Algebra

Linear Inequalities - Forming and solving linear inequalities in one unknown

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

- State the meaning of a linear inequality and identify the inequality symbols (>, <, ≥, ≤) and their interpretations.
- Solve linear inequalities in one unknown including cases where the inequality sign reverses.
- Appreciate the use of inequalities in representing real-life constraints such as budgets and resource limits.

In groups, learners are guided to:

- Discuss why resources such as bursary funds are sometimes shared unequally and form inequalities to represent such scenarios.
- Form and solve linear inequalities from real-life word problems involving trophies, school fees and class sizes.
- Work out inequalities involving all four operations and discuss the rule for reversing the sign when multiplying or dividing by a negative number.

How do we form and solve linear inequalities in one unknown?

- Oxford Active Mathematics Grade 9 pg. 72
- Writing materials

- Oral questions - Written assignments - Observation

Algebra

Linear Inequalities - Graphical representation of linear inequalities in one unknown

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

- Describe the graphical representation of linear inequalities and explain the difference between a solid and broken boundary line.
- Draw the boundary line and shade the region that does not satisfy the inequality on a Cartesian plane.
- Value the clarity of graphical methods in displaying the solution set of a linear inequality.

In groups, learners are guided to:

- Draw a Cartesian plane and draw the boundary line for inequalities such as x>2 and y≤3 using a table of values.
- Determine whether the boundary line should be solid (≤,≥) or broken (>,<) and discuss the reason for each.
- Shade the region that does NOT satisfy the inequality and verify by substituting test point coordinates.

How do we represent linear inequalities in one unknown on a Cartesian plane?

- Oxford Active Mathematics Grade 9 pg. 73
- Graph paper and ruler

- Oral questions - Written assignments - Observation

Algebra

Linear Inequalities - Graphical representation of linear inequalities in one unknown

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

- Describe the graphical representation of linear inequalities and explain the difference between a solid and broken boundary line.
- Draw the boundary line and shade the region that does not satisfy the inequality on a Cartesian plane.
- Value the clarity of graphical methods in displaying the solution set of a linear inequality.

In groups, learners are guided to:

- Draw a Cartesian plane and draw the boundary line for inequalities such as x>2 and y≤3 using a table of values.
- Determine whether the boundary line should be solid (≤,≥) or broken (>,<) and discuss the reason for each.
- Shade the region that does NOT satisfy the inequality and verify by substituting test point coordinates.

How do we represent linear inequalities in one unknown on a Cartesian plane?

- Oxford Active Mathematics Grade 9 pg. 73
- Graph paper and ruler

- Oral questions - Written assignments - Observation

Algebra

Linear Inequalities - Graphical representation of linear inequalities in two unknowns

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

- Describe what a linear inequality in two unknowns represents and how it differs from one in one unknown.
- Draw the boundary line for a linear inequality in two unknowns and identify the correct region.
- Appreciate the power of graphical methods in representing constraints involving two variables simultaneously.

In groups, learners are guided to:

- Form inequalities in two unknowns from contexts such as age comparisons, costs and total capacity of transport.
- Draw a straight line from a table of values for equations such as x+y=5 and determine the region satisfying x+y<5.
- Choose test points on each side of the boundary line, substitute into the inequality and shade the region that satisfies it.

How do we represent linear inequalities in two unknowns graphically?

- Oxford Active Mathematics Grade 9 pg. 74
- Graph paper and ruler
- Writing materials

- Oral questions - Written assignments - Observation

Algebra

Linear Inequalities - Graphical representation of inequalities in two unknowns: applications

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

- Explain the steps for identifying and shading the feasible region for a linear inequality in two unknowns.
- Determine coordinate points in the feasible region that satisfy a given linear inequality.
- Develop confidence in constructing and interpreting graphical representations of two-variable inequalities.

In groups, learners are guided to:

- Represent inequalities in two unknowns such as x+y≥5 and x−y≤3 graphically on a Cartesian plane.
- Determine all coordinate points in the unshaded region and verify that each satisfies the given inequality.
- Solve problems involving school enrolment, transport planning and resource allocation using two-variable graphical inequalities.

How do we identify the feasible region satisfying a linear inequality in two unknowns?

- Oxford Active Mathematics Grade 9 pg. 75
- Graph paper and ruler

- Written assignments - Oral questions - Observation

Algebra

Linear Inequalities - Application of linear inequalities in real life

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

- Identify real-life situations where linear inequalities are used to model constraints and support decisions.
- Solve inequalities from real-life scenarios such as budgeting, capacity limits and resource sharing.
- Appreciate the role of linear inequalities in making informed and equitable decisions in everyday life.

In groups, learners are guided to:

- Solve a real-life budget problem: given a Ksh 600 budget for games and videos, form and solve a two-variable inequality and identify feasible combinations.
- Form and solve inequalities from real-life scenarios involving charity donations, factory workers' hours and county government planning.
- Discuss with family members how the knowledge of linear inequalities is applied to share resources equitably in the community.

How are linear inequalities applied in making real-life decisions?

