Data Handling and Probability

Data Interpretation - Appropriate class width
Data Interpretation - Finding range and creating groups

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
-KLB Mathematics Grade 9 Textbook page 245
-Data sets
-Chart with examples

-Oral questions -Group presentations -Written exercise -Observation

Data Handling and Probability

Data Interpretation - Frequency distribution tables
Data Interpretation - Creating frequency tables with different class intervals

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
-Graph paper
-Worksheets with data

-Oral questions -Group presentations -Written exercise -Checklist

Data Handling and Probability

Data Interpretation - Modal class
Data Interpretation - Mean of ungrouped data

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

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

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
Data Interpretation - Median of grouped data

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
-KLB Mathematics Grade 9 Textbook page 252
-Chart showing cumulative frequency tables

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

Data Handling and Probability

Data Interpretation - Calculating median using formula
Data Interpretation - Median calculations in real-life situations

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

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

Data Handling and Probability

Probability - Equally likely outcomes
Probability - Range of probability

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
-KLB Mathematics Grade 9 Textbook page 257
-Dice
-Chart showing probability scale (0-1)

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

Data Handling and Probability

Probability - Complementary events
Probability - Mutually exclusive 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
-Coins
-Chart with examples of mutually exclusive events
-Flashcards with different scenarios

-Oral questions -Written exercise -Group work assessment -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 - Independent events
Probability - Calculating probabilities of 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
-KLB Mathematics Grade 9 Textbook page 261
-Calculator
-Chart showing multiplication rule
-Worksheets with problems

-Oral questions -Practical activity -Group discussions -Observation

Data Handling and Probability

Probability - Tree diagrams for single outcomes
Probability - Complex tree diagrams

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

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

Data Handling and Probability
Geometry

Probability - Complex tree diagrams
4.1 Geometrical Constructions - Constructing parallel and perpendicular lines (2)

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

-MENTOR mathematics Learner's Book Grade 8 pg. 132
-Pair of compasses
-Ruler

Geometry

4.1 Geometrical Constructions - Constructing parallel and perpendicular lines (2)

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

-Construct parallel lines using a set square and ruler
-Appreciate the importance of accurate construction of geometric shapes

-Practice constructing parallel lines using a set square and ruler
-Share drawings with other learners in class

How do we construct polygons?

MENTOR mathematics Learner's Book Grade 8 pg. 133
-Set square
-Ruler

-Observation -Written assignments

Geometry

4.1 Geometrical Constructions - Constructing perpendicular lines (2)

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

-Construct a perpendicular bisector to a given line
-Show interest in geometric constructions

-Practice constructing perpendicular bisectors using a ruler and pair of compasses
-Share drawings with other learners in class

Where do we use polygons in real life situations?

MENTOR mathematics Learner's Book Grade 8 pg. 135
-Pair of compasses
-Ruler
MENTOR mathematics Learner's Book Grade 8 pg. 136

-Observation -Written assignments

Geometry

4.1 Geometrical Constructions - Constructing perpendicular lines (2)
4.1 Geometrical Constructions - Dividing a line proportionally (1)

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

-Construct a perpendicular line from a point to a given line
-Appreciate the importance of accurate construction of geometric shapes

-Practice constructing perpendicular lines from a point to a given line using a ruler and pair of compasses
-Share drawings with other learners in class

How do we construct polygons?

MENTOR mathematics Learner's Book Grade 8 pg. 137
-Pair of compasses
-Ruler
MENTOR mathematics Learner's Book Grade 8 pg. 139
-Set square

-Observation -Written assignments

Geometry

4.1 Geometrical Constructions - Angle properties of polygons (1)
4.1 Geometrical Constructions - Constructing regular polygons (1)

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

-Identify angle properties of polygons
-Show interest in geometric constructions

-Discuss angle properties of polygons and relate the number of right angles to the number of sides
-Determine the angles in a given polygon

Where do we use polygons in real life situations?

