Measurements and Geometry

Area of a Part of a Circle - Calculating common area
Area of a Part of a Circle - Complex problems

By the end of the lesson, the learner should be able to:
- Calculate area of common region
- Sum areas of two segments
- Solve problems involving intersecting circles

In groups, learners are guided to:
- Calculate area of each segment
- Sum to get common area
- Solve practical problems

How do we calculate the common area?

- Mentor Core Mathematics Grade 10 pg. 177
- Calculators
- Geometrical instruments
- Mentor Core Mathematics Grade 10 pg. 179
- Reference materials
- Digital devices
- Calculators

- Written tests - Class exercises - Observation

Measurements and Geometry

Area of a Part of a Circle - Making dartboard and necklaces
Area of a Part of a Circle - Review and assessment

By the end of the lesson, the learner should be able to:
- Make dartboard using concentric circles
- Create beaded necklaces using annular sectors
- Apply concepts creatively

In groups, learners are guided to:
- Make dartboard from available materials
- Create necklaces using beading techniques
- Present projects

How do we apply area concepts in creating designs?

- Mentor Core Mathematics Grade 10 pg. 180
- Cardboard
- Beads
- Paints
- Compasses
- Mentor Core Mathematics Grade 10 pg. 181
- Calculators
- Past papers

- Project assessment - Peer evaluation - Observation

Measurements and Geometry

Surface Area and Volume - Rectangular prism
Surface Area and Volume - Triangular and other prisms

By the end of the lesson, the learner should be able to:
- Determine surface area of rectangular prisms
- Draw nets of rectangular prisms
- Apply to packaging and construction

In groups, learners are guided to:
- Collect models of rectangular prisms
- Sketch nets
- Calculate surface area

How do we calculate surface area of rectangular prisms?

- Mentor Core Mathematics Grade 10 pg. 182
- Models of prisms
- Nets
- Calculators
- Mentor Core Mathematics Grade 10 pg. 185

- Written assignments - Practical activities - Observation

Measurements and Geometry

Surface Area and Volume - Pyramids
Surface Area and Volume - Cones

By the end of the lesson, the learner should be able to:
- Determine surface area of pyramids
- Draw nets of pyramids
- Apply to structures like Egyptian pyramids

In groups, learners are guided to:
- Measure edges of pyramid models
- Cut and open to get nets
- Calculate surface area

How do we calculate surface area of pyramids?

- Mentor Core Mathematics Grade 10 pg. 191
- Models of pyramids
- Calculators
- Mentor Core Mathematics Grade 10 pg. 193
- Manila paper
- Compasses

- Written assignments - Practical assessment - Observation

Measurements and Geometry

Surface Area and Volume - Frustum of cone

By the end of the lesson, the learner should be able to:
- Calculate surface area of frustum of a cone
- Use similar cone properties
- Apply to lampshades and buckets

In groups, learners are guided to:
- Make frustum by cutting cone
- Calculate surfaces of original and cut-off cone
- Find surface area of frustum

How do we calculate surface area of a frustum?

- Mentor Core Mathematics Grade 10 pg. 195
- Cone models
- Scissors
- Calculators

- Written assignments - Practical assessment - Observation

Measurements and Geometry

Surface Area and Volume - Frustum of pyramid
Surface Area and Volume - Spheres and hemispheres

By the end of the lesson, the learner should be able to:
- Calculate surface area of frustum of a pyramid
- Apply similar figure properties
- Connect to kitchen worktops and counters

In groups, learners are guided to:
- Sketch original pyramid
- Use similar figures to find dimensions
- Calculate surface area

How do we find surface area of pyramid frustum?

- Mentor Core Mathematics Grade 10 pg. 197
- Models
- Calculators
- Reference materials
- Mentor Core Mathematics Grade 10 pg. 200
- Spherical objects
- Calculators

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Surface Area and Volume - Composite solids
Surface Area and Volume - Volume of prisms and pyramids

By the end of the lesson, the learner should be able to:
- Calculate surface area of composite solids
- Identify component solids
- Apply to real structures and objects

In groups, learners are guided to:
- Identify components of composite solids
- Calculate surface area of each component
- Combine appropriately

How do we find surface area of composite solids?

- Mentor Core Mathematics Grade 10 pg. 202
- Models of composite solids
- Calculators
- Mentor Core Mathematics Grade 10 pg. 206
- Models of solids

- Written tests - Project work - Oral questions

Measurements and Geometry

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

By the end of the lesson, the learner should be able to:
- Calculate volume of spheres using (4/3)πr³
- Calculate volume of hemispheres
- Apply to balls, tanks and containers

In groups, learners are guided to:
- Apply sphere volume formula
- Calculate hemisphere volumes
- Solve practical problems

How do we calculate volume of spheres?

