - Written assignments

Geometry

Coordinates and Graphs - Drawing linear graphs on a Cartesian plane

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

- Draw a linear graph on a Cartesian plane from a table of values
- Recognise that a linear equation produces a straight-line graph
- Use IT graphing tools to draw and verify linear graphs

In groups, learners are guided to:
- Set up an appropriate scale on the Cartesian plane
- Plot points from the table of values and join them with a straight line
- Draw linear graphs for equations: x+y=6, 2x+y=8, y=2x+3, 3x+y=9
- Use IT graphing tools to draw and compare linear graphs

Where do we use linear graphs in real life?

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

- Written assignments - Oral questions

Geometry

Coordinates and Graphs - Drawing linear graphs on a Cartesian plane

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

- Draw a linear graph on a Cartesian plane from a table of values
- Recognise that a linear equation produces a straight-line graph
- Use IT graphing tools to draw and verify linear graphs

In groups, learners are guided to:
- Set up an appropriate scale on the Cartesian plane
- Plot points from the table of values and join them with a straight line
- Draw linear graphs for equations: x+y=6, 2x+y=8, y=2x+3, 3x+y=9
- Use IT graphing tools to draw and compare linear graphs

Where do we use linear graphs in real life?

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

- Written assignments - Oral questions

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

- 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:
- 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
- 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

How do we solve simultaneous equations graphically?
Where do we use simultaneous equations in real life?

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

- Written assignments - Oral questions
- Written tests - Oral questions

Geometry

Coordinates and Graphs - Simultaneous equations graphically (application)

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

- Written tests - Oral questions

Geometry

Coordinates and Graphs - Review and consolidation

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

- Written tests - Oral questions - Observation