Data Handling and Probability

Data Interpretation - Appropriate class width

By the end of the lesson, the learner should be able to:

Determine appropriate class width for grouping data;
Work with data to establish suitable class widths;
Appreciate the importance of appropriate class widths in data representation.

Learners work in groups to consider masses of 40 people in kilograms.
Learners find the difference between the smallest and highest mass (range).
Learners group the masses in smaller groups with different class widths and identify the number of groups formed in each case.

How do we determine an appropriate class width for a given set of data?

-KLB Mathematics Grade 9 Textbook page 244
-Calculator
-Graph paper
-Manila paper
-Rulers
-Colored markers

-Oral questions -Group presentations -Written exercise -Observation

Data Handling and Probability

Data Interpretation - Appropriate class width

By the end of the lesson, the learner should be able to:

Determine appropriate class width for grouping data;
Work with data to establish suitable class widths;
Appreciate the importance of appropriate class widths in data representation.

Learners work in groups to consider masses of 40 people in kilograms.
Learners find the difference between the smallest and highest mass (range).
Learners group the masses in smaller groups with different class widths and identify the number of groups formed in each case.

How do we determine an appropriate class width for a given set of data?

-KLB Mathematics Grade 9 Textbook page 244
-Calculator
-Graph paper
-Manila paper
-Rulers
-Colored markers

-Oral questions -Group presentations -Written exercise -Observation

Data Handling and Probability

Data Interpretation - Finding range and creating groups

By the end of the lesson, the learner should be able to:

Calculate the range of a set of data;
Divide data into suitable class intervals;
Show interest in grouping data for better representation.

Learners are presented with marks scored by 40 students in a mathematics test.
Learners find the range of the data.
Learners complete a table using a class width of 10 and determine the number of classes formed.

How does the range of data help us determine appropriate class intervals?

-KLB Mathematics Grade 9 Textbook page 245
-Calculator
-Manila paper
-Data sets
-Chart with examples
-Colored markers

-Oral questions -Written exercise -Observation -Group work assessment

Data Handling and Probability

Data Interpretation - Frequency distribution tables

By the end of the lesson, the learner should be able to:

Draw frequency distribution tables of grouped data;
Use tally marks to organize data into frequency tables;
Value the importance of organizing data in tables.

Learners are presented with data on the number of tree seedlings that survived in 50 different schools.
Learners copy and complete a frequency distribution table using tally marks and frequencies.
Learners discuss and share their completed tables with other groups.

How do we organize data in a frequency distribution table?

-KLB Mathematics Grade 9 Textbook page 247
-Chart paper
-Ruler
-Calculator
-Manila paper
-Colored markers

-Oral questions -Group presentations -Written exercise -Checklist

Data Handling and Probability

Data Interpretation - Frequency distribution tables

By the end of the lesson, the learner should be able to:

Draw frequency distribution tables of grouped data;
Use tally marks to organize data into frequency tables;
Value the importance of organizing data in tables.

Learners are presented with data on the number of tree seedlings that survived in 50 different schools.
Learners copy and complete a frequency distribution table using tally marks and frequencies.
Learners discuss and share their completed tables with other groups.

How do we organize data in a frequency distribution table?

-KLB Mathematics Grade 9 Textbook page 247
-Chart paper
-Ruler
-Calculator
-Manila paper
-Colored markers

-Oral questions -Group presentations -Written exercise -Checklist

Data Handling and Probability

Data Interpretation - Creating frequency tables with different class intervals

By the end of the lesson, the learner should be able to:

Construct frequency tables starting with different class intervals;
Use tally marks to represent data in frequency tables;
Appreciate the use of different class intervals in data representation.

Learners construct a frequency table for given data starting from the class interval 60-64.
Learners use tally marks to count frequency of data in each class.
Learners compare and discuss different frequency tables.

How do we choose appropriate starting points for class intervals?

-KLB Mathematics Grade 9 Textbook page 247
-Calculator
-Ruler
-Graph paper
-Manila paper
-Worksheets with data

-Oral questions -Written exercise -Group presentations -Observation

Data Handling and Probability

Data Interpretation - Modal class

By the end of the lesson, the learner should be able to:

Identify the modal class of grouped data;
Determine the class with the highest frequency;
Develop interest in finding the modal class in real-life data.

Learners are presented with assessment marks in a mathematics test for 32 learners.
Learners draw a frequency distribution table to represent the information.
Learners identify and write down the class with the highest frequency (modal class).

