Measurements and Geometry

Trigonometry 1 - Trigonometric ratios from table of tangents

By the end of the lesson, the learner should be able to:
- Determine the tangent of acute angles from mathematical tables
- Read and interpret the table of tangents including main columns and mean difference columns
- Relate the tangent ratio to real-life applications such as determining the slope of a roof or a ramp

In groups, learners are guided to:
- Identify from the immediate environment shapes that make right-angled triangles
- Draw right-angled triangles and use them to define the tangent ratio
- Use mathematical tables to obtain tangent values

What is trigonometry?

- Master Core Mathematics Grade 10 pg. 123
- Mathematical tables
- Rulers and geometrical set
- Calculators

- Observation - Oral questions - Written assignments

Measurements and Geometry

Trigonometry 1 - Trigonometric ratios from table of sines
Trigonometry 1 - Trigonometric ratios from table of cosines
Trigonometry 1 - Trigonometric ratios from calculators
Trigonometry 1 - Sines and cosines of complementary angles

By the end of the lesson, the learner should be able to:
- Determine the sine of acute angles from mathematical tables
- Read and interpret the table of sines including main columns and mean difference columns
- Connect the sine ratio to practical problems such as determining the height reached by a ladder against a wall

In groups, learners are guided to:
- Use mathematical tables to read and obtain sines of acute angles
- Determine angles whose sine values are given using tables
- Solve problems involving the sine ratio in right-angled triangles

What is trigonometry?

- Master Core Mathematics Grade 10 pg. 127
- Mathematical tables
- Rulers and geometrical set
- Calculators
- Master Core Mathematics Grade 10 pg. 130
- Master Core Mathematics Grade 10 pg. 132
- Scientific calculators
- Mathematical tables
- Master Core Mathematics Grade 10 pg. 134
- Rulers and geometrical set

- Observation - Oral questions - Written assignments

Measurements and Geometry

Trigonometry 1 - Relationship between sine, cosine and tangent of acute angles
Trigonometry 1 - Trigonometric ratios of special angles (45°)
Trigonometry 1 - Trigonometric ratios of special angles (30°, 60° and 90°)

By the end of the lesson, the learner should be able to:
- Relate the sine, cosine and tangent of acute angles using tan θ = sin θ / cos θ
- Determine one trigonometric ratio given the other two
- Apply the relationship to solve problems involving right-angled triangles in practical contexts

In groups, learners are guided to:
- Work in a group and using different acute angles, generate a table of the ratios of sine, cosine and tangents to establish the relationship
- Use a right-angled triangle to derive the relationship tan θ = sin θ / cos θ

How do we use trigonometry in real-life situations?

- Master Core Mathematics Grade 10 pg. 136
- Scientific calculators
- Mathematical tables
- Rulers
- Master Core Mathematics Grade 10 pg. 138
- Rulers and geometrical set
- Plain paper
- Calculators (for verification)
- Master Core Mathematics Grade 10 pg. 139

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry 1 - Angles of elevation
Trigonometry 1 - Angles of depression

By the end of the lesson, the learner should be able to:
- Apply trigonometric ratios to solve problems involving angles of elevation
- Draw sketches and use trigonometric ratios to determine unknown heights and distances
- Relate angles of elevation to practical situations such as measuring the height of buildings, trees and towers

In groups, learners are guided to:
- Identify a tall object within the school compound
- Use a protractor or clinometer to estimate the angle of elevation to the top of the object
- Use trigonometric ratios to determine the height of the object

How do we use trigonometry in real-life situations?

- Master Core Mathematics Grade 10 pg. 141
- Protractors or clinometers
- Measuring tapes
- Calculators
- Master Core Mathematics Grade 10 pg. 142

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry 1 - Combined problems on angles of elevation and depression
Area of Polygons - Area of a triangle given two sides and an included angle
Area of Polygons - Area of a triangle using Heron's formula

By the end of the lesson, the learner should be able to:
- Solve combined problems involving both angles of elevation and depression
- Draw accurate diagrams for combined elevation and depression problems
- Apply trigonometric problem-solving to real-life scenarios such as determining distances between ships from a control tower or heights of flagpoles on buildings

In groups, learners are guided to:
- Work out combined problems involving two or more angles of elevation and depression
- Use digital devices and other resources such as books, manuals and journals to learn more about trigonometric ratios

How do we use trigonometry in real-life situations?