- Oxford Active Mathematics Grade 9 pg. 77
- Writing materials
- Digital resources and internet access

- Written tests - Oral questions - Observation

Algebra

Linear Inequalities - Application of linear inequalities in real life

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

- Identify real-life situations where linear inequalities are used to model constraints and support decisions.
- Solve inequalities from real-life scenarios such as budgeting, capacity limits and resource sharing.
- Appreciate the role of linear inequalities in making informed and equitable decisions in everyday life.

In groups, learners are guided to:

- Solve a real-life budget problem: given a Ksh 600 budget for games and videos, form and solve a two-variable inequality and identify feasible combinations.
- Form and solve inequalities from real-life scenarios involving charity donations, factory workers' hours and county government planning.
- Discuss with family members how the knowledge of linear inequalities is applied to share resources equitably in the community.

How are linear inequalities applied in making real-life decisions?

- Oxford Active Mathematics Grade 9 pg. 77
- Writing materials
- Digital resources and internet access

- Written tests - Oral questions - Observation

Measurements

Area - Area of a regular pentagon
Area - Area of a regular hexagon

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

- State the formula for the area of a regular pentagon and explain the relationship between the central triangle and the polygon.
- Calculate the area of a regular pentagon by dividing it into five equal triangles.
- Appreciate the relevance of area of regular polygons in design and architecture.

In groups, learners are guided to:

- Discuss the properties of a regular pentagon and use cut-outs to divide it into triangles.
- Measure the base and height of one triangle, calculate its area and multiply by five.
- Solve real-life problems involving the area of regular pentagons such as pentagonal tiles and floor designs.

How do we work out the area of different surfaces?

- Oxford Active Mathematics Grade 9 pg. 79
- Ruler, protractor and sheets of paper
- Oxford Active Mathematics Grade 9 pg. 81
- Ruler, protractor, sheets of paper

- Oral questions - Written assignments - Observation

Measurements

Area - Surface area of prisms

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

- Identify the faces of triangular and rectangular-based prisms.
- Calculate the surface area of prisms by summing the areas of all faces using the formula 2(cross-section area) + (perimeter × length).
- Appreciate the relationship between surface area and material requirements in packaging and construction.

In groups, learners are guided to:

- Collect triangular-based prism models, open them to form nets and label all faces.
- Calculate the area of each face and add them together to find total surface area.
- Discuss and sketch nets of rectangular-based prisms, calculate the area of each face and sum.

How do we work out the area of different surfaces?

- Oxford Active Mathematics Grade 9 pg. 85
- Triangular and rectangular-based prism models
- Ruler, sheets of paper

- Written assignments - Oral questions - Observation

Measurements

Area - Surface area of pyramids
Area - Area of a sector and segment of a circle

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

- Describe the structure of triangular, rectangular and square-based pyramids.
- Calculate the surface area of pyramids by summing the areas of all faces including the base.
- Value the skill of surface area calculation in making architectural models and constructing real structures.

In groups, learners are guided to:

- Open pyramid nets, draw and label all faces including the base and lateral triangular faces.
- Calculate the area of each triangular face and the base, then sum all areas.
- Identify objects from the environment that are pyramid-shaped and calculate their surface areas.

How do we work out the area of different surfaces?

- Oxford Active Mathematics Grade 9 pg. 87
- Pyramid models, sheets of paper, ruler
- Oxford Active Mathematics Grade 9 pg. 89
- Pair of compasses, ruler, protractor
- Sheets of paper

- Written tests - Oral questions - Observation

Measurements

Area - Surface area of a cone

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

- Identify the faces of a cone and state the formula for its total surface area.
- Calculate the surface area of a cone using the formula SA = πr² + πrl.
- Appreciate the relevance of cone surface area in packaging, manufacturing and everyday objects.

In groups, learners are guided to:

- Open a paper cone to form a net, identify the circular base and curved surface.
- Measure the radius and slant height, calculate the area of each part and sum them.
- Collect cone-shaped objects from the environment and calculate their surface areas using the formula.

How do we work out the area of different surfaces?

- Oxford Active Mathematics Grade 9 pg. 93
- Paper cones, scissors, ruler, protractor

- Oral questions - Written assignments - Observation

Measurements

Area - Surface area of a sphere

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

- State the formulas for the surface area of a sphere and a hemisphere.
- Calculate the surface area of a sphere and hemisphere using SA = 4πr² and SA = 3πr² respectively.
- Value the practical application of sphere surface area in manufacturing, painting and design.

In groups, learners are guided to:

- Collect balls of different sizes, measure their diameters, calculate radii and compute surface area using 4πr².
- Discuss real-life spherical objects such as globes, sports balls and storage tanks and estimate their surface areas.
- Discuss with family members the importance of calculating surface area in painting and manufacturing.

How do we work out the area of different surfaces?

- Oxford Active Mathematics Grade 9 pg. 95
- Spherical balls of different sizes
- Ruler and writing materials

- Written tests - Oral questions - Observation

Measurements

Volume of Solids - Volume of a triangular-based prism
Volume of Solids - Volume of a rectangular-based prism

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

- State the formula for the volume of a triangular-based prism and identify its cross-section.
- Calculate the volume of a triangular-based prism using V = cross-sectional area × length.
- Appreciate the use of prism volume calculations in determining the capacity of structures such as roofs and channels.