What is the modal class and how is it determined?

-KLB Mathematics Grade 9 Textbook page 248
-Calculator
-Ruler
-Graph paper
-Chart showing frequency distribution tables
-Colored markers

-Oral questions -Group work -Written exercise -Peer assessment

Data Handling and Probability

Data Interpretation - Modal class

By the end of the lesson, the learner should be able to:

Identify the modal class of grouped data;
Determine the class with the highest frequency;
Develop interest in finding the modal class in real-life data.

Learners are presented with assessment marks in a mathematics test for 32 learners.
Learners draw a frequency distribution table to represent the information.
Learners identify and write down the class with the highest frequency (modal class).

What is the modal class and how is it determined?

-KLB Mathematics Grade 9 Textbook page 248
-Calculator
-Ruler
-Graph paper
-Chart showing frequency distribution tables
-Colored markers

-Oral questions -Group work -Written exercise -Peer assessment

Data Handling and Probability

Data Interpretation - Mean of ungrouped data

By the end of the lesson, the learner should be able to:

Calculate the mean of ungrouped data in a frequency table;
Multiply each value by its frequency and find their sum;
Show interest in calculating mean in real-life situations.

Learners consider the height, in metres, of 10 people recorded in a frequency distribution table.
Learners complete a table showing the product of height and frequency (fx).
Learners find the sum of frequencies, sum of fx, and divide to find the mean.

How do we calculate the mean of data presented in a frequency table?

-KLB Mathematics Grade 9 Textbook page 249
-Calculator
-Chart showing frequency tables
-Worksheets
-Manila paper
-Colored markers

-Oral questions -Written exercise -Observation -Assessment rubrics

Data Handling and Probability

Data Interpretation - Mean of grouped data

By the end of the lesson, the learner should be able to:

Calculate the mean of grouped data;
Find the midpoint of class intervals and use in calculations;
Value the importance of mean in summarizing data.

Learners consider a frequency distribution table representing masses in kilograms of learners in a class.
Learners complete a table by finding midpoints of class intervals and calculating fx.
Learners find the sum of frequencies, sum of fx, and divide to find the mean.

How do we calculate the mean of grouped data?

-KLB Mathematics Grade 9 Textbook page 250
-Calculator
-Graph paper
-Manila paper
-Chart with examples
-Worksheets

-Oral questions -Written exercise -Group presentations -Checklist

Data Handling and Probability

Data Interpretation - Mean of grouped data

By the end of the lesson, the learner should be able to:

Calculate the mean of grouped data;
Find the midpoint of class intervals and use in calculations;
Value the importance of mean in summarizing data.

Learners consider a frequency distribution table representing masses in kilograms of learners in a class.
Learners complete a table by finding midpoints of class intervals and calculating fx.
Learners find the sum of frequencies, sum of fx, and divide to find the mean.

How do we calculate the mean of grouped data?

-KLB Mathematics Grade 9 Textbook page 250
-Calculator
-Graph paper
-Manila paper
-Chart with examples
-Worksheets

-Oral questions -Written exercise -Group presentations -Checklist

Data Handling and Probability

Data Interpretation - Mean calculation in real-life situations

By the end of the lesson, the learner should be able to:

Calculate the mean of grouped data from real-life situations;
Apply the formula for finding mean of grouped data;
Appreciate the use of mean in summarizing data in real life.

Learners are presented with data about plants that survived in 50 sampled schools during an environmental week.
Learners find midpoints of class intervals, multiply by frequencies, and sum them up.
Learners calculate the mean number of plants that survived by dividing the sum of fx by the sum of f.

How is the mean used to summarize real-life data?

-KLB Mathematics Grade 9 Textbook page 251
-Calculator
-Manila paper
-Chart with examples
-Worksheets
-Colored markers

-Oral questions -Group work -Written exercise -Assessment rubrics

Data Handling and Probability

Data Interpretation - Mean calculation in real-life situations

By the end of the lesson, the learner should be able to:

Calculate the mean of grouped data from real-life situations;
Apply the formula for finding mean of grouped data;
Appreciate the use of mean in summarizing data in real life.

Learners are presented with data about plants that survived in 50 sampled schools during an environmental week.
Learners find midpoints of class intervals, multiply by frequencies, and sum them up.
Learners calculate the mean number of plants that survived by dividing the sum of fx by the sum of f.