- Master Core Mathematics Grade 10 pg. 143
- Scientific calculators
- Mathematical tables
- Rulers and geometrical set
- Master Core Mathematics Grade 10 pg. 145
- Rulers and geometrical set
- Mathematical tables
- Master Core Mathematics Grade 10 pg. 148
- Rulers
- Scientific calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of Polygons - Area of parallelograms and rhombus
Area of Polygons - Area of trapeziums and kites
Area of Polygons - Area of regular heptagon

By the end of the lesson, the learner should be able to:
- Determine the area of parallelograms using A = ab sin θ
- Determine the area of a rhombus using A = a² sin θ
- Apply the formulae to real-life objects such as cloth pieces, tiles and parking lots

In groups, learners are guided to:
- Consider a parallelogram divided into two equal triangles and derive the area formula
- Work out the area of parallelograms and rhombuses using the sine of included angles

How do we work out the area of polygons?

- Master Core Mathematics Grade 10 pg. 149
- Rulers and geometrical set
- Scientific calculators
- Mathematical tables
- Master Core Mathematics Grade 10 pg. 150
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 152
- Rulers, compasses and geometrical set
- Protractors

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Area of regular octagon
Area of Polygons - Area of irregular polygons
Area of Polygons - Application of area of irregular polygons
Area of Polygons - Application of area of polygons to real-life situations

By the end of the lesson, the learner should be able to:
- Work out the area of a regular octagon by dividing it into triangles from the centre
- Calculate the central angle and use the sine formula for triangles
- Apply the area of a regular octagon to real-life objects such as nut openers, bolt heads and floor tile patterns

In groups, learners are guided to:
- Draw a circle and divide the circumference into eight equal parts to form a regular octagon
- Join the vertices to the centre and calculate the area of each triangle formed
- Use the formula for area of a regular polygon

How do we apply the concept of the area of polygons in real-life situations?

- Master Core Mathematics Grade 10 pg. 155
- Rulers, compasses and geometrical set
- Scientific calculators
- Protractors
- Master Core Mathematics Grade 10 pg. 158
- Rulers and geometrical set
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 159
- Digital resources
- Mathematical tables

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of a Part of a Circle - Area of an annulus
Area of a Part of a Circle - Area of a sector of a circle
Area of a Part of a Circle - Area of an annular sector

By the end of the lesson, the learner should be able to:
- Determine the area of an annulus in different situations
- Calculate the area of the region between two concentric circles
- Apply the area of an annulus to real-life objects such as swimming pool pavements, roundabouts and car tyres

In groups, learners are guided to:
- Use circular shapes or objects to identify concentric rings formed by inner and outer space
- Work out the area of an annulus as the difference between the area of the outer circle and the inner circle

How do we use the concept of the area of a part of a circle in real life?

- Master Core Mathematics Grade 10 pg. 161
- Circular objects
- Compasses
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 163
- Compasses and protractors
- Paper cutouts
- Master Core Mathematics Grade 10 pg. 166
- Rulers

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of a Part of a Circle - Application of area of an annular sector
Area of a Part of a Circle - Area of a segment of a circle
Area of a Part of a Circle - Application of area of a segment
Area of a Part of a Circle - Area of common region between two intersecting circles

By the end of the lesson, the learner should be able to:
- Solve more problems involving the area of an annular sector
- Apply the concept to various real-life contexts
- Use annular sector area in practical problems such as assembly grounds, brake pads and dart boards

In groups, learners are guided to:
- Work out more examples involving area of annular sectors
- Solve problems related to annular sectors from real-life situations

How do we use the concept of the area of a part of a circle in real life?