In groups, learners are guided to:

- Collect models of triangular-based prisms, identify the cross-section and measure its dimensions and the length.
- Calculate the area of the triangular cross-section and multiply by the length to obtain the volume.
- Solve real-life problems involving the volume of triangular-based prisms such as rooftops and swimming channels.

How do we determine the volume of different solids?

- Oxford Active Mathematics Grade 9 pg. 98
- Triangular-based prism models
- Ruler and writing materials
- Oxford Active Mathematics Grade 9 pg. 100
- Rectangular-based prism models

- Oral questions - Written assignments - Observation

Measurements

Volume of Solids - Volume of a pyramid

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

- State the formula for the volume of triangular, rectangular and square-based pyramids.
- Calculate the volume of various pyramids using V = ⅓ × base area × height.
- Appreciate the geometry of pyramids and their significance in architecture and cultural heritage.

In groups, learners are guided to:

- Collect or construct pyramid models, measure the base dimensions and perpendicular height.
- Apply the formula V = ⅓bh to calculate the volumes of pyramids of different shapes.
- Use relevant formulas to compare the volumes of a prism and a pyramid with the same base and height.

How do we determine the volume of different solids?

- Oxford Active Mathematics Grade 9 pg. 101
- Pyramid models (clay or cut paper)
- Ruler and writing materials

- Written assignments - Oral questions - Observation

Measurements

Volume of Solids - Volume of a pyramid

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

- State the formula for the volume of triangular, rectangular and square-based pyramids.
- Calculate the volume of various pyramids using V = ⅓ × base area × height.
- Appreciate the geometry of pyramids and their significance in architecture and cultural heritage.

In groups, learners are guided to:

- Collect or construct pyramid models, measure the base dimensions and perpendicular height.
- Apply the formula V = ⅓bh to calculate the volumes of pyramids of different shapes.
- Use relevant formulas to compare the volumes of a prism and a pyramid with the same base and height.

How do we determine the volume of different solids?

- Oxford Active Mathematics Grade 9 pg. 101
- Pyramid models (clay or cut paper)
- Ruler and writing materials

- Written assignments - Oral questions - Observation

Measurements

Volume of Solids - Volume of a cone

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

- State the formula for the volume of a cone and explain each variable.
- Calculate the volume of a cone using the formula V = ⅓πr²h.
- Appreciate the application of cone volume in everyday containers such as funnels, ice cream cones and silos.

In groups, learners are guided to:

- Collect cone-shaped objects such as funnels and party hats, measure the radius and height.
- Apply the formula V = ⅓πr²h to calculate the volume of the cone.
- Compare the volume of a cone with a cylinder of the same base and height and discuss the relationship.

How do we determine the volume of different solids?

- Oxford Active Mathematics Grade 9 pg. 103
- Cone-shaped models and containers
- Ruler and writing materials

- Oral questions - Written assignments - Observation

Measurements

Volume of Solids - Volume of a frustum

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

- Describe a frustum and explain how it is derived by cutting a pyramid or cone.
- Calculate the volume of a frustum by subtracting the volume of the smaller solid from the larger one.
- Value the ability to calculate the volume of frustums in real-life containers such as buckets and flower pots.

In groups, learners are guided to:

- Cut a pyramid model into two parts to form a frustum and a smaller pyramid, calculate the volume of each.
- Use the formula: volume of frustum = volume of large pyramid − volume of small pyramid.
- Solve real-life problems involving the volume of frustum-shaped containers and objects.

How do we determine the volume of different solids?

- Oxford Active Mathematics Grade 9 pg. 105
- Pyramid models
- Ruler and writing materials

- Written tests - Oral questions - Observation

Measurements

Volume of Solids - Volume of a sphere

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

- State the formula for the volume of a sphere and explain each term.
- Calculate the volume of a sphere using the formula V = 4/3πr³.
- Appreciate the application of sphere volume in manufacturing spherical tanks, balls and globes.

In groups, learners are guided to:

- Collect balls of different sizes, measure the diameter, calculate the radius and compute volume using V = 4/3πr³.
- Discuss real-life spherical objects and estimate their volumes using the formula.
- Play games involving different-sized balls and work out their volumes using the formula.

How do we use the volume of solids in real-life situations?

- Oxford Active Mathematics Grade 9 pg. 107
- Spherical balls of different sizes
- Ruler and writing materials

- Oral questions - Written assignments - Observation

Measurements

Volume of Solids - Volume of a sphere

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

- State the formula for the volume of a sphere and explain each term.
- Calculate the volume of a sphere using the formula V = 4/3πr³.
- Appreciate the application of sphere volume in manufacturing spherical tanks, balls and globes.

In groups, learners are guided to:

- Collect balls of different sizes, measure the diameter, calculate the radius and compute volume using V = 4/3πr³.
- Discuss real-life spherical objects and estimate their volumes using the formula.
- Play games involving different-sized balls and work out their volumes using the formula.

How do we use the volume of solids in real-life situations?