How is the mean used to summarize real-life data?

-KLB Mathematics Grade 9 Textbook page 251
-Calculator
-Manila paper
-Chart with examples
-Worksheets
-Colored markers

-Oral questions -Group work -Written exercise -Assessment rubrics

Data Handling and Probability

Data Interpretation - Median of grouped data

By the end of the lesson, the learner should be able to:

Determine the median of grouped data;
Find cumulative frequencies to locate the median class;
Value the importance of median in data interpretation.

Learners consider the mass of 50 learners recorded in a table.
Learners complete the column for cumulative frequency.
Learners find the sum of frequency, divide by 2, and identify the position of the median mass.

How do we determine the median of grouped data?

-KLB Mathematics Grade 9 Textbook page 252
-Calculator
-Chart showing cumulative frequency tables
-Worksheets
-Manila paper
-Colored markers

-Oral questions -Written exercise -Group presentations -Observation

Data Handling and Probability

Data Interpretation - Calculating median using formula

By the end of the lesson, the learner should be able to:

Apply the formula for calculating median of grouped data;
Identify class boundaries, frequencies, and cumulative frequencies;
Show interest in finding median from real-life data.

Learners consider marks scored by 40 learners in a test presented in a table.
Learners complete the column for cumulative frequency and identify the median class.
Learners identify the lower class boundary, cumulative frequency above median class, class width, and frequency of median class to substitute in the formula.

How do we use the formula to calculate the median of grouped data?

-KLB Mathematics Grade 9 Textbook page 253
-Calculator
-Graph paper
-Chart showing median formula
-Worksheets
-Manila paper

-Oral questions -Written exercise -Group work assessment -Assessment rubrics

Data Handling and Probability

Data Interpretation - Calculating median using formula

By the end of the lesson, the learner should be able to:

Apply the formula for calculating median of grouped data;
Identify class boundaries, frequencies, and cumulative frequencies;
Show interest in finding median from real-life data.

Learners consider marks scored by 40 learners in a test presented in a table.
Learners complete the column for cumulative frequency and identify the median class.
Learners identify the lower class boundary, cumulative frequency above median class, class width, and frequency of median class to substitute in the formula.

How do we use the formula to calculate the median of grouped data?

-KLB Mathematics Grade 9 Textbook page 253
-Calculator
-Graph paper
-Chart showing median formula
-Worksheets
-Manila paper

-Oral questions -Written exercise -Group work assessment -Assessment rubrics

Data Handling and Probability

Data Interpretation - Median calculations in real-life situations

By the end of the lesson, the learner should be able to:

Calculate median in real-life data situations;
Apply the median formula to various data sets;
Appreciate the role of median in data interpretation.

Learners are presented with data on number of nights spent by people in a table.
Learners complete the cumulative frequency column and determine the median class.
Learners apply the median formula to calculate the median value.

How is the median used to interpret real-life data?

-KLB Mathematics Grade 9 Textbook page 254
-Calculator
-Chart with example calculations
-Worksheets with real-life data
-Manila paper
-Colored markers

-Oral questions -Written exercise -Group presentations -Peer assessment

Data Handling and Probability

Probability - Equally likely outcomes

By the end of the lesson, the learner should be able to:

Perform experiments involving equally likely outcomes;
Record outcomes of chance experiments;
Appreciate that some events have equal chances of occurring.

Learners work in groups to flip a fair coin 20 times.
Learners record the number of times heads and tails come up.
Learners divide the number of times heads or tails comes up by the total number of tosses to find probabilities.

What makes events equally likely to occur?

-KLB Mathematics Grade 9 Textbook page 256
-Coins
-Chart paper
-Table for recording outcomes
-Manila paper
-Colored markers

-Oral questions -Practical activity -Group work assessment -Observation

Data Handling and Probability

Probability - Range of probability

By the end of the lesson, the learner should be able to:

Determine the range of probability of an event;
Understand that probability ranges from 0 to 1;
Value the concept of probability range in real-life situations.

Learners use a fair die in this activity and toss it 20 times.
Learners record the number of times each face shows up and calculate relative frequencies.
Learners find the sum of the fractions and discuss that probabilities range from 0 to 1.

What is the range of probability values and what do these values signify?