- Master Core Mathematics Grade 10 pg. 167
- Scientific calculators
- Rulers
- Protractors
- Master Core Mathematics Grade 10 pg. 169
- Compasses and protractors
- Rulers and geometrical set
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 171
- Master Core Mathematics Grade 10 pg. 173
- Compasses and rulers

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of a Part of a Circle - Common region (finding radii and angles)
Area of a Part of a Circle - Further problems on common region

By the end of the lesson, the learner should be able to:
- Calculate the area of the common region when radii need to be determined first
- Use trigonometric ratios and simultaneous equations to find missing dimensions
- Apply the concept to problems involving overlapping umbrella shadows, intersecting street lights and coat of arms designs

In groups, learners are guided to:
- Work out more complex problems involving the common area between two intersecting circles
- Use tangent and cosine ratios to determine unknown radii and angles

How do we use the concept of the area of a part of a circle in real life?

- Master Core Mathematics Grade 10 pg. 175
- Scientific calculators
- Rulers and geometrical set
- Protractors
- Master Core Mathematics Grade 10 pg. 177
- Digital resources
- Rulers and geometrical set

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of a Part of a Circle - Application to real-life situations
Surface Area and Volume of Solids - Surface area of prisms
Surface Area and Volume of Solids - Surface area of pyramids

By the end of the lesson, the learner should be able to:
- Apply the area of a part of a circle to solve mixed real-life problems
- Combine different concepts (annulus, sector, annular sector, segment, common region)
- Relate the area of a part of a circle to practical projects such as making dartboards and beaded necklaces

In groups, learners are guided to:
- Relate and work out the area of a part of a circle in real-life situations
- Make a dartboard of different numbers of concentric circles from locally available materials
- Discuss and create rules for scoring the game

How do we use the concept of the area of a part of a circle in real life?

- Master Core Mathematics Grade 10 pg. 177
- Locally available materials
- Scientific calculators
- Digital resources
- Master Core Mathematics Grade 10 pg. 179
- Models of prisms
- Scissors
- Rulers and geometrical set
- Master Core Mathematics Grade 10 pg. 184
- Models of pyramids
- Rulers and geometrical set
- Scientific calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area and Volume of Solids - Surface area of cones
Surface Area and Volume of Solids - Surface area of frustums
Surface Area and Volume of Solids - Surface area of spheres and hemispheres
Surface Area and Volume of Solids - Surface area of composite solids

By the end of the lesson, the learner should be able to:
- Determine the surface area of cones
- Calculate the curved surface area and total surface area of a cone
- Apply surface area of cones to real-life objects such as paper cups, conical hats and tents

In groups, learners are guided to:
- Cut out the circular base and curved surface of a cone to form a net
- Calculate the surface area using Area = πr² + πrl
- Solve problems involving surface area of cones

How do we determine the surface area and volume of solids?

- Master Core Mathematics Grade 10 pg. 186
- Models of cones
- Rulers and geometrical set
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 188
- Models of frustums
- Master Core Mathematics Grade 10 pg. 191
- Spherical objects
- String and rulers
- Master Core Mathematics Grade 10 pg. 193
- Models of composite solids

- Observation - Oral questions - Written assignments

Measurements and Geometry

Surface Area and Volume of Solids - Volume of prisms
Surface Area and Volume of Solids - Volume of pyramids
Surface Area and Volume of Solids - Volume of cones

By the end of the lesson, the learner should be able to:
- Calculate the volume of prisms (triangular, rectangular, cylindrical, hexagonal)
- Apply the formula Volume = Cross-section area × Length
- Relate the volume of prisms to real-life applications such as aquariums, water pipes and metal bars

In groups, learners are guided to:
- Collect different models of prisms and discuss how to determine their volume
- Work out the cross-sectional area and multiply by the length to get the volume

How do we determine the surface area and volume of solids?