- Mentor Core Mathematics Grade 10 pg. 210
- Spherical objects
- Calculators
- Mentor Core Mathematics Grade 10 pg. 212
- Models
- Calculators
- Reference materials

- Written assignments - Practical activities - Observation

Measurements and Geometry

Surface Area and Volume - Composite solids volume
Vectors I - Introduction to vectors

By the end of the lesson, the learner should be able to:
- Calculate volume of composite solids
- Identify and separate components
- Apply to real objects like test tubes and tanks

In groups, learners are guided to:
- Identify composite solid components
- Calculate volume of each part
- Sum up total volume

How do we find volume of composite solids?

- Mentor Core Mathematics Grade 10 pg. 216
- Models of composite solids
- Calculators
- Mentor Core Mathematics Grade 10 pg. 220
- Charts
- Reference materials

- Written assignments - Project assessment - Observation

Measurements and Geometry

Vectors I - Vector notation

By the end of the lesson, the learner should be able to:
- Use vector notations correctly
- Represent vectors as directed line segments
- Write vectors in different forms

In groups, learners are guided to:
- Practice writing vector notations
- Draw vectors on charts
- Use bold letters and arrows

How do we write and represent vectors?

- Mentor Core Mathematics Grade 10 pg. 221
- Charts
- Graph papers
- Rulers

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Vectors I - Equivalent vectors
Vectors I - Adding vectors

By the end of the lesson, the learner should be able to:
- Identify equivalent vectors
- Determine conditions for equivalent vectors
- Find equivalent vectors in shapes

In groups, learners are guided to:
- Identify vectors with same magnitude and direction
- Use grids to compare vectors
- Identify equivalent vectors in solids

When are two vectors equivalent?

- Mentor Core Mathematics Grade 10 pg. 223
- Graph papers
- Geometrical instruments
- Mentor Core Mathematics Grade 10 pg. 225
- Rulers
- Protractors

- Written assignments - Practical work - Observation

Measurements and Geometry

Vectors I - Scalar multiplication
Vectors I - Column vectors

By the end of the lesson, the learner should be able to:
- Multiply vectors by scalars
- Understand effect of positive and negative scalars
- Apply in solving problems

In groups, learners are guided to:
- Multiply vectors by positive scalars
- Multiply by negative scalars
- Observe effect on magnitude and direction

What happens when we multiply a vector by a scalar?

- Mentor Core Mathematics Grade 10 pg. 228
- Graph papers
- Rulers
- Mentor Core Mathematics Grade 10 pg. 230
- Calculators

- Written assignments - Class exercises - Observation

Measurements and Geometry

Vectors I - Position vectors
Vectors I - Magnitude of a vector

By the end of the lesson, the learner should be able to:
- Determine position vectors
- Express vectors in terms of position vectors
- Use position vectors in calculations

In groups, learners are guided to:
- Define position vectors from origin
- Calculate vectors using a⃗ = OB⃗ - OA⃗
- Solve problems using position vectors

What are position vectors?

- Mentor Core Mathematics Grade 10 pg. 234
- Graph papers
- Calculators

- Written assignments - Practical work - Observation

Measurements and Geometry

Vectors I - Midpoint of a vector

By the end of the lesson, the learner should be able to:
- Determine midpoint of a vector
- Use midpoint formula
- Apply in geometry problems

In groups, learners are guided to:
- Calculate midpoint coordinates
- Use formula (x₁+x₂)/2, (y₁+y₂)/2
- Solve problems involving midpoints

How do we find the midpoint of a vector?

- Mentor Core Mathematics Grade 10 pg. 238
- Graph papers
- Calculators

- Written assignments - Practical assessment - Observation

Measurements and Geometry

Vectors I - Translation as transformation
Vectors I - Applications and problems

By the end of the lesson, the learner should be able to:
- Determine translation vector
- Perform translation on objects
- Relate translation to sliding motion

In groups, learners are guided to:
- Demonstrate translation
- Find translation vector from object and image
- Find image given object and translation

What is translation and how is it represented?

- Mentor Core Mathematics Grade 10 pg. 240
- Graph papers
- Geometrical instruments
- Mentor Core Mathematics Grade 10 pg. 242
- Calculators
- Digital devices

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Linear Motion - Basic terms
Linear Motion - Calculating velocity and acceleration

By the end of the lesson, the learner should be able to:
- Define distance, displacement, speed, velocity and acceleration
- Distinguish between distance and displacement
- Relate to vehicle motion and athletics

In groups, learners are guided to:
- Demonstrate motion using objects
- Discuss meanings of terms
- Give real-life examples

What is the difference between speed and velocity?