- Oxford Active Mathematics Grade 9 pg. 107
- Spherical balls of different sizes
- Ruler and writing materials

- Oral questions - Written assignments - Observation

Measurements

Volume of Solids - Application of volume of solids in real life

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

- Identify real-life contexts where volumes of prisms, pyramids, cones, frustums and spheres are applied.
- Solve real-life problems involving volumes of different solids using appropriate formulas.
- Value the knowledge of volume in making practical decisions in construction and manufacturing.

In groups, learners are guided to:

- Solve multi-step problems involving volumes of containers, tanks and structures using relevant formulas.
- Discuss with family members how knowledge of volume is used in construction and packaging.
- Use IT tools to explore and calculate the volumes of different solid objects in engineering contexts.

How do we use the volume of solids in real-life situations?

- Oxford Active Mathematics Grade 9 pg. 108
- Writing materials
- Internet access

- Written tests - Oral questions - Observation

Measurements

Mass, Volume, Weight and Density - Conversion of units of mass

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

- State the units of mass and explain the relationships between kg, g, mg, Dg, hg and tonne.
- Convert units of mass from one form to another in different situations.
- Appreciate the importance of accurate mass measurement in trade and consumer protection.

In groups, learners are guided to:

- Study and identify different instruments used for measuring mass including balances and scales.
- Discuss the units of mass (kg, g, mg, hg, Dg, t) and their conversion factors using the ×10/÷10 rule.
- Solve problems involving conversion of mass units in real-life contexts such as weighing produce and luggage.

How do you weigh materials and objects?

- Oxford Active Mathematics Grade 9 pg. 110
- Beam balance or electronic balance
- Objects of different masses

- Oral questions - Written assignments - Observation

Measurements

Mass, Volume, Weight and Density - Conversion of units of mass

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

- State the units of mass and explain the relationships between kg, g, mg, Dg, hg and tonne.
- Convert units of mass from one form to another in different situations.
- Appreciate the importance of accurate mass measurement in trade and consumer protection.

In groups, learners are guided to:

- Study and identify different instruments used for measuring mass including balances and scales.
- Discuss the units of mass (kg, g, mg, hg, Dg, t) and their conversion factors using the ×10/÷10 rule.
- Solve problems involving conversion of mass units in real-life contexts such as weighing produce and luggage.

How do you weigh materials and objects?

- Oxford Active Mathematics Grade 9 pg. 110
- Beam balance or electronic balance
- Objects of different masses

- Oral questions - Written assignments - Observation

Measurements

Mass, Volume, Weight and Density - Conversion of units of mass: applications

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

- Identify practical situations where mass unit conversions are necessary.
- Solve problems requiring conversion of mass units in different real-life situations.
- Value the skill of mass conversion in ensuring accurate measurement and consumer protection.

In groups, learners are guided to:

- Collect and weigh different materials using a beam balance or electronic balance and record masses in different units.
- Convert between units by multiplying or dividing by the appropriate factor and verify answers.
- Solve real-life problems involving mass conversion such as weighing farm produce, ingredients and packages.

How do you weigh materials and objects?

- Oxford Active Mathematics Grade 9 pg. 111
- Beam balance and electronic balance
- Sand, stones and other materials

- Written assignments - Oral questions - Observation

Measurements

Mass, Volume, Weight and Density - Mass and weight

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

- Explain the difference between mass and weight and state the formula W = mg.
- Calculate weight from mass using the gravitational constant g = 10 N/kg.
- Value accurate measurement of mass and weight in ensuring consumer protection and health safety.

In groups, learners are guided to:

- Discuss the difference between mass and weight using different objects on a balance.
- Measure the mass of objects, then calculate weight using W = mg.
- Discuss contexts where both mass and weight are used such as weighing luggage, food and body health.

How do you weigh materials and objects?

- Oxford Active Mathematics Grade 9 pg. 113
- Beam balance or electronic balance
- Objects of different masses

- Oral questions - Written assignments - Observation

Measurements

Mass, Volume, Weight and Density - Mass, volume and density

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

- Define density and state the formula ρ = m/V.
- Calculate density given the mass and volume of a substance.
- Appreciate the concept of density in explaining why some objects float and others sink.

In groups, learners are guided to:

- Collect cuboid-shaped blocks of different materials, measure their mass using a balance and dimensions using a ruler.
- Calculate the volume of each block and divide by mass to obtain density.
- Compare densities of different materials and discuss why denser objects sink in water.

How do you weigh materials and objects?

- Oxford Active Mathematics Grade 9 pg. 114
- Cuboid blocks of different substances
- Beam balance and ruler

- Oral questions - Written assignments - Observation

Measurements

Mass, Volume, Weight and Density - Calculating mass, volume and density

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

- Describe the relationships among mass, volume and density using the formula ρ = m/V.
- Calculate mass, volume and density of different substances using the relevant formula.
- Value the use of density calculations in science, engineering and identifying materials.

In groups, learners are guided to:

- Fill containers of known volume with different substances (water, sand), measure the mass and calculate density.
- Rearrange the density formula to calculate mass (m = ρV) and volume (V = m/ρ) in different problems.
- Solve problems involving mass, volume and density in different real-life situations using IT devices or other resources.

How do you weigh materials and objects?