-KLB Mathematics Grade 9 Textbook page 257
-Dice
-Table for recording outcomes
-Chart showing probability scale (0-1)
-Manila paper
-Colored markers

-Oral questions -Practical activity -Written exercise -Group presentations

Data Handling and Probability

Probability - Range of probability

By the end of the lesson, the learner should be able to:

Determine the range of probability of an event;
Understand that probability ranges from 0 to 1;
Value the concept of probability range in real-life situations.

Learners use a fair die in this activity and toss it 20 times.
Learners record the number of times each face shows up and calculate relative frequencies.
Learners find the sum of the fractions and discuss that probabilities range from 0 to 1.

What is the range of probability values and what do these values signify?

-KLB Mathematics Grade 9 Textbook page 257
-Dice
-Table for recording outcomes
-Chart showing probability scale (0-1)
-Manila paper
-Colored markers

-Oral questions -Practical activity -Written exercise -Group presentations

Data Handling and Probability

Probability - Complementary events

By the end of the lesson, the learner should be able to:

Calculate probability of complementary events;
Understand that sum of probabilities of complementary events is 1;
Show interest in applying complementary probability in real-life situations.

Learners discuss examples of complementary events.
Learners solve problems where the probability of one event is given and they need to find the probability of its complement.
Learners verify that the sum of probabilities of an event and its complement equals 1.

How are complementary events related in terms of their probabilities?

-KLB Mathematics Grade 9 Textbook page 258
-Calculator
-Chart showing complementary events
-Worksheets with problems
-Manila paper
-Colored markers

-Oral questions -Written exercise -Group work assessment -Observation

Data Handling and Probability

Probability - Complementary events

By the end of the lesson, the learner should be able to:

Calculate probability of complementary events;
Understand that sum of probabilities of complementary events is 1;
Show interest in applying complementary probability in real-life situations.

Learners discuss examples of complementary events.
Learners solve problems where the probability of one event is given and they need to find the probability of its complement.
Learners verify that the sum of probabilities of an event and its complement equals 1.

How are complementary events related in terms of their probabilities?

-KLB Mathematics Grade 9 Textbook page 258
-Calculator
-Chart showing complementary events
-Worksheets with problems
-Manila paper
-Colored markers

-Oral questions -Written exercise -Group work assessment -Observation

Data Handling and Probability

Probability - Mutually exclusive events

By the end of the lesson, the learner should be able to:

Identify mutually exclusive events in real-life situations;
Recognize events that cannot occur simultaneously;
Appreciate the concept of mutually exclusive events.

Learners flip a fair coin several times and record the face that shows up.
Learners discuss that heads and tails cannot show up at the same time (mutually exclusive).
Learners identify mutually exclusive events from various examples.

What makes events mutually exclusive?

-KLB Mathematics Grade 9 Textbook page 258
-Coins
-Chart with examples of mutually exclusive events
-Flashcards with different scenarios
-Manila paper
-Colored markers

-Oral questions -Group discussions -Written exercise -Observation

Data Handling and Probability

Probability - Experiments with mutually exclusive events

By the end of the lesson, the learner should be able to:

Perform experiments of single chance involving mutually exclusive events;
Calculate probability of mutually exclusive events;
Value the application of mutually exclusive events in real-life.

Learners toss a fair die several times and record the numbers that show up.
Learners solve problems involving mutually exclusive events like picking a pen of a specific color from a box.
Learners find probabilities of individual events and their union.

How do we calculate the probability of mutually exclusive events?

-KLB Mathematics Grade 9 Textbook page 259
-Dice
-Colored objects in boxes
-Calculator
-Chart showing probability calculations
-Worksheets with problems

-Oral questions -Practical activity -Written exercise -Assessment rubrics

Data Handling and Probability

Probability - Experiments with mutually exclusive events

By the end of the lesson, the learner should be able to:

Perform experiments of single chance involving mutually exclusive events;
Calculate probability of mutually exclusive events;
Value the application of mutually exclusive events in real-life.

Learners toss a fair die several times and record the numbers that show up.
Learners solve problems involving mutually exclusive events like picking a pen of a specific color from a box.
Learners find probabilities of individual events and their union.

How do we calculate the probability of mutually exclusive events?

-KLB Mathematics Grade 9 Textbook page 259
-Dice
-Colored objects in boxes
-Calculator
-Chart showing probability calculations
-Worksheets with problems

-Oral questions -Practical activity -Written exercise -Assessment rubrics

Data Handling and Probability

Probability - Independent events

By the end of the lesson, the learner should be able to:

Perform experiments involving independent events;
Understand that outcome of one event doesn't affect another;
Show interest in applying independent events probability in real-life.

