Measurements and Geometry

Area of Polygons - Area of a triangle given two sides and an included angle

By the end of the lesson, the learner should be able to:
- Derive the formula for the area of a triangle given two sides and an included angle
- Work out the area of a triangle given two sides and an included angle
- Apply the formula to real-life problems such as calculating the area of triangular plots, fields and gardens

In groups, learners are guided to:
- Discuss in groups and use trigonometric ratios to generate the formula for the area of a triangle given two sides and an included angle (Area = ½abSinC)
- Use the formula to calculate the area of different triangular shapes

How do we work out the area of polygons?

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Area of a triangle using Heron's formula

By the end of the lesson, the learner should be able to:
- Determine the area of a triangle using Heron's formula
- Calculate the semi-perimeter and apply it in Heron's formula
- Use Heron's formula to find the area of triangular shapes in real life such as door mats, garden plots and samosa faces

In groups, learners are guided to:
- Work out the perimeter and semi-perimeter of a triangle
- Apply Heron's formula: Area = √[s(s−a)(s−b)(s−c)] to calculate the area of triangles
- Compare results with the ½abSinC formula

How do we work out the area of polygons?

- Master Core Mathematics Grade 10 pg. 148
- Rulers
- Scientific calculators

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Area of a triangle using Heron's formula

By the end of the lesson, the learner should be able to:
- Determine the area of a triangle using Heron's formula
- Calculate the semi-perimeter and apply it in Heron's formula
- Use Heron's formula to find the area of triangular shapes in real life such as door mats, garden plots and samosa faces

In groups, learners are guided to:
- Work out the perimeter and semi-perimeter of a triangle
- Apply Heron's formula: Area = √[s(s−a)(s−b)(s−c)] to calculate the area of triangles
- Compare results with the ½abSinC formula

How do we work out the area of polygons?

- Master Core Mathematics Grade 10 pg. 148
- Rulers
- Scientific calculators

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Area of parallelograms and rhombus

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Area of parallelograms and rhombus

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Area of parallelograms and rhombus

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Area of trapeziums and kites

By the end of the lesson, the learner should be able to:
- Determine the area of trapeziums using trigonometric methods
- Determine the area of kites by dividing into triangles
- Relate the area of trapeziums and kites to practical applications such as bridge supports and shutters

In groups, learners are guided to:
- Work out the area of trapeziums by finding the height using trigonometric ratios
- Divide kites into triangles and calculate the total area
- Solve problems involving real-life trapezoidal and kite shapes

How do we work out the area of polygons?

- Master Core Mathematics Grade 10 pg. 150
- Rulers and geometrical set
- Scientific calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of Polygons - Area of trapeziums and kites

By the end of the lesson, the learner should be able to:
- Determine the area of trapeziums using trigonometric methods
- Determine the area of kites by dividing into triangles
- Relate the area of trapeziums and kites to practical applications such as bridge supports and shutters

In groups, learners are guided to:
- Work out the area of trapeziums by finding the height using trigonometric ratios
- Divide kites into triangles and calculate the total area
- Solve problems involving real-life trapezoidal and kite shapes

How do we work out the area of polygons?

- Master Core Mathematics Grade 10 pg. 150
- Rulers and geometrical set
- Scientific calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of Polygons - Area of regular heptagon
Area of Polygons - Area of regular octagon
Area of Polygons - Area of irregular polygons
Area of Polygons - Application of area of irregular polygons

By the end of the lesson, the learner should be able to:
- Work out the area of a regular heptagon 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 heptagon to real-life objects such as road signs, logos and window designs

In groups, learners are guided to:
- Draw a circle and divide the circumference into seven equal parts to form a regular heptagon
- 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. 152
- Rulers, compasses and geometrical set
- Scientific calculators
- Protractors
- Master Core Mathematics Grade 10 pg. 155
- Master Core Mathematics Grade 10 pg. 158
- Rulers and geometrical set
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 159
- Digital resources

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of Polygons - Application of area of polygons to real-life situations
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

By the end of the lesson, the learner should be able to:
- Apply the concept of area of polygons to solve mixed real-life problems
- Combine different formulae to solve problems involving various polygons
- Relate area of polygons to practical applications such as landscaping, painting surfaces and material estimation

In groups, learners are guided to:
- Work out the area of various polygons from combined real-life contexts
- Use digital devices and other resources to explore more on the area of polygons in real-life situations

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

- Master Core Mathematics Grade 10 pg. 159
- Scientific calculators
- Mathematical tables
- Digital resources
- Master Core Mathematics Grade 10 pg. 161
- Circular objects
- Compasses
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 163
- Compasses and protractors
- Paper cutouts