- Oxford Active Mathematics Grade 9 pg. 115
- Cylindrical containers, beam balance
- Sand, water and different substances

- Written assignments - Oral questions - Observation

Measurements

Mass, Volume, Weight and Density - Calculating mass, volume and density

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

- Describe the relationships among mass, volume and density using the formula ρ = m/V.
- Calculate mass, volume and density of different substances using the relevant formula.
- Value the use of density calculations in science, engineering and identifying materials.

In groups, learners are guided to:

- Fill containers of known volume with different substances (water, sand), measure the mass and calculate density.
- Rearrange the density formula to calculate mass (m = ρV) and volume (V = m/ρ) in different problems.
- Solve problems involving mass, volume and density in different real-life situations using IT devices or other resources.

How do you weigh materials and objects?

- Oxford Active Mathematics Grade 9 pg. 115
- Cylindrical containers, beam balance
- Sand, water and different substances

- Written assignments - Oral questions - Observation

Measurements

Mass, Volume, Weight and Density - Application of density

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

- Identify real-life situations where density is applied such as in materials science and fluid mechanics.
- Determine the density of different liquids and solids through practical investigation.
- Appreciate the role of density in differentiating substances and making informed materials choices.

In groups, learners are guided to:

- Fill a cylindrical container with water, measure mass and calculate density; repeat with salty water and cooking oil.
- Compare densities of different liquids and discuss floatation using the concept of relative density.
- Solve complex problems involving density, volume and mass of different solid and liquid substances.

How do you weigh materials and objects?

- Oxford Active Mathematics Grade 9 pg. 116
- Cylindrical containers, measuring cylinder
- Liquids (water, oil), solid objects

- Oral questions - Written tests - Observation

Measurements

Mass, Volume, Weight and Density - Application of density

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

- Identify real-life situations where density is applied such as in materials science and fluid mechanics.
- Determine the density of different liquids and solids through practical investigation.
- Appreciate the role of density in differentiating substances and making informed materials choices.

In groups, learners are guided to:

- Fill a cylindrical container with water, measure mass and calculate density; repeat with salty water and cooking oil.
- Compare densities of different liquids and discuss floatation using the concept of relative density.
- Solve complex problems involving density, volume and mass of different solid and liquid substances.

How do you weigh materials and objects?

- Oxford Active Mathematics Grade 9 pg. 116
- Cylindrical containers, measuring cylinder
- Liquids (water, oil), solid objects

- Oral questions - Written tests - Observation

Measurements

Mass, Volume, Weight and Density - Application of density in real life

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

- Discuss real-life applications of density including floatation, construction and food science.
- Solve complex problems involving mass, volume, weight and density in different contexts.
- Value the knowledge of density and its applications in making informed daily decisions.

In groups, learners are guided to:

- Investigate whether different objects float or sink in water and relate the observations to their densities.
- Use IT tools to explore how density is measured and applied in industry and food science.
- Discuss with family members situations where density knowledge is applied in solving daily problems.

How do you weigh materials and objects?

- Oxford Active Mathematics Grade 9 pg. 117
- Water containers, objects of different densities
- Internet access

- Written tests - Oral questions - Observation

Measurements

Time, Distance and Speed - Speed in metres per second

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

- State the formula for speed and explain the relationship between distance, time and speed.
- Calculate speed in metres per second from given distance and time values.
- Appreciate the use of speed calculations in sports, transport and safety planning.

- Run or walk a 100 m race, record the time taken for each learner and calculate speed in m/s.
- Discuss the formula speed = distance ÷ time and solve problems using different units.
- Solve real-life problems involving athletes, vehicles and animals using speed in m/s.

How do we observe speed in daily activities?

- Oxford Active Mathematics Grade 9 pg. 121
- Stopwatches or clocks
- Tape measure

- Oral questions - Written assignments - Observation

Measurements

Time, Distance and Speed - Speed in kilometres per hour

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

- Describe the relationship between speed in m/s and km/h and state the conversion factor.
- Calculate speed in km/h and convert between m/s and km/h accurately.
- Value the application of speed in km/h in road transport, journey planning and road safety.

In groups, learners are guided to:

- Use distance-time graphs to determine speed in km/h for different journeys.
- Calculate speed using distances between real Kenyan towns and actual journey times.
- Solve problems involving journeys between towns and discuss speed limits and road safety.

How do we observe speed in daily activities?

- Oxford Active Mathematics Grade 9 pg. 122
- Graph paper and ruler
- Writing materials

- Oral questions - Written assignments - Observation

Measurements

Time, Distance and Speed - Speed in kilometres per hour

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

- Describe the relationship between speed in m/s and km/h and state the conversion factor.
- Calculate speed in km/h and convert between m/s and km/h accurately.
- Value the application of speed in km/h in road transport, journey planning and road safety.

In groups, learners are guided to:

- Use distance-time graphs to determine speed in km/h for different journeys.
- Calculate speed using distances between real Kenyan towns and actual journey times.
- Solve problems involving journeys between towns and discuss speed limits and road safety.

How do we observe speed in daily activities?

- Oxford Active Mathematics Grade 9 pg. 122
- Graph paper and ruler
- Writing materials

- Oral questions - Written assignments - Observation

Measurements

Time, Distance and Speed - Average speed

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

- Explain the concept of average speed and how it differs from instantaneous speed.
- Calculate average speed for journeys with different speeds over different distances.
- Appreciate the relevance of average speed in planning multi-stage journeys and road safety.