- Master Core Mathematics Grade 10 pg. 196
- Models of prisms
- Rulers
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 198
- Models of pyramids
- Rulers and geometrical set
- Master Core Mathematics Grade 10 pg. 200
- Models of cones and cylinders
- Sand or water

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area and Volume of Solids - Volume of frustums
Surface Area and Volume of Solids - Volume of spheres and hemispheres

By the end of the lesson, the learner should be able to:
- Calculate the volume of frustums of cones and pyramids
- Extend slant heights to form the original solid and subtract the volume of the cut-off part
- Apply the volume of frustums to real-life objects such as buckets, water tanks and washing sinks

In groups, learners are guided to:
- Extend the slant heights of a frustum to obtain the original solid
- Calculate the volume of the original solid and the small solid cut off
- Subtract to get the volume of the frustum

How do we determine the surface area and volume of solids?

- Master Core Mathematics Grade 10 pg. 201
- Models of frustums
- Rulers
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 204
- Spherical objects
- String and rulers

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area and Volume of Solids - Volume of composite solids

By the end of the lesson, the learner should be able to:
- Determine the volume of composite solids
- Identify the component shapes, calculate individual volumes and sum them
- Relate composite solids to real-life objects such as LPG tanks, silos and trophies

In groups, learners are guided to:
- Collect a model of a composite solid and identify all the basic shapes
- Work out the volume of each shape and add the volumes
- Solve problems involving composite solids

Why do we determine the surface area and volume of solids?

- Master Core Mathematics Grade 10 pg. 206
- Models of composite solids
- Rulers
- Scientific calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area and Volume of Solids - Application to real-life situations
Vectors I - Vector and scalar quantities
Vectors I - Vector notation
Vectors I - Representation of vectors

By the end of the lesson, the learner should be able to:
- Apply surface area and volume of solids to solve mixed real-life problems
- Combine different formulae to solve problems involving various solids
- Use the concepts of surface area and volume in practical situations such as determining quantities of materials for construction, painting and storage capacity

In groups, learners are guided to:
- Use appropriate containers from the local environment to work out the volume and capacity
- Use digital devices and other resources to work out the surface area and volume of solids
- Solve combined problems involving surface area and volume

Why do we determine the surface area and volume of solids?

- Master Core Mathematics Grade 10 pg. 206
- Containers from the local environment
- Scientific calculators
- Digital resources
- Master Core Mathematics Grade 10 pg. 208
- Measuring tape
- Magnetic compass
- Stopwatch
- Master Core Mathematics Grade 10 pg. 209
- Charts
- Rulers
- Master Core Mathematics Grade 10 pg. 210
- Graph papers

- Observation - Oral questions - Written tests

Measurements and Geometry

Vectors I - Equivalent vectors
Vectors I - Addition of vectors using head-to-tail method
Vectors I - Addition of vectors using parallelogram method

By the end of the lesson, the learner should be able to:
- Define equivalent vectors and state their properties
- Identify equivalent vectors from grids and plane figures such as cuboids
- Relate equivalent vectors to parallel lanes on a highway where vehicles move the same distance in the same direction

In groups, learners are guided to:
- Brainstorm on the meaning of equivalent vectors
- Draw different pairs of vectors with the same magnitude and direction on a graph
- Identify equivalent vectors from cuboids and grids and discuss real-life examples

When are two vectors said to be equivalent?

- Master Core Mathematics Grade 10 pg. 211
- Graph papers
- Rulers
- Charts showing cuboids
- Digital resources
- Master Core Mathematics Grade 10 pg. 213
- Geometrical set
- Master Core Mathematics Grade 10 pg. 214

- Oral questions - Observation - Written assignments

Measurements and Geometry

Vectors I - Multiplication of vectors by scalar
Vectors I - Column vectors
Vectors I - Position vectors

By the end of the lesson, the learner should be able to:
- Multiply vectors by positive, negative and zero scalars
- Simplify expressions involving scalar multiplication of vectors
- Connect scalar multiplication to real-life situations such as doubling or tripling a journey's displacement or reversing direction

In groups, learners are guided to:
- Draw a vector on a graph paper and multiply its length by 2, -2 and 0
- Draw the new vectors and compare length and direction
- Simplify vector expressions involving scalar multiples and share work with peers

What happens to a vector when it is multiplied by a scalar?