- Mentor Core Mathematics Grade 10 pg. 244
- Stopwatches
- Measuring tapes
- Mentor Core Mathematics Grade 10 pg. 246
- Measuring tapes
- Calculators

- Oral questions - Written assignments - Observation

Measurements and Geometry

Linear Motion - Drawing displacement-time graphs
Linear Motion - Interpreting displacement-time graphs

By the end of the lesson, the learner should be able to:
- Draw displacement-time graphs
- Plot data accurately
- Interpret simple graphs

In groups, learners are guided to:
- Collect data on displacement and time
- Plot graphs on Cartesian plane
- Draw graphs from given data

How do we draw displacement-time graphs?

- Mentor Core Mathematics Grade 10 pg. 247
- Graph papers
- Rulers
- Mentor Core Mathematics Grade 10 pg. 249
- Calculators

- Written assignments - Practical assessment - Observation

Measurements and Geometry

Linear Motion - Drawing velocity-time graphs
Linear Motion - Interpreting velocity-time graphs

By the end of the lesson, the learner should be able to:
- Draw velocity-time graphs
- Plot data correctly
- Represent different motion types

In groups, learners are guided to:
- Record velocity and time data
- Plot velocity-time graphs
- Draw graphs from given information

How do we draw velocity-time graphs?

- Mentor Core Mathematics Grade 10 pg. 253
- Graph papers
- Rulers
- Calculators
- Mentor Core Mathematics Grade 10 pg. 256

- Written assignments - Practical work - Observation

Measurements and Geometry

Linear Motion - Relative speed (opposite directions)

By the end of the lesson, the learner should be able to:
- Define relative speed
- Calculate relative speed of bodies moving in opposite directions
- Apply to vehicles meeting on roads

In groups, learners are guided to:
- Demonstrate bodies moving towards each other
- Calculate relative speed (sum of speeds)
- Solve problems on meeting times

What is relative speed?

- Mentor Core Mathematics Grade 10 pg. 261
- Digital devices
- Calculators

- Written assignments - Practical activities - Observation

Measurements and Geometry
Statistics and Probability

Linear Motion - Relative speed (same direction)
Linear Motion - Real-life applications
Statistics I - Meaning of data and data sources

By the end of the lesson, the learner should be able to:
- Calculate relative speed of bodies in same direction
- Solve overtaking problems
- Connect to traffic and transport safety

In groups, learners are guided to:
- Demonstrate bodies moving in same direction
- Calculate relative speed (difference of speeds)
- Solve overtaking problems

How do we calculate relative speed for same direction?

- Mentor Core Mathematics Grade 10 pg. 263
- Calculators
- Reference materials
- Mentor Core Mathematics Grade 10 pg. 265
- Reference materials
- Digital devices
- Mentor Core Mathematics Grade 10 pg. 268
- Digital devices
- Reference books

- Written tests - Class exercises - Oral questions

Statistics and Probability

Statistics I - Methods of data collection
Statistics I - Frequency distribution table for ungrouped data
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 different methods of collecting data
- Collect data using appropriate methods
- Connect data collection methods to research in agriculture, health and social sciences

In groups, learners are guided to:
- Discuss methods of data collection including interviews, questionnaires and observations
- Collect data on shoe sizes of classmates
- Record collected data appropriately

Which methods are used to collect data in different situations?

- Mentor Core Mathematics Grade 10 pg. 268
- Questionnaires
- Tally sheets
- Measuring instruments
- Tape measures
- Graph paper
- Mentor Core Mathematics Grade 10 pg. 270
- Calculators
- Graph paper
- Digital devices
- Mentor Core Mathematics Grade 10 pg. 272
- Weighing scales

- Oral questions - Observation - Class activities

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:
- Define mode and median
- Determine the mode and median of ungrouped data
- Connect mode and median to identifying most common products and middle values in salary surveys

In groups, learners are guided to:
- Collect marks from classmates and determine the most frequent mark
- Arrange data in order and identify the middle value
- Work out exercises involving mode and median

How do we determine the mode and median of a data set?

- Mentor Core Mathematics Grade 10 pg. 273
- Calculators
- Number cards
- Mentor Core Mathematics Grade 10 pg. 277
- Mathematical tables
- Mentor Core Mathematics Grade 10 pg. 278
- Charts

- Written exercises - Class activities - Oral questions

Statistics and Probability

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

By the end of the lesson, the learner should be able to:
- Identify the median class of grouped data
- Calculate the median of grouped data using the formula
- Use median to determine middle income levels and central tendencies in large populations

In groups, learners are guided to:
- Calculate cumulative frequencies
- Identify the median class
- Apply the median formula for grouped data

How do we determine the median of grouped data?