In groups, learners are guided to:

- Analyse scenarios where a vehicle travels at different speeds on different legs of a journey.
- Work out average speed using total distance ÷ total time taken for the whole journey.
- Solve problems involving average speed in real-life transport scenarios such as bus, lorry and cyclist journeys.

How do we observe speed in daily activities?

- Oxford Active Mathematics Grade 9 pg. 123
- Writing materials

- Oral questions - Written assignments - Observation

Measurements

Time, Distance and Speed - Average speed: applications

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

- Identify situations where average speed calculations are applied in real life.
- Solve multi-step problems involving average speed with stops and different legs of a journey.
- Develop a positive attitude towards using mathematical tools to plan and optimise travel.

In groups, learners are guided to:

- Calculate average speed for journeys with rest stops, different speeds on different sections and return trips.
- Analyse distance-time graphs to determine average speed for each segment of a journey.
- Solve problems involving journeys with multiple speed changes and stops at intermediate points.

How do we observe speed in daily activities?

- Oxford Active Mathematics Grade 9 pg. 124
- Graph paper and writing materials

- Written tests - Oral questions - Observation

Measurements

Time, Distance and Speed - Velocity

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

- Explain the difference between speed and velocity and define displacement.
- Distinguish between speed and velocity and calculate velocity in given real-life situations.
- Appreciate the precision of velocity in describing motion in physics and engineering.

In groups, learners are guided to:

- Discuss the difference between distance and displacement using diagrams with directional arrows.
- Determine velocity of objects moving in specified directions and compare with speed values.
- Solve problems that distinguish between speed and velocity in real-life contexts.

How do we observe speed in daily activities?

- Oxford Active Mathematics Grade 9 pg. 125
- Writing materials

- Oral questions - Written assignments - Observation

Measurements

Time, Distance and Speed - Velocity

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

- Explain the difference between speed and velocity and define displacement.
- Distinguish between speed and velocity and calculate velocity in given real-life situations.
- Appreciate the precision of velocity in describing motion in physics and engineering.

In groups, learners are guided to:

- Discuss the difference between distance and displacement using diagrams with directional arrows.
- Determine velocity of objects moving in specified directions and compare with speed values.
- Solve problems that distinguish between speed and velocity in real-life contexts.

How do we observe speed in daily activities?

- Oxford Active Mathematics Grade 9 pg. 125
- Writing materials

- Oral questions - Written assignments - Observation

Measurements

Time, Distance and Speed - Acceleration

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

- Define acceleration and state the formula a = (v−u)/t.
- Calculate acceleration and deceleration using given initial velocity, final velocity and time values.
- Value the understanding of acceleration in road safety, sport science and engineering applications.

In groups, learners are guided to:

- Participate in short running events, record the starting and finishing velocities, calculate acceleration.
- Use stopwatch and tape measure to measure time and distance, then determine acceleration.
- Solve problems involving acceleration and deceleration using the formula a = (v−u)/t.

How do we observe speed in daily activities?

- Oxford Active Mathematics Grade 9 pg. 126
- Stopwatch and tape measure

- Written assignments - Oral questions - Observation

Measurements

Time, Distance and Speed - Longitudes on the globe

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

- Identify and describe longitudes on the globe including the Greenwich Meridian and their labelling.
- Distinguish between longitudes east and west of the Greenwich Meridian using a globe or map.
- Appreciate the global system of longitudes and their role in navigation and geography.

In groups, learners are guided to:

- Study a globe or maps and identify longitudes as imaginary lines running from north to south.
- Identify the Greenwich Meridian and distinguish east (0°–180°E) and west (0°–180°W) longitudes.
- Use a globe and maps to identify the longitudes of different cities in Kenya and across the world.

Why does time vary in different places of the world?

- Oxford Active Mathematics Grade 9 pg. 126
- Globe or map of the world

- Oral questions - Written assignments - Observation

Measurements

Time, Distance and Speed - Longitudes on the globe

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

- Identify and describe longitudes on the globe including the Greenwich Meridian and their labelling.
- Distinguish between longitudes east and west of the Greenwich Meridian using a globe or map.
- Appreciate the global system of longitudes and their role in navigation and geography.

In groups, learners are guided to:

- Study a globe or maps and identify longitudes as imaginary lines running from north to south.
- Identify the Greenwich Meridian and distinguish east (0°–180°E) and west (0°–180°W) longitudes.
- Use a globe and maps to identify the longitudes of different cities in Kenya and across the world.

Why does time vary in different places of the world?

- Oxford Active Mathematics Grade 9 pg. 126
- Globe or map of the world

- Oral questions - Written assignments - Observation

Measurements

Time, Distance and Speed - Longitudes and local time

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

- Explain how the earth's rotation relates to time differences across longitudes.
- Calculate the local time of a place given its longitude and the time at another location.
- Appreciate the global significance of time zones in international communication and travel.