- Master Core Mathematics Grade 10 pg. 216
- Graph papers
- Rulers
- Charts
- Digital resources
- Master Core Mathematics Grade 10 pg. 218
- Grids
- Master Core Mathematics Grade 10 pg. 221
- Geometrical set
- Calculators

- Oral questions - Observation - Written assignments

Measurements and Geometry

Vectors I - Magnitude of a vector and midpoint of a vector
Vectors I - Translation vector

By the end of the lesson, the learner should be able to:
- Determine the magnitude of a vector using the Pythagorean theorem
- Calculate the midpoint of a vector given coordinates of two points
- Relate magnitude and midpoint to real-life applications such as finding the straight-line distance between two towns or the halfway point of a journey

In groups, learners are guided to:
- Draw a right-angled triangle from a vector on a grid and use Pythagoras' theorem to find the magnitude
- Calculate magnitude of different vectors and determine midpoints of given vectors
- Solve problems involving magnitude and midpoint and share work with peers

How do we determine the length of a vector and the midpoint between two points?

- Master Core Mathematics Grade 10 pg. 224
- Graph papers
- Rulers
- Calculators
- Digital resources
- Master Core Mathematics Grade 10 pg. 227
- Paper cutouts
- Geometrical set

- Oral questions - Observation - Written assignments

Measurements and Geometry

Linear Motion - Distance, displacement, speed, velocity and acceleration
Linear Motion - Velocity
Linear Motion - Acceleration and deceleration

By the end of the lesson, the learner should be able to:
- Define the terms distance, displacement, speed, velocity and acceleration
- Differentiate between distance and displacement, and between speed and velocity
- Relate the terms to everyday experiences such as walking to school, road signposts showing distances to towns and vehicle speedometers

In groups, learners are guided to:
- Use a digital device or other sources to search for the meaning of the terms distance, displacement, speed, velocity and acceleration
- Explain the difference between distance and displacement, and between speed and velocity
- Identify real-life examples from road signs and share findings with peers

What is the difference between distance and displacement?

- Master Core Mathematics Grade 10 pg. 231
- Measuring tape
- Stopwatch
- Digital resources
- Master Core Mathematics Grade 10 pg. 232
- Rulers
- Toy car or marble
- Wooden plank
- Master Core Mathematics Grade 10 pg. 234
- Ball
- Ramp
- Calculators

- Oral questions - Observation - Written assignments

Measurements and Geometry

Linear Motion - Displacement-time graph
Linear Motion - Interpreting displacement-time graph
Linear Motion - Velocity-time graph
Linear Motion - Interpreting velocity-time graph

By the end of the lesson, the learner should be able to:
- Draw displacement-time graphs from given data tables
- Select suitable scales for axes when plotting graphs
- Connect displacement-time graphs to real-life journeys such as plotting an athlete's race or a cyclist's trip between towns

In groups, learners are guided to:
- Mark a straight track and walk at a steady pace, recording displacement at intervals
- Use data tables to plot displacement-time graphs on graph paper
- Draw displacement-time graphs for journeys involving stops and return trips and share work

How do we represent a journey using a displacement-time graph?

- Master Core Mathematics Grade 10 pg. 236
- Graph papers
- Rulers
- Stopwatch
- Measuring tape
- Calculators
- Master Core Mathematics Grade 10 pg. 238
- Calculators
- Digital resources
- Master Core Mathematics Grade 10 pg. 241
- Ball
- Tape measure
- Master Core Mathematics Grade 10 pg. 244

- Oral questions - Observation - Written assignments

Measurements and Geometry
Statistics and Probability

Linear Motion - Relative speed of bodies moving in opposite and same directions
Linear Motion - Relative speed involving delayed departure and passing lengths
Statistics I - Collection of data

By the end of the lesson, the learner should be able to:
- Define relative speed and determine it for bodies moving in opposite and same directions
- Solve problems involving relative speed of vehicles
- Relate relative speed to real-life situations such as two vehicles approaching each other on a highway, one vehicle overtaking another or two trains passing on parallel tracks

In groups, learners are guided to:
- Roll two balls towards each other and in the same direction along a track to demonstrate relative speed
- Calculate relative speed for bodies moving in opposite directions (sum) and same direction (difference)
- Solve problems involving meeting times and catching up and share findings

How do we determine the speed at which two moving bodies approach or separate from each other?