Learners toss a fair coin and a fair die at the same time and record outcomes.
Learners repeat the experiment several times.
Learners discuss that the outcome of the coin toss doesn't affect the outcome of the die roll (independence).

What makes events independent from each other?

-KLB Mathematics Grade 9 Textbook page 260
-Coins and dice
-Table for recording outcomes
-Chart showing examples of independent events
-Manila paper
-Colored markers

-Oral questions -Practical activity -Group discussions -Observation

Data Handling and Probability

Probability - Independent events

By the end of the lesson, the learner should be able to:

Perform experiments involving independent events;
Understand that outcome of one event doesn't affect another;
Show interest in applying independent events probability in real-life.

Learners toss a fair coin and a fair die at the same time and record outcomes.
Learners repeat the experiment several times.
Learners discuss that the outcome of the coin toss doesn't affect the outcome of the die roll (independence).

What makes events independent from each other?

-KLB Mathematics Grade 9 Textbook page 260
-Coins and dice
-Table for recording outcomes
-Chart showing examples of independent events
-Manila paper
-Colored markers

-Oral questions -Practical activity -Group discussions -Observation

Data Handling and Probability

Probability - Calculating probabilities of independent events

By the end of the lesson, the learner should be able to:

Calculate probabilities of independent events;
Apply the multiplication rule for independent events;
Appreciate the application of independent events in real-life situations.

Learners solve problems involving independent events.
Learners calculate probabilities of individual events and multiply them to find joint probability.
Learners solve problems involving machines breaking down independently and other real-life examples.

How do we calculate the probability of independent events occurring together?

-KLB Mathematics Grade 9 Textbook page 261
-Calculator
-Chart showing multiplication rule
-Worksheets with problems
-Manila paper
-Colored markers

-Oral questions -Written exercise -Group presentations -Assessment rubrics

Data Handling and Probability

Probability - Tree diagrams for single outcomes

By the end of the lesson, the learner should be able to:

Draw a probability tree diagram for a single outcome;
Represent probability situations using tree diagrams;
Value the use of tree diagrams in organizing probability information.

Learners write down possible outcomes when a fair coin is flipped once.
Learners find the total number of all outcomes and probability of each outcome.
Learners complete a tree diagram with possible outcomes and their probabilities.

How do tree diagrams help us understand probability situations?

-KLB Mathematics Grade 9 Textbook page 262
-Chart paper
-Ruler
-Worksheets with blank tree diagrams
-Chart showing completed tree diagrams
-Colored markers

-Oral questions -Practical activity -Group work assessment -Checklist

Data Handling and Probability

Probability - Tree diagrams for single outcomes

By the end of the lesson, the learner should be able to:

Draw a probability tree diagram for a single outcome;
Represent probability situations using tree diagrams;
Value the use of tree diagrams in organizing probability information.

Learners write down possible outcomes when a fair coin is flipped once.
Learners find the total number of all outcomes and probability of each outcome.
Learners complete a tree diagram with possible outcomes and their probabilities.

How do tree diagrams help us understand probability situations?

-KLB Mathematics Grade 9 Textbook page 262
-Chart paper
-Ruler
-Worksheets with blank tree diagrams
-Chart showing completed tree diagrams
-Colored markers

-Oral questions -Practical activity -Group work assessment -Checklist

Data Handling and Probability

Probability - Complex tree diagrams

By the end of the lesson, the learner should be able to:

Draw more complex probability tree diagrams;
Use tree diagrams to solve probability problems;
Appreciate the value of tree diagrams in visualizing probability.

Learners draw tree diagrams for various probability scenarios like balls of different colors in a bag.
Learners use tree diagrams to find probabilities of different outcomes.
Learners interpret tree diagrams to solve probability problems.

How do we use tree diagrams to solve more complex probability problems?

-KLB Mathematics Grade 9 Textbook page 263
-Chart paper
-Ruler
-Calculator
-Chart showing complex tree diagrams
-Worksheets with problems
-Colored markers

-Oral questions -Written exercise -Group presentations -Assessment rubrics

Data Handling and Probability

Probability - Complex tree diagrams

By the end of the lesson, the learner should be able to:

Data Handling and Probability

Probability - Complex tree diagrams

By the end of the lesson, the learner should be able to: