Measurements and Geometry

Surface Area and Volume - Rectangular prism

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

- Written assignments - Practical activities - Observation

Measurements and Geometry

Surface Area and Volume - Triangular and other prisms
Surface Area and Volume - Pyramids

By the end of the lesson, the learner should be able to:
- Calculate surface area of triangular prisms
- Calculate surface area of other prisms
- Apply to tents and buildings

In groups, learners are guided to:
- Draw nets of triangular prisms
- Calculate surface areas
- Solve practical problems

How do we find surface area of triangular prisms?

- Mentor Core Mathematics Grade 10 pg. 185
- Models of prisms
- Calculators
- Mentor Core Mathematics Grade 10 pg. 191
- Models of pyramids

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Surface Area and Volume - Cones

By the end of the lesson, the learner should be able to:
- Calculate surface area of cones
- Use formulas for curved surface and base
- Apply to ice cream cones and funnels

In groups, learners are guided to:
- Make cone models from manila paper
- Calculate curved surface area πrl
- Calculate total surface area

How do we calculate surface area of cones?

- Mentor Core Mathematics Grade 10 pg. 193
- Manila paper
- Compasses
- Calculators

- Written tests - Practical work - Oral questions

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

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

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Surface Area and Volume - Spheres and hemispheres

By the end of the lesson, the learner should be able to:
- Calculate surface area of spheres using 4πr²
- Calculate surface area of hemispheres
- Apply to balls, domes and bowls

In groups, learners are guided to:
- Brainstorm on spheres
- Apply formula 4πr²
- Calculate hemisphere surface area (3πr²)

How do we calculate surface area of spheres?

- Mentor Core Mathematics Grade 10 pg. 200
- Spherical objects
- Calculators

- Written assignments - Practical activities - Observation

Measurements and Geometry

Surface Area and Volume - Composite solids
Surface Area and Volume - Volume of cones

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. 205
- Cone and cylinder models
- Sand/water

- Written tests - Project work - Oral questions

Measurements and Geometry

Surface Area and Volume - Volume of prisms and pyramids

By the end of the lesson, the learner should be able to:
- Calculate volume of various prisms
- Calculate volume of pyramids using ⅓Bh
- Apply to buildings and storage

In groups, learners are guided to:
- Calculate volumes of prisms
- Apply pyramid volume formula
- Solve real-life problems

How do we calculate volumes of prisms and pyramids?

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

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Surface Area and Volume - Volume of spheres and hemispheres

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

- Written assignments - Practical activities - Observation

Measurements and Geometry

Surface Area and Volume - Volume of frustums

By the end of the lesson, the learner should be able to:
- Calculate volume of frustum of cone and pyramid
- Use similar figure relationships
- Apply to buckets, lampshades and pots

In groups, learners are guided to:
- Calculate volume of original solid
- Subtract volume of cut-off part
- Solve problems involving frustums

How do we calculate volume of a frustum?

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

- Written tests - Class exercises - Oral questions

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

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

- Written assignments - Practical work - Observation

Measurements and Geometry

Vectors I - Adding vectors

By the end of the lesson, the learner should be able to:
- Add vectors graphically
- Determine resultant vector
- Apply to finding net force or displacement

In groups, learners are guided to:
- Draw vectors head to tail
- Determine resultant vector
- Practice with multiple vectors

How do we add vectors?

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

- Written tests - Practical assessment - Oral questions

Measurements and Geometry

Vectors I - Scalar multiplication

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

- Written assignments - Class exercises - Observation

Measurements and Geometry

Vectors I - Column vectors
Vectors I - Position vectors

By the end of the lesson, the learner should be able to:
- Express vectors in column form
- Determine horizontal and vertical components
- Add and subtract column vectors

In groups, learners are guided to:
- Determine horizontal and vertical displacements
- Write vectors in column form
- Perform operations on column vectors

How do we express vectors in column form?

- Mentor Core Mathematics Grade 10 pg. 230
- Graph papers
- Calculators
- Mentor Core Mathematics Grade 10 pg. 234

- Written tests - Oral questions - Class exercises

Measurements and Geometry

Vectors I - Magnitude of a vector

By the end of the lesson, the learner should be able to:
- Calculate magnitude of vectors
- Use Pythagoras theorem
- Apply magnitude in solving problems

In groups, learners are guided to:
- Use formula

v

How do we calculate the magnitude of a vector?

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

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

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Vectors I - Applications and problems
Linear Motion - Basic terms

By the end of the lesson, the learner should be able to:
- Apply vector concepts in solving problems
- Solve mixed problems on vectors
- Connect vectors to physics and engineering

In groups, learners are guided to:
- Solve combined vector problems
- Apply to real-life situations
- Use digital devices to explore applications

Where do we use vectors in real life?

- Mentor Core Mathematics Grade 10 pg. 242
- Calculators
- Digital devices
- Mentor Core Mathematics Grade 10 pg. 244
- Stopwatches
- Measuring tapes

- Written assignments - Project work - Observation

Measurements and Geometry

Linear Motion - Calculating velocity and acceleration

By the end of the lesson, the learner should be able to:
- Calculate velocity and acceleration
- Use appropriate formulas
- Apply to vehicle motion and sports

In groups, learners are guided to:
- Participate in races and record time
- Calculate velocity
- Calculate acceleration

How do we calculate velocity and acceleration?