- Master Core Mathematics Grade 10 pg. 248
- Tape measure
- Stopwatch
- Balls
- Calculators
- Digital resources
- Master Core Mathematics Grade 10 pg. 250
- Rulers
- Graph papers
- Master Core Mathematics Grade 10 pg. 252
- Digital resources
- Charts

- Oral questions - Observation - Written assignments

Statistics and Probability

Statistics I - Frequency distribution table for ungrouped data
Frequency distribution table for ungrouped data - Practice
Statistics I - Frequency distribution table for grouped data
Statistics I - Mean of ungrouped data

By the end of the lesson, the learner should be able to:
- Identify the components of a frequency distribution table
- Draw a frequency distribution table for ungrouped data using tally marks
- Relate frequency tables to real life situations like recording the number of siblings in a family or shoe sizes in a class

- Discuss the components of a frequency distribution table including data value, tally and frequency columns
- Collect data on the number of siblings each member of the class has
- Organise the data in a frequency distribution table arranging values from smallest to largest
- Share work with other learners in class

How do we organise raw data for easy interpretation?

- Master Core Mathematics Grade 10 pg. 254
- Digital resources
- Rulers
- Master Core Mathematics Grade 10 pg. 256
- Master Core Mathematics Grade 10 pg. 258
- Master Core Mathematics Grade 10 pg. 260
- Calculators
- Digital resources

- Oral questions - Written assignments

Statistics and Probability

Statistics I - Mode and median of ungrouped data
Statistics I - Mean of grouped data
Statistics I - Mode of grouped data

By the end of the lesson, the learner should be able to:
- Determine the mode and modal frequency of ungrouped data
- Calculate the median of ungrouped data with both odd and even number of values
- Relate mode and median to real life situations like identifying the most common shoe size, the middle age in an interview group or the most delivered quantity of milk

In groups, learners are guided to:
- Discuss the meaning of mode and identify the most occurring value in different data sets
- Identify bimodal and multimodal data sets
- Arrange data in ascending or descending order and determine the median using the position formula
- Calculate the median as the average of two middle values when the number of values is even

How do we identify the most common and middle values in a data set?

- Master Core Mathematics Grade 10 pg. 264
- Calculators
- Digital resources
- Master Core Mathematics Grade 10 pg. 268
- Master Core Mathematics Grade 10 pg. 270

- Written assignments - Oral questions

Statistics and Probability

Statistics I - Median of grouped data
Statistics I - Histograms with equal class width

By the end of the lesson, the learner should be able to:
- Construct a cumulative frequency column for grouped data
- Calculate the median of grouped data using the median formula
- Relate median of grouped data to real life situations like finding the middle age of hospital patients, the median salary of factory workers or the median power consumption of households

- Collect marks scored by learners and group into appropriate classes
- Complete a frequency distribution table with a cumulative frequency column
- Identify the median class and apply the median formula: Median = L + ((N/2 - cf)/f) × i
- Share work with other groups in class

How do we find the middle value when data is grouped into classes?

- Master Core Mathematics Grade 10 pg. 274
- Calculators
- Digital resources
- Master Core Mathematics Grade 10 pg. 278
- Graph papers
- Rulers
- Calculators

- Written assignments - Oral questions

Statistics and Probability

Statistics I - Histograms with unequal class width
Statistics I - Frequency polygons

By the end of the lesson, the learner should be able to:
- Calculate frequency density for classes with unequal widths
- Draw histograms with unequal class widths using frequency density
- Relate histograms with unequal class widths to real life situations like representing speeds of vehicles recorded at a checkpoint or heights of recruits in varying class intervals

In groups, learners are guided to:
- Discuss why frequency density is used when class widths are not uniform
- Calculate frequency density using the formula: frequency density = frequency ÷ class width
- Draw histograms using frequency density as the height of each bar
- Compare histograms with equal and unequal class widths

How do we draw histograms when classes have different widths?