- Observation - Oral questions - Written tests

Measurements and Geometry

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

By the end of the lesson, the learner should be able to:
- Determine the area of an annular sector
- Apply the formula Area = (θ/360) × π(R² − r²)
- Connect the area of an annular sector to real-life objects such as car wiper blade sweeps and javelin landing sectors

In groups, learners are guided to:
- Draw two concentric circles and a sector to illustrate the annular sector
- Calculate the area of the annular sector as the difference between the outer and inner sectors

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

- Master Core Mathematics Grade 10 pg. 166
- Compasses and protractors
- Rulers
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 167
- Scientific calculators
- Protractors
- Master Core Mathematics Grade 10 pg. 169
- Rulers and geometrical set

- Observation - Oral questions - Written assignments

Measurements and Geometry

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
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:
- Solve more complex problems involving the area of a segment
- Work out the area of segments when the chord length and radius are given
- Apply segment area calculations to greenhouse cross-sections, door arches and other curved structures

In groups, learners are guided to:
- Calculate the area of segments given different sets of information
- Work out problems involving segments from real-life contexts

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

- Master Core Mathematics Grade 10 pg. 171
- Scientific calculators
- Rulers and geometrical set
- Protractors
- Master Core Mathematics Grade 10 pg. 173
- Compasses and rulers
- Master Core Mathematics Grade 10 pg. 175
- 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

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area and Volume of Solids - Surface area of pyramids
Surface Area and Volume of Solids - Surface area of cones
Surface Area and Volume of Solids - Surface area of frustums

By the end of the lesson, the learner should be able to:
- Determine the surface area of pyramids (square-based, rectangular-based, hexagonal-based)
- Draw the nets of pyramids and calculate the area of each face
- Apply surface area of pyramids to real-life objects such as tents, roofs and monuments

In groups, learners are guided to:
- Determine the number of faces of each pyramid
- Draw the nets of the pyramids and calculate areas using Heron's formula and other methods
- Add the base area and the triangular face areas

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

- Master Core Mathematics Grade 10 pg. 184
- Models of pyramids
- Rulers and geometrical set
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 186
- Models of cones
- Master Core Mathematics Grade 10 pg. 188
- Models of frustums

- Observation - Oral questions - Written assignments

Measurements and Geometry

Surface Area and Volume of Solids - Surface area of spheres and hemispheres
Surface Area and Volume of Solids - Surface area of composite solids
Surface Area and Volume of Solids - Volume of prisms
Surface Area and Volume of Solids - Volume of pyramids

By the end of the lesson, the learner should be able to:
- Determine the surface area of spheres and hemispheres
- Apply the formulae SA = 4πr² (sphere) and SA = 3πr² (hemisphere)
- Relate surface area of spheres to real-life objects such as balls, chocolates and water tanks

In groups, learners are guided to:
- Collect spherical objects and measure their circumference
- Work out the radius and calculate the surface area
- Discuss how to work out the surface area of a hemisphere

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

- Master Core Mathematics Grade 10 pg. 191
- Spherical objects
- String and rulers
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 193
- Models of composite solids
- Rulers and geometrical set
- Master Core Mathematics Grade 10 pg. 196
- Models of prisms
- Rulers
- Master Core Mathematics Grade 10 pg. 198
- Models of pyramids

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area and Volume of Solids - Volume of cones
Surface Area and Volume of Solids - Volume of frustums

By the end of the lesson, the learner should be able to:
- Calculate the volume of cones
- Apply the formula Volume = ⅓πr²h
- Relate volume of cones to real-life objects such as cupcakes, grain silos and ice cream dispensers

In groups, learners are guided to:
- Collect a model of a cone and measure the base radius and slanting height
- Work out the height using Pythagoras' theorem and determine the volume
- Use models of a cone and a cylinder to demonstrate that the volume of a cone is a third of the volume of the cylinder

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

- Master Core Mathematics Grade 10 pg. 200
- Models of cones and cylinders
- Sand or water
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 201
- Models of frustums
- Rulers

- Observation - Oral questions - Written tests

Measurements and Geometry

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 spheres and hemispheres
- Apply the formulae V = ⁴⁄₃πr³ (sphere) and V = ²⁄₃πr³ (hemisphere)
- Relate volume of spheres to real-life objects such as balls, ornaments, bowls and water tanks

In groups, learners are guided to:
- Collect spherical objects and measure their circumference
- Work out the radius and calculate the volume
- Discuss and work out the volume of hemispheres

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

- Master Core Mathematics Grade 10 pg. 204
- Spherical objects
- String and rulers
- Scientific calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area and Volume of Solids - Volume of composite solids
Surface Area and Volume of Solids - Application to real-life situations
Vectors I - Vector and scalar quantities

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
- Containers from the local environment
- Scientific calculators
- Digital resources
- Master Core Mathematics Grade 10 pg. 208
- Measuring tape
- Magnetic compass
- Stopwatch

- Observation - Oral questions - Written tests

Measurements and Geometry

Vectors I - Vector notation
Vectors I - Representation of vectors
Vectors I - Equivalent vectors

By the end of the lesson, the learner should be able to:
- Write vectors using correct notation in print and handwriting
- Practise writing vector notations using bold letters, arrows and wavy lines on charts
- Relate vector notation to real-life directional signs such as road arrows and signposts that guide movement

In groups, learners are guided to:
- Use digital devices or other resources to search for vector notations
- Practise writing vector notations using charts
- Compare different ways of denoting vectors in print and handwriting and share work with peers

How do we write and identify vectors using correct notation?