In groups, learners are guided to:

- Discuss the relationship between longitudes and time using a globe and a light source.
- Calculate time differences between two places using longitude difference × 4 minutes per degree.
- Use IT devices to explore time zones in different parts of the world and solve real-life time problems.

Why does time vary in different places of the world?

- Oxford Active Mathematics Grade 9 pg. 127
- Globe, maps
- Digital resources and internet access

- Written tests - Oral questions - Observation

Measurements

Money - Currencies of other countries

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

- Identify currencies used in different countries and explain the concept of currency exchange.
- Distinguish between buying and selling rates of currency exchange.
- Appreciate the global nature of currency exchange in international trade and travel.

In groups, learners are guided to:

- Collect cut-outs of different currencies from old newspapers and magazines and match each to its country.
- Use digital devices to search for and list currencies of various countries.
- Visit a nearby bank or financial institution to find out the buying and selling rates of different currencies.

Why do we change currencies from one form to another?

- Oxford Active Mathematics Grade 9 pg. 132
- Old newspapers and magazines
- Digital devices and internet access

- Oral questions - Written assignments - Observation

Measurements

Money - Conversion of currencies

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

- Describe how currency conversion works using buying and selling rates from financial institutions.
- Calculate the amount received when converting currencies using given exchange rates.
- Value accurate currency conversion in protecting consumers during trade and travel.

In groups, learners are guided to:

- Use newspapers or visit financial institutions to find current exchange rates for different currencies.
- Fill in a currency exchange rate table and use it to convert between currencies.
- Solve worked examples converting Kenya shillings to foreign currencies and vice versa.

Why do we change currencies from one form to another?

- Oxford Active Mathematics Grade 9 pg. 133
- Newspapers with currency exchange rates
- Digital devices

- Oral questions - Written assignments - Observation

Measurements

Money - Conversion of currencies

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

- Describe how currency conversion works using buying and selling rates from financial institutions.
- Calculate the amount received when converting currencies using given exchange rates.
- Value accurate currency conversion in protecting consumers during trade and travel.

In groups, learners are guided to:

- Use newspapers or visit financial institutions to find current exchange rates for different currencies.
- Fill in a currency exchange rate table and use it to convert between currencies.
- Solve worked examples converting Kenya shillings to foreign currencies and vice versa.

Why do we change currencies from one form to another?

- Oxford Active Mathematics Grade 9 pg. 133
- Newspapers with currency exchange rates
- Digital devices

- Oral questions - Written assignments - Observation

Measurements

Money - Conversion of currencies: applications

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

- Identify situations where currency conversion is used in international trade and travel.
- Solve real-life problems involving conversion between different world currencies.
- Develop awareness of financial literacy and consumer protection in international transactions.

In groups, learners are guided to:

- Solve multi-step problems converting US dollars, Euros, Pounds, Yen and other currencies to and from Kenya shillings.
- Discuss the effect of exchange rate changes on the cost of imported goods.
- Use IT tools to find current exchange rates and apply them to solve real-life problems.

Why do we change currencies from one form to another?

- Oxford Active Mathematics Grade 9 pg. 134
- Writing materials
- Internet access

- Written tests - Oral questions - Observation

Measurements

Money - Import duty and excise duty

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

- Define import duty, excise duty and customs value and explain when each applies.
- Calculate import duty and excise duty charged on goods using given rates.
- Appreciate the role of import and excise duty in generating government revenue and protecting local industries.

In groups, learners are guided to:

- Visit the Kenya Revenue Authority (KRA) or invite a resource person to discuss import and excise duties.
- Work out import duty from given customs values and rates using the formula: duty = rate × customs value.
- Research goods exempted from import duty in Kenya and discuss the economic rationale.

How do we determine taxes charged on different goods?

- Oxford Active Mathematics Grade 9 pg. 136
- KRA resource materials
- Writing materials

- Written assignments - Oral questions - Observation

Measurements

Money - Import duty and excise duty

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

- Define import duty, excise duty and customs value and explain when each applies.
- Calculate import duty and excise duty charged on goods using given rates.
- Appreciate the role of import and excise duty in generating government revenue and protecting local industries.

In groups, learners are guided to:

- Visit the Kenya Revenue Authority (KRA) or invite a resource person to discuss import and excise duties.
- Work out import duty from given customs values and rates using the formula: duty = rate × customs value.
- Research goods exempted from import duty in Kenya and discuss the economic rationale.

How do we determine taxes charged on different goods?

- Oxford Active Mathematics Grade 9 pg. 136
- KRA resource materials
- Writing materials

- Written assignments - Oral questions - Observation

Measurements

Money - Value Added Tax

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

- Define Value Added Tax (VAT) and explain how it is calculated on goods and services.
- Calculate VAT using the formula VAT = rate × (customs value + import duty + excise duty).
- Value the role of VAT in public revenue generation and recognise it on shopping receipts.

In groups, learners are guided to:

- Collect shopping receipts and identify the VAT charged and the rate applied.
- Work out VAT on different items using the given formula and the 16% standard rate.
- Discuss imported and local goods that attract VAT and calculate the total cost of goods inclusive of VAT.

How do we determine taxes charged on different goods?