- Master Core Mathematics Grade 10 pg. 280
- Graph papers
- Rulers
- Calculators
- Master Core Mathematics Grade 10 pg. 282

- Written assignments - Observation

Statistics and Probability

Statistics I - Interpretation of data from histograms

By the end of the lesson, the learner should be able to:
- Read and extract information from histograms including modal class and frequencies
- Determine the median class and draw a vertical line showing the median on a histogram
- Relate interpretation of histograms to real life situations like analysing ages of people attending a medical camp, marks in assessments or heights of finger millets on a school farm

In groups, learners are guided to:
- Study given histograms and prepare frequency distribution tables from them
- Determine the total number of items, modal frequency and modal class from histograms
- Identify the median class and draw a vertical line to show where the median lies
- Calculate the number of items above or below certain values using the histogram

What information can we extract from a histogram?

- Master Core Mathematics Grade 10 pg. 284
- Graph papers
- Rulers
- Calculators

- Written assignments - Oral questions

Statistics and Probability

Statistics I - Interpretation of data from frequency polygons
Probability I - Experimental probability

By the end of the lesson, the learner should be able to:
- Read and extract information from frequency polygons including modal class and total frequency
- Compare and analyse data from two or more frequency polygons drawn on the same axes
- Relate interpretation of frequency polygons to real life situations like analysing internet data usage by customers, bags of maize delivered by farmers or comparing daily temperatures between two towns

In groups, learners are guided to:
- Study given frequency polygons and determine the total number of items
- Identify the modal class and modal frequency from frequency polygons
- Determine the number of items above or below certain values from frequency polygons
- Compare two frequency polygons on the same axes to draw conclusions about data stability and trends

How do we use frequency polygons to make informed decisions?

- Master Core Mathematics Grade 10 pg. 286
- Graph papers
- Rulers
- Calculators
- Coins
- Dice
- Digital resources

- Written assignments - Oral questions

Statistics and Probability

Probability I - Range of probability measure
Probability I - Probability space

By the end of the lesson, the learner should be able to:
- Identify certain events and impossible events and state their probabilities
- Apply the relationship P(A) + P(A') = 1 to calculate probabilities
- Relate probability range to real life situations like the certainty of the sun rising, impossibility of being older than your parent or the chance of a factory bulb being defective

In groups, learners are guided to:
- Place three blue pens in a bag, draw one and determine the probability of getting a blue or black pen
- Roll a die once and determine the sum of probabilities of all faces showing up
- Discuss and give real life examples of impossible and certain events
- Apply the relationship P(A) + P(A') = 1 to solve problems

What are the limits of probability and what do they mean?

- Master Core Mathematics Grade 10 pg. 289
- Coins
- Dice
- Coloured pens
- Master Core Mathematics Grade 10 pg. 290
- Cards
- Spinning wheel

- Written assignments - Oral questions

Statistics and Probability

Probability I - Mutually exclusive events
Mutually exclusive events - Practice

By the end of the lesson, the learner should be able to:
- Define mutually exclusive events and identify them in different situations
- Calculate probabilities of mutually exclusive events
- Relate mutually exclusive events to real life situations like choosing between bus or walking to school, voting for one candidate in an election or selecting between STEM and Social Sciences pathways

In groups, learners are guided to:
- Discuss the meaning of mutually exclusive events and why the occurrence of one prevents the other
- Toss a coin once and determine the probability of getting a head or a tail
- Identify real life events that are mutually exclusive such as elections and career pathway choices
- Calculate probabilities where P(A and B) = 0 and P(A or B) = 1

Why can't two mutually exclusive events happen at the same time?