- Master Core Mathematics Grade 10 pg. 209
- Charts
- Rulers
- Digital resources
- Master Core Mathematics Grade 10 pg. 210
- Graph papers
- Master Core Mathematics Grade 10 pg. 211
- Charts showing cuboids

- Oral questions - Observation - Written assignments

Measurements and Geometry

Vectors I - Addition of vectors using head-to-tail method
Vectors I - Addition of vectors using parallelogram method
Vectors I - Multiplication of vectors by scalar

By the end of the lesson, the learner should be able to:
- Add vectors using the head-to-tail (triangle) method
- Draw the resultant vector from given component vectors on a grid
- Connect vector addition to real-life situations such as combining two flight paths or two forces acting on an object

In groups, learners are guided to:
- Draw vectors on a grid and place the tail of the second vector at the head of the first
- Draw the resultant vector from the tail of the first vector to the head of the second
- Illustrate sums of vectors on graph paper and share work with peers

How do we find the resultant of two or more vectors?

- Master Core Mathematics Grade 10 pg. 213
- Graph papers
- Rulers
- Geometrical set
- Digital resources
- Master Core Mathematics Grade 10 pg. 214
- Master Core Mathematics Grade 10 pg. 216
- Charts

- Oral questions - Observation - Written assignments

Measurements and Geometry

Vectors I - Column vectors
Vectors I - Position vectors
Vectors I - Magnitude of a vector and midpoint of a vector

By the end of the lesson, the learner should be able to:
- Express vectors in column form showing horizontal and vertical components
- Represent column vectors graphically and perform operations on them
- Relate column vectors to real-life movement such as an aircraft moving a given distance east and a given distance upward

In groups, learners are guided to:
- Mark a starting point on a grid and move steps right/left and up/down to form vectors
- Write and represent column vectors graphically
- Perform addition, subtraction and scalar multiplication of column vectors and share work

How do we express a vector in column form?

- Master Core Mathematics Grade 10 pg. 218
- Graph papers
- Rulers
- Grids
- Digital resources
- Master Core Mathematics Grade 10 pg. 221
- Geometrical set
- Calculators
- Master Core Mathematics Grade 10 pg. 224

- Oral questions - Observation - Written assignments

Measurements and Geometry

Vectors I - Translation vector
Linear Motion - Distance, displacement, speed, velocity and acceleration

By the end of the lesson, the learner should be able to:
- Define and determine translation vectors as a transformation
- Find the image of a point or shape under a given translation
- Relate translation vectors to real-life movements such as sliding furniture across a room or shifting objects on a conveyor belt without rotating them

In groups, learners are guided to:
- Draw a Cartesian plane and place a triangular paper cutout, then slide it and record new coordinates
- Express the movement as a column vector and determine images of points under translation
- Draw objects and their images under translation on the same axes and share work

How do we use vectors to describe the movement of objects without turning?

- Master Core Mathematics Grade 10 pg. 227
- Graph papers
- Rulers
- Paper cutouts
- Geometrical set
- Digital resources
- Master Core Mathematics Grade 10 pg. 231
- Measuring tape
- Stopwatch

- Oral questions - Observation - Written assignments

Measurements and Geometry

Linear Motion - Velocity
Linear Motion - Acceleration and deceleration
Linear Motion - Displacement-time graph

By the end of the lesson, the learner should be able to:
- Calculate velocity given displacement and time
- Convert velocity between m/s and km/h
- Connect velocity calculations to real-life scenarios such as determining how fast an athlete runs a race or a helicopter flies between two towns

In groups, learners are guided to:
- Make an inclined plane and release a toy car or marble, timing its motion to calculate average velocity
- Work out velocity problems involving athletes, vehicles and ships
- Convert units between m/s and km/h and share work with peers

How do we calculate and use velocity in real-life situations?