- Oxford Active Mathematics Grade 9 pg. 139
- Shopping receipts
- Writing materials

- Oral questions - Written assignments - Observation

Measurements

Money - Export duty and application of taxes in real life

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

- Define export duty and identify goods that attract export duty.
- Calculate export duty charged on exported goods using given rates.
- Appreciate the importance of paying taxes in supporting national development and public services.

In groups, learners are guided to:

- Discuss and research goods that attract export duty and those that are exempted in Kenya.
- Solve problems calculating export duty using the formula: duty = rate × value of export.
- Discuss with family members the different types of taxes and why paying taxes is important for national development.

How do we determine taxes charged on different goods?

- Oxford Active Mathematics Grade 9 pg. 140
- KRA resource materials
- Internet access

- Written tests - Oral questions - Observation

Measurements

Approximations and Errors - Approximation of quantities using arbitrary units

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

- Define an arbitrary unit and describe its use in approximating measurements of different quantities.
- Approximate lengths, areas, volumes, capacities and masses using arbitrary units.
- Appreciate the role of approximation in everyday measurement when standard tools are unavailable.

In groups, learners are guided to:

- Measure the classroom length in palm lengths, foot lengths and strides and compare results.
- Approximate the area of a surface using small and large squares and record findings.
- Approximate the volume of a box using small and large cubes and the capacity of containers using cups and jugs.

How do we estimate measurements of different quantities?

- Oxford Active Mathematics Grade 9 pg. 142
- Sticks, string, cups, jugs
- Small and large squares (cut paper)

- Oral questions - Written assignments - Observation

Measurements

Approximations and Errors - Errors in estimation of measurements

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

- Explain the concept of measurement error and how it arises from estimation.
- Calculate the error in a measurement by computing the difference between estimated and actual values.
- Develop a sense of responsibility in minimising errors when measuring quantities.

In groups, learners are guided to:

- Estimate the length of objects using palm lengths then measure with a ruler; record both values.
- Calculate the error = estimated measurement − actual measurement for each object.
- Discuss real-life situations where estimation errors have consequences such as in construction and medicine.

How do we estimate measurements of different quantities?

- Oxford Active Mathematics Grade 9 pg. 144
- Ruler, beam balance
- Objects of different sizes

- Written assignments - Oral questions - Observation

Measurements

Approximations and Errors - Errors in estimation of measurements

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

- Explain the concept of measurement error and how it arises from estimation.
- Calculate the error in a measurement by computing the difference between estimated and actual values.
- Develop a sense of responsibility in minimising errors when measuring quantities.

In groups, learners are guided to:

- Estimate the length of objects using palm lengths then measure with a ruler; record both values.
- Calculate the error = estimated measurement − actual measurement for each object.
- Discuss real-life situations where estimation errors have consequences such as in construction and medicine.

How do we estimate measurements of different quantities?

- Oxford Active Mathematics Grade 9 pg. 144
- Ruler, beam balance
- Objects of different sizes

- Written assignments - Oral questions - Observation

Measurements

Approximations and Errors - Percentage errors

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

- Describe percentage error and explain how it relates the error to the actual measurement.
- Calculate percentage error using the formula: percentage error = (error ÷ actual measurement) × 100%.
- Appreciate the use of percentage error in quality control and scientific measurement contexts.

In groups, learners are guided to:

- Estimate and measure different quantities (length, capacity, mass) and calculate the raw error for each.
- Apply the percentage error formula to each measurement and compare results across different quantities.
- Use IT devices to compute percentage errors and relate findings to consumer protection and quality assurance.

How do we estimate measurements of different quantities?

- Oxford Active Mathematics Grade 9 pg. 146
- Ruler, measuring cylinder, beam balance
- Internet access

- Written tests - Oral questions - Observation

Measurements

Approximations and Errors - Percentage errors

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

- Describe percentage error and explain how it relates the error to the actual measurement.
- Calculate percentage error using the formula: percentage error = (error ÷ actual measurement) × 100%.
- Appreciate the use of percentage error in quality control and scientific measurement contexts.

In groups, learners are guided to:

- Estimate and measure different quantities (length, capacity, mass) and calculate the raw error for each.
- Apply the percentage error formula to each measurement and compare results across different quantities.
- Use IT devices to compute percentage errors and relate findings to consumer protection and quality assurance.

How do we estimate measurements of different quantities?

- Oxford Active Mathematics Grade 9 pg. 146
- Ruler, measuring cylinder, beam balance
- Internet access

- Written tests - Oral questions - Observation

Measurements

Approximations and Errors - Application of approximations and errors in real life

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

- Identify real-life situations where approximations and errors are relevant such as in trade, science and engineering.
- Solve problems involving approximations and errors in various measurement contexts.
- Value accuracy and precision in measurement as a foundation for consumer protection and scientific inquiry.

In groups, learners are guided to:

- Solve real-life problems involving errors and percentage errors in capacity, mass and length measurements.
- Discuss how errors in measurement affect trade and consumer protection in everyday buying and selling.
- Discuss with family members how knowledge of approximations and errors is applied in their daily work and home activities.

How do we estimate measurements of different quantities?

- Oxford Active Mathematics Grade 9 pg. 148
- Writing materials
- Digital resources and internet access

- Written tests - Oral questions - Observation