- Master Core Mathematics Grade 10 pg. 293
- Coins
- Marbles
- Digital resources
- Master Core Mathematics Grade 10 pg. 295
- Calculators

- Written assignments - Oral questions

Statistics and Probability

Probability I - Independent events

By the end of the lesson, the learner should be able to:
- Define independent events and distinguish them from mutually exclusive events
- Calculate the probability of independent events using P(A and B) = P(A) × P(B)
- Relate independent events to real life situations like the probability of two factory machines failing on the same day, a learner being absent while it rains or drawing balls from two separate bags

In groups, learners are guided to:
- Discuss the meaning of independent events where one event does not affect the other
- Toss a coin twice and determine the probability of getting two heads, two tails or a head and a tail
- Calculate probabilities of combined independent events using multiplication
- Solve problems involving independent events from two separate groups

How do we calculate the probability of two events that do not affect each other?

- Master Core Mathematics Grade 10 pg. 296
- Coins
- Dice
- Bags with balls

- Written assignments - Oral questions

Statistics and Probability

Probability I - Addition law of probability
Probability I - Multiplication law of probability

By the end of the lesson, the learner should be able to:
- State and apply the addition law of probability: P(A or B) = P(A) + P(B)
- Calculate the probability of either event occurring in mutually exclusive situations
- Relate addition law to real life situations like the probability of picking either a yellow or white ball from a box, rolling an odd or even number on a die or getting a specific number or a prime number

- Discuss the meaning of 'or' in probability using Junior School knowledge
- Roll a fair die and determine the probability of getting 1 or 2, an odd number or an even number
- Apply the addition law P(A or B) = P(A) + P(B) to solve problems involving mutually exclusive events
- Share work with other learners in class

When do we add probabilities together?

- Master Core Mathematics Grade 10 pg. 298
- Dice
- Balls of different colours
- Calculators
- Master Core Mathematics Grade 10 pg. 299
- Coins
- Fruit baskets

- Written assignments - Oral questions

Statistics and Probability

Probability I - Probability tree diagrams
Probability tree diagrams - Without replacement

By the end of the lesson, the learner should be able to:
- Draw probability tree diagrams showing all possible outcomes and their probabilities
- Calculate probabilities of combined events by multiplying along branches of a tree diagram
- Relate tree diagrams to real life situations like drawing coloured pens from a bag, picking counters without replacement or selecting marbles with replacement

In groups, learners are guided to:
- Toss a fair coin twice and draw a tree diagram showing all possible outcomes
- Put coloured pens in a bag, draw one, replace it and draw another, then represent using a tree diagram
- Multiply probabilities along branches to find probabilities of specific outcomes
- Determine probabilities of events such as getting two of the same colour or at least one of a specific colour

How do tree diagrams help us visualise and calculate probabilities?

- Master Core Mathematics Grade 10 pg. 301
- Coins
- Coloured pens
- Marbles
- Bags
- Master Core Mathematics Grade 10 pg. 303
- Balls of different colours
- Bags
- Calculators

- Written assignments - Oral questions - Observation

Statistics and Probability

Probability tree diagrams - Application to real life

By the end of the lesson, the learner should be able to:
- Apply probability tree diagrams to solve complex real life problems involving multiple stages
- Determine probabilities involving combined conditions from tree diagrams
- Relate probability tree diagrams to real life situations like predicting whether a learner using a motorbike or matatu will be late, determining chances of being a left-handed or right-handed boy or girl or creating and playing games related to probability

In groups, learners are guided to:
- Solve complex problems involving probability tree diagrams with real life contexts such as transport and lateness
- Draw tree diagrams for scenarios involving fractions and percentages of groups
- Calculate probabilities of compound events such as P(late), P(not late), P(right-handed girl or left-handed boy)
- Discuss, create and play games related to probability using digital devices and other resources

How do we use probability to make predictions in everyday life?

- Master Core Mathematics Grade 10 pg. 305
- Calculators
- Digital resources
- Coins
- Dice

- Written assignments - Oral questions - Observation