- Master Core Mathematics Grade 10 pg. 232
- Rulers
- Stopwatch
- Toy car or marble
- Wooden plank
- Digital resources
- Master Core Mathematics Grade 10 pg. 234
- Measuring tape
- Ball
- Ramp
- Calculators
- Master Core Mathematics Grade 10 pg. 236
- Graph papers
- Calculators

- Oral questions - Observation - Written assignments

Measurements and Geometry

Linear Motion - Interpreting displacement-time graph
Linear Motion - Velocity-time graph
Linear Motion - Interpreting velocity-time graph
Linear Motion - Relative speed of bodies moving in opposite and same directions

By the end of the lesson, the learner should be able to:
- Interpret displacement-time graphs to describe motion of a body
- Calculate velocity from the gradient of a displacement-time graph
- Relate graph interpretation to real-life situations such as determining the speed of a car from its journey graph or identifying when a motorist stopped to rest

In groups, learners are guided to:
- Consider displacement-time graphs and describe the motion at each section
- Calculate the gradient of each section of the graph to determine velocity
- Determine displacement, velocity and rest periods from graphs and share findings

What does the gradient of a displacement-time graph represent?

- Master Core Mathematics Grade 10 pg. 238
- Graph papers
- Rulers
- Calculators
- Digital resources
- Master Core Mathematics Grade 10 pg. 241
- Stopwatch
- Ball
- Tape measure
- Calculators
- Master Core Mathematics Grade 10 pg. 244
- Master Core Mathematics Grade 10 pg. 248
- Balls

- Oral questions - Observation - Written assignments

Measurements and Geometry
Statistics and Probability
Statistics and Probability

Linear Motion - Relative speed involving delayed departure and passing lengths
Statistics I - Collection of data
Statistics I - Frequency distribution table for ungrouped data

By the end of the lesson, the learner should be able to:
- Solve problems on relative speed involving delayed departure, meeting points and passing lengths
- Determine the time and distance at which two bodies meet given different start times or breakdowns
- Relate these problems to real-life situations such as a learner chasing a school bus that left earlier, a truck overtaking a longer vehicle or a train crossing a bridge

In groups, learners are guided to:
- Solve problems involving vehicles leaving at different times and meeting en route
- Calculate the time and distance for one vehicle to catch up with another
- Solve problems involving trains crossing bridges and trucks passing through tunnels and share work

How do we solve problems when moving bodies start at different times or have different lengths?

- Master Core Mathematics Grade 10 pg. 250
- Calculators
- Rulers
- Graph papers
- Digital resources
- Master Core Mathematics Grade 10 pg. 252
- Digital resources
- Charts
- Master Core Mathematics Grade 10 pg. 254
- Rulers

- Oral questions - Observation - Written tests

Statistics and Probability

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:
- Construct frequency distribution tables for various sets of ungrouped data
- Interpret information from frequency distribution tables accurately
- Relate frequency distribution tables to real life data such as marks scored, bags of fertiliser distributed or goals scored

In groups, learners are guided to:
- Draw frequency distribution tables for different sets of data including marks, favourite sports and number of items
- Use tally marks to count and record data accurately
- Determine the sum of frequencies and verify it equals the total number of items in the distribution
- Compare and discuss results with peers

How do we use frequency distribution tables to make sense of collected data?

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

- Written assignments - Oral questions

Statistics and Probability

Statistics I - Mode and median of ungrouped data
Statistics I - Mean of grouped data
Statistics I - Mode of grouped data
Statistics I - Median 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
- Master Core Mathematics Grade 10 pg. 274

- Written assignments - Oral questions

Statistics and Probability

Statistics I - Histograms with equal class width

By the end of the lesson, the learner should be able to:
- Determine class boundaries from grouped data
- Draw histograms with equal class widths to represent grouped data
- Relate histograms to real life situations like representing scores of learners in tests, masses of athletes or goals scored by teams in a tournament

In groups, learners are guided to:
- Discuss the components of a histogram including class boundaries and frequency
- Calculate class boundaries for each class in a frequency distribution table
- Draw rectangular bars with heights proportional to frequency ensuring bars touch each other
- Use a suitable scale to represent data accurately on a histogram

How do we represent grouped data using a histogram?

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

- Written assignments - Observation

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
Statistics I - Interpretation of data from frequency polygons

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
- Master Core Mathematics Grade 10 pg. 286

- Written assignments - Oral questions

Statistics and Probability

Probability I - Experimental probability

By the end of the lesson, the learner should be able to:
- Define experimental probability and identify trials and outcomes in experiments
- Calculate experimental probability from results of experiments
- Relate experimental probability to real life situations like predicting rainfall days in a month, chances of a team winning based on past results or likelihood of arriving to school on time

- Toss a coin ten times and record the outcome as head or tail
- Carry out experiments such as throwing a die and recording the number on the top face
- Calculate experimental probability using the formula: number of favourable outcomes ÷ total number of trials
- Share findings with other learners in class

How do we use past results to predict future outcomes?

- Master Core Mathematics Grade 10 pg. 286
- Coins
- Dice
- Digital resources

- Oral questions - Observation - Written assignments

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
Probability tree diagrams - Application to real life

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

- Written assignments - Oral questions - Observation