Measurements and Geometry

Vectors I - Vector and scalar quantities

By the end of the lesson, the learner should be able to:
- Define vector and scalar quantities with illustrations
- Distinguish between vector and scalar quantities using real-life examples
- Relate vectors and scalars to everyday experiences such as wind direction, vehicle speed and displacement walked to school

In groups, learners are guided to:
- Use a digital device or other resources to search and brainstorm on the meaning of vector and scalar quantities
- Walk a specified distance and direction on the school playground to demonstrate displacement as a vector and distance as a scalar
- Name and categorise physical quantities as vector or scalar and share findings with peers

What makes a physical quantity a vector or a scalar?

- Master Core Mathematics Grade 10 pg. 208
- Measuring tape
- Magnetic compass
- Stopwatch
- Digital resources

- Oral questions - Observation - Written assignments

Measurements and Geometry

Vectors I - Vector notation
Vectors I - Representation of 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

- Oral questions - Observation - Written assignments

Measurements and Geometry

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

- Oral questions - Observation - Written assignments

Measurements and Geometry

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 parallelogram method
- Draw the resultant vector as the diagonal of a completed parallelogram
- Relate the parallelogram method to real-life scenarios such as a boat crossing a river while being pushed by a current from a different direction

In groups, learners are guided to:
- Draw two vectors from a common point on a grid
- Complete the parallelogram and draw the diagonal as the resultant vector
- Solve problems on addition and subtraction of vectors and share work with peers

How is the parallelogram method used to add vectors?

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

- Oral questions - Observation - Written assignments

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 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

- Oral questions - Observation - Written assignments

Measurements and Geometry

Vectors I - Magnitude of a vector and midpoint of a 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

- Oral questions - Observation - Written assignments

Measurements and Geometry

Vectors I - Translation vector

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

- Oral questions - Observation - Written assignments

Measurements and Geometry

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

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

- Oral questions - Observation - Written assignments

Measurements and Geometry

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

By the end of the lesson, the learner should be able to:
- Define acceleration and deceleration and state their units
- Calculate acceleration given initial velocity, final velocity and time
- Relate acceleration and deceleration to real-life situations such as a vehicle speeding up on a highway, braking to stop at a red light or a rocket launching into space

In groups, learners are guided to:
- Roll a ball down a ramp and measure velocity at two intervals to determine acceleration
- Calculate acceleration and deceleration from given data
- Solve problems involving motorbikes, planes and trains and share work with peers

How do we determine how quickly a body speeds up or slows down?

- Master Core Mathematics Grade 10 pg. 234
- Measuring tape
- Stopwatch
- Ball
- Ramp
- Calculators
- Digital resources
- Master Core Mathematics Grade 10 pg. 236
- Graph papers
- Rulers
- Calculators

- Oral questions - Observation - Written assignments

Measurements and Geometry

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

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

- Oral questions - Observation - Written assignments

Measurements and Geometry

Linear Motion - Interpreting velocity-time graph
Linear Motion - Relative speed of bodies moving in opposite and same directions
Linear Motion - Relative speed involving delayed departure and passing lengths

By the end of the lesson, the learner should be able to:
- Interpret velocity-time graphs to determine acceleration, deceleration and distance
- Calculate acceleration from the gradient and distance from the area under a velocity-time graph
- Relate graph interpretation to real-life situations such as determining a rally car's acceleration on different road sections or total distance covered by a train between stations

In groups, learners are guided to:
- Consider velocity-time graphs and describe the motion at each section
- Calculate the gradient at each section to determine acceleration or deceleration
- Work out the area under the graph to determine total distance covered and share findings

What do the gradient and area under a velocity-time graph represent?

- Master Core Mathematics Grade 10 pg. 244
- Graph papers
- Rulers
- Calculators
- Digital resources
- Master Core Mathematics Grade 10 pg. 248
- Tape measure
- Stopwatch
- Balls
- Master Core Mathematics Grade 10 pg. 250

- Oral questions - Observation - Written assignments

Statistics and Probability

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:
- Define the term data and identify different sources of data
- Collect and record data using appropriate methods such as interviews, observations and questionnaires
- Relate data collection to real life situations like recording daily class attendance, transport modes or market surveys

- Discuss the meaning of the term data and explore different data sources
- Identify and use different methods of collecting data such as interviews, observations, experimentations and questionnaires
- Collect data on the mode of transport learners use to school and record findings in a table
- Share findings with other learners in class

What is data and why do we collect it?

- Master Core Mathematics Grade 10 pg. 252
- Digital resources
- Charts
- Master Core Mathematics Grade 10 pg. 254
- Rulers

- Oral questions - Observation - Written assignments

Statistics and Probability

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

- Written assignments - Oral questions

Statistics and Probability

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:
- Calculate the mean of ungrouped data from a list of values and from a frequency distribution table
- Apply the formula x̄ = Σfx/Σf to determine mean from a frequency table
- Relate mean to real life situations like calculating average temperature of patients, average height of seedlings or combined mean marks of classes

In groups, learners are guided to:
- Brainstorm on the meaning of the term mean from Junior School knowledge
- Measure heights of group members and work out the mean height
- Calculate mean from a list of values by dividing the sum of all values by the total number of values
- Use the formula x̄ = Σfx/Σf to calculate mean from a frequency distribution table

How do we determine the average value of a set of data?

- Master Core Mathematics Grade 10 pg. 260
- Calculators
- Digital resources
- Master Core Mathematics Grade 10 pg. 264

- Written assignments - 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 midpoint of each class in a grouped frequency distribution
- Determine the mean of grouped data using the formula x̄ = Σfx/Σf
- Relate mean of grouped data to real life situations like determining average marks in a Mathematics assessment, average heights of learners or average ages of bus passengers

- Collect marks scored by learners and group them into appropriate classes
- Calculate the midpoint of each class and complete a frequency distribution table with columns for class, midpoint, frequency and fx
- Work out the mean using the formula x̄ = Σfx/Σf
- Share work with other learners in class

How do we calculate the mean when data is grouped into classes?

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

- Written assignments - Oral questions

Statistics and Probability

Statistics I - Median of grouped data

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

- 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

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

- Written assignments - Observation

Statistics and Probability

Statistics I - Frequency polygons

By the end of the lesson, the learner should be able to:
- Calculate midpoints of classes and plot frequency against midpoints
- Draw frequency polygons for single and comparative data sets
- Relate frequency polygons to real life situations like comparing daily temperatures of two towns, comparing delivery records across months or comparing marks in different subjects

In groups, learners are guided to:
- Calculate the midpoint of each class in a frequency distribution table
- Plot points of frequency against midpoints on graph paper and join them with straight lines
- Extend the polygon by adding imaginary classes at both ends with frequency zero
- Draw two or more frequency polygons on the same axes for comparison

How do we use frequency polygons to compare data sets?

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

- 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

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

- Written assignments - Oral questions

Statistics and Probability

Probability I - Probability space

By the end of the lesson, the learner should be able to:
- List the probability space for single and combined events
- Generate probability spaces using tables and lists for coins and dice
- Relate probability spaces to real life situations like listing possible weather outcomes, possible results of tossing two coins or possible outcomes when rolling two dice

In groups, learners are guided to:
- List all possible outcomes when a coin is tossed once and when tossed twice
- Generate the probability space for two dice tossed together using a two-way table
- Make a spinning wheel and list all possible outcomes after spinning
- Record outcomes in a frequency table and share results with peers

How do we list all possible outcomes of an experiment?

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

- Written assignments - Oral questions - Observation

Statistics and Probability

Probability I - Mutually exclusive events

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

- Written assignments - Oral questions

Statistics and Probability

Mutually exclusive events - Practice

By the end of the lesson, the learner should be able to:
- Solve problems involving mutually exclusive events with multiple outcomes
- Determine probabilities of selecting items from bags or groups with multiple categories
- Relate mutually exclusive events to real life situations like probability of a traffic light being red, yellow or green, choosing tea or coffee in a cafeteria or selecting a boy or girl from a class

In groups, learners are guided to:
- Calculate the probability of picking specific coloured marbles from a bag containing multiple colours
- Solve problems where probabilities of mutually exclusive events must sum to 1
- Determine unknown probabilities given other probabilities in mutually exclusive scenarios
- Share solutions and compare approaches with peers

How do we calculate probabilities when there are more than two mutually exclusive outcomes?

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

- 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

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

- Written assignments - Oral questions

Statistics and Probability

Probability I - Multiplication law of probability

By the end of the lesson, the learner should be able to:
- State and apply the multiplication law of probability: P(A and B) = P(A) × P(B)
- Calculate the probability of both events occurring in independent situations
- Relate multiplication law to real life situations like selecting vehicles from two branches of an organisation, picking fruits with and without replacement or selecting learners randomly from a class

In groups, learners are guided to:
- Discuss the meaning of 'and' in probability using Junior School knowledge
- Roll two fair dice and determine the probability of rolling specific numbers on each die
- Apply the multiplication law P(A and B) = P(A) × P(B) to solve problems
- Solve problems involving selection with replacement and without replacement

When do we multiply probabilities together?

- Master Core Mathematics Grade 10 pg. 299
- Dice
- Coins
- Fruit baskets
- Calculators

- Written assignments - Oral questions

Statistics and Probability

Probability I - Probability tree diagrams

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

- Written assignments - Oral questions - Observation

Statistics and Probability

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 for events without replacement
- Calculate probabilities from tree diagrams where the total number of items changes after each pick
- Relate tree diagrams without replacement to real life situations like drawing balls from a box without returning them, selecting apples from a basket or choosing learners from a class

- Draw probability tree diagrams for picking two items from a bag without replacement noting how probabilities change
- Calculate probabilities of getting same colour, different colour or at least one of a specific colour
- Solve problems involving fractions of groups such as boys and girls with different characteristics
- Share work and compare solutions with other learners

How do probabilities change when items are not replaced?

- Master Core Mathematics Grade 10 pg. 303
- Balls of different colours
- Bags
- Calculators
- Master Core Mathematics Grade 10 pg. 305
- Calculators
- Digital resources
- Coins
- Dice

- Written assignments - Oral questions