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

- Written tests - Practical activities - Oral questions

Measurements and Geometry

Linear Motion - Drawing 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

- Written assignments - Practical assessment - Observation

Measurements and Geometry

Linear Motion - Interpreting displacement-time graphs

By the end of the lesson, the learner should be able to:
- Interpret displacement-time graphs
- Calculate velocity from gradient
- Identify periods of rest

In groups, learners are guided to:
- Calculate gradients of graphs
- Identify when object is stationary
- Determine maximum displacement

What information can we get from displacement-time graphs?

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

- Written tests - Class exercises - Oral questions

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

Linear Motion - Relative speed (same direction)

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

- Written tests - Class exercises - Oral questions

Measurements and Geometry
Statistics and Probability

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:
- Apply linear motion concepts to real-life
- Solve problems involving trains, cars and planes
- Relate to transport and logistics

In groups, learners are guided to:
- Solve real-life problems
- Apply all concepts learned
- Discuss applications in transport

Where do we use linear motion concepts?

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

- Written assignments - Project assessment - Observation

Statistics and Probability

Statistics I - Methods of data collection
Statistics I - Frequency distribution table for 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

- Oral questions - Observation - Class activities

Statistics and Probability

Statistics I - Frequency distribution table for grouped data
Statistics I - Mean of ungrouped data
Statistics I - Mode and median of ungrouped data

By the end of the lesson, the learner should be able to:
- Group data into appropriate classes
- Prepare frequency distribution tables for grouped data
- Connect grouped data to analysing large datasets in population studies and economics

In groups, learners are guided to:
- Discuss suitable class widths for grouping data
- Group collected data into appropriate classes
- Generate frequency distribution tables for grouped data

Why do we group data into classes?

- Mentor Core Mathematics Grade 10 pg. 270
- Calculators
- Graph paper
- Digital devices
- Mentor Core Mathematics Grade 10 pg. 272
- Weighing scales
- Mentor Core Mathematics Grade 10 pg. 273
- Number cards

- Written exercises - Class activities - Oral questions

Statistics and Probability

Statistics I - Mean of grouped data
Statistics I - Mode of grouped data

By the end of the lesson, the learner should be able to:
- Calculate the mean of grouped data using midpoints
- Apply the formula for mean of grouped data
- Use mean of grouped data to analyse examination results and production statistics

In groups, learners are guided to:
- Determine midpoints of class intervals
- Calculate mean using the formula x̄ = Σfx/Σf
- Work out exercises involving mean of grouped data

How do we calculate the mean of grouped data?

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

- Written exercises - Oral questions - Observation

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

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

- Practical work - Written exercises - Observation

Statistics and Probability

Statistics I - Frequency polygons

By the end of the lesson, the learner should be able to:
- Define a frequency polygon
- Draw frequency polygons from frequency tables
- Relate frequency polygons to comparing distributions in climate data and market trends

In groups, learners are guided to:
- Discuss features of frequency polygons
- Calculate midpoints of class intervals
- Plot frequency against midpoints and join with straight lines

What is a frequency polygon and how is it drawn?

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

- Practical work - Observation - Written exercises

Statistics and Probability

Statistics I - Interpreting data from histograms

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

- Written exercises - Oral questions - Class activities

Statistics and Probability

Statistics I - Interpreting data from frequency polygons
Probability I - Meaning of probability and experimental probability

By the end of the lesson, the learner should be able to:
- Read and interpret information from frequency polygons
- Generate frequency tables from frequency polygons
- Connect data interpretation to informed decision making in health, education and economics

In groups, learners are guided to:
- Generate frequency distribution tables from frequency polygons
- Calculate mean and median from frequency polygons
- Discuss and compare different distributions

How do we interpret data from frequency polygons?

- Mentor Core Mathematics Grade 10 pg. 296
- Sample frequency polygons
- Calculators
- Graph paper
- Mentor Core Mathematics Grade 10 pg. 304
- Coins
- Dice
- Tally sheets

- Written exercises - Class activities - Oral questions

Statistics and 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:
- Perform probability experiments using dice
- Calculate experimental probability from results
- Connect experimental probability to quality control in manufacturing and testing

In groups, learners are guided to:
- Throw a die multiple times and record outcomes
- Calculate probability of different outcomes
- Compare experimental results with expected outcomes

How do we perform probability experiments?

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

- Practical work - Written exercises - Observation

Statistics and Probability

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

- Oral questions - Written exercises - Observation

Statistics and Probability

Probability I - Identifying independent events
Probability I - Probability of independent events
Probability I - Combined laws of probability

By the end of the lesson, the learner should be able to:
- Define independent events
- Identify independent events
- Connect independent events to simultaneous occurrences like weather and traffic conditions

In groups, learners are guided to:
- Toss a coin and die simultaneously
- Discuss why outcomes do not affect each other
- Identify independent events from given scenarios

What are independent events?

- Mentor Core Mathematics Grade 10 pg. 312
- Coins
- Dice
- Recording sheets
- Calculators
- Mentor Core Mathematics Grade 10 pg. 314
- Number cards
- Calculators
- Coloured objects

- Oral questions - Written exercises - Observation

Statistics and Probability

Probability I - Drawing tree diagrams

By the end of the lesson, the learner should be able to:
- Draw tree diagrams for probability problems
- Show all possible outcomes on a tree diagram
- Relate tree diagrams to mapping out decision pathways in business and project planning

In groups, learners are guided to:
- Discuss the structure of tree diagrams
- Draw tree diagrams for tossing coins
- Show probabilities on tree diagram branches

What is a tree diagram and how is it drawn?

- Mentor Core Mathematics Grade 10 pg. 317
- Graph paper
- Rulers
- Pencils

- Practical work - Observation - Written exercises

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