- Mentor Core Mathematics Grade 10 pg. 280
- Calculators
- Charts
- Mentor Core Mathematics Grade 10 pg. 285
- Graph paper
- Rulers
- Pencils

- Written exercises - Oral questions - Observation

Statistics and Probability

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

By the end of the lesson, the learner should be able to:
- Calculate frequency density for unequal class intervals
- Draw histograms using frequency density
- Use histograms with unequal intervals to represent wage distribution and age demographics

In groups, learners are guided to:
- Calculate frequency density (f/i) for each class
- Draw histograms using frequency density against class boundaries
- Work out exercises involving unequal class intervals

How do we draw histograms when class intervals are unequal?

- Mentor Core Mathematics Grade 10 pg. 287
- Graph paper
- Calculators
- Rulers
- Mentor Core Mathematics Grade 10 pg. 290
- Rulers
- Pencils

- Practical work - Written exercises - Observation

Statistics and Probability

Statistics I - Interpreting data from histograms
Statistics I - Interpreting data from frequency polygons

By the end of the lesson, the learner should be able to:
- Read and interpret information from histograms
- Determine median and other statistics from histograms
- Use histogram interpretation to make decisions in business planning and resource allocation

In groups, learners are guided to:
- Generate frequency distribution tables from histograms
- Calculate mean, mode and median from histograms
- Answer questions based on histogram interpretation

How do we extract information from histograms?

- Mentor Core Mathematics Grade 10 pg. 293
- Sample histograms
- Calculators
- Graph paper
- Mentor Core Mathematics Grade 10 pg. 296
- Sample frequency polygons

- Written exercises - Oral questions - Class activities

Statistics and Probability

Probability I - Meaning of probability and experimental probability
Probability I - Performing probability experiments
Probability I - Range of probability measure
Probability I - Generating probability space

By the end of the lesson, the learner should be able to:
- Define probability
- Perform experiments to determine probability
- Relate probability to predicting outcomes in games, weather forecasting and insurance

In groups, learners are guided to:
- Toss a coin and record outcomes
- Calculate probability based on experimental results
- Discuss the meaning of probability

What is probability and how is it determined experimentally?

- Mentor Core Mathematics Grade 10 pg. 304
- Coins
- Dice
- Tally sheets
- Recording sheets
- Mentor Core Mathematics Grade 10 pg. 306
- Number cards
- Dice
- Mentor Core Mathematics Grade 10 pg. 308

- Oral questions - Observation - Practical work

Statistics and Probability

Probability I - Identifying mutually exclusive events
Probability I - Probability of mutually exclusive events
Probability I - Identifying independent events

By the end of the lesson, the learner should be able to:
- Define mutually exclusive events
- Identify mutually exclusive events
- Relate mutually exclusive events to situations like choosing one item from alternatives

In groups, learners are guided to:
- Roll a die and discuss why getting odd and even numbers simultaneously is impossible
- Identify mutually exclusive events from given scenarios
- Work out exercises on mutually exclusive events

What are mutually exclusive events?

- Mentor Core Mathematics Grade 10 pg. 309
- Dice
- Coloured balls
- Bags
- Mentor Core Mathematics Grade 10 pg. 310
- Cards
- Calculators
- Mentor Core Mathematics Grade 10 pg. 312
- Coins
- Recording sheets

- Oral questions - Written exercises - Observation

Statistics and Probability

Probability I - Probability of independent events
Probability I - Combined laws of probability
Probability I - Drawing tree diagrams

By the end of the lesson, the learner should be able to:
- Apply the multiplication law for independent events
- Calculate P(A and B) = P(A) × P(B)
- Use probability of independent events to calculate combined chances in machine operations and medical testing

In groups, learners are guided to:
- Discuss the multiplication law of probability
- Calculate probability of both events occurring
- Work out exercises involving independent events

How do we calculate the probability of independent events?

- Mentor Core Mathematics Grade 10 pg. 312
- Dice
- Coins
- Calculators
- Mentor Core Mathematics Grade 10 pg. 314
- Number cards
- Calculators
- Coloured objects
- Mentor Core Mathematics Grade 10 pg. 317
- Graph paper
- Rulers
- Pencils

- Written exercises - Class activities - Oral questions

Statistics and Probability

Probability I - Using tree diagrams to calculate probability

By the end of the lesson, the learner should be able to:
- Use tree diagrams to determine probabilities
- Calculate probabilities of various outcomes from tree diagrams
- Apply tree diagrams to solve problems in genetics, quality control and transport planning

In groups, learners are guided to:
- Draw tree diagrams for given situations
- Calculate probabilities by multiplying along branches
- Solve complex probability problems using tree diagrams

How do we use tree diagrams to calculate probabilities?

- Mentor Core Mathematics Grade 10 pg. 318
- Graph paper
- Calculators
- Sample problems

- Written exercises - Class activities - Oral questions