MENTOR mathematics Learner's Book Grade 8 pg. 140
-Cut-out polygons
MENTOR mathematics Learner's Book Grade 8 pg. 144
-Pair of compasses
-Ruler
-Protractor

-Observation -Written assignments

Geometry

4.1 Geometrical Constructions - Constructing regular polygons (1)
4.1 Geometrical Constructions - Constructing irregular polygons (1)

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

-Construct a regular hexagon
-Show interest in geometric constructions

-Construct regular hexagons using pair of compasses, rulers, protractors
-Share work with other groups in class

How do we construct polygons?

MENTOR mathematics Learner's Book Grade 8 pg. 146
-Pair of compasses
-Ruler
-Protractor
MENTOR mathematics Learner's Book Grade 8 pg. 149

-Observation -Written assignments

Geometry

4.1 Geometrical Constructions - Constructing irregular polygons (1)

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

-Construct irregular quadrilaterals
-Appreciate the importance of accuracy in construction

-Construct irregular quadrilaterals - rectangles, rhombuses, parallelograms and trapeziums
-Share drawings with other groups in class

Where do we use polygons in real life situations?

MENTOR mathematics Learner's Book Grade 8 pg. 152
-Pair of compasses
-Ruler
-Protractor

-Observation -Written assignments

Geometry

4.1 Geometrical Constructions - Constructing irregular polygons (1)

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

-Construct an irregular pentagon
-Appreciate the importance of accuracy in construction

-Construct irregular pentagons given different measurements
-Share work with other groups in class

How do we construct polygons?

-KLB Mathematics Learner's Book Grade 8 pg. 158
-Pair of compasses
-Ruler
-Protractor
MENTOR mathematics Learner's Book Grade 8 pg. 161

-Observation -Written assignments

Geometry

4.1 Geometrical Constructions - Constructing circles related to triangles (1)

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

-Construct circles passing through the vertices of a triangle
-Show interest in geometric constructions

-Practice constructing circles passing through vertices of given triangles
-Share drawings with other groups in class

Where do we use polygons in real life situations?

MENTOR mathematics Learner's Book Grade 8 pg. 163
-Pair of compasses
-Ruler
MENTOR mathematics Learner's Book Grade 8 pg. 164

-Observation -Written assignments

Geometry

4.2 Coordinates and Graphs - The Cartesian plane (2)

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

-Draw a labelled Cartesian plane
-Identify points on the Cartesian plane
-Show interest in learning about coordinates

-Draw and appropriately label the axes on the Cartesian plane
-Practice locating points on a Cartesian plane appropriately

How do we plot coordinates on a Cartesian plane?

MENTOR mathematics Learner's Book Grade 8 pg. 167
-Graph paper
-Ruler
MENTOR mathematics Learner's Book Grade 8 pg. 171

-Observation -Written assignments

Geometry

4.2 Coordinates and Graphs - Table of values for linear equations (2)

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

-Generate a table of values for a linear equation
-Show interest in plotting coordinates

-Discuss and make an appropriate table of values for a given linear equation
-Generate values for linear equations

Where do we use linear graphs in real life?

MENTOR mathematics Learner's Book Grade 8 pg. 174
-Graph paper

-Observation -Written assignments

Geometry

4.2 Coordinates and Graphs - Table of values for linear equations (2)
4.2 Coordinates and Graphs - Linear graphs (2)

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

-Determine an appropriate scale for a linear equation
-Show interest in plotting coordinates

-Discuss, choose and use appropriate scale for given data
-Practice using different scales

Where do we use linear graphs in real life?

MENTOR mathematics Learner's Book Grade 8 pg. 178
-Graph paper
MENTOR mathematics Learner's Book Grade 8 pg. 180
-Ruler

-Observation -Written assignments

Geometry

4.2 Coordinates and Graphs - Linear graphs (2)
4.2 Coordinates and Graphs - Graphical solution of simultaneous linear equations (2)

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

-Draw a linear graph from table of values
-Appreciate the use of graphs in real life

-Draw linear graphs from tables of values on Cartesian plane
-Share work with other learners in class

How do we plot coordinates on a Cartesian plane?

MENTOR mathematics Learner's Book Grade 8 pg. 183
-Graph paper
-Ruler
MENTOR mathematics Learner's Book Grade 8 pg. 185

-Observation -Written assignments

Geometry

4.2 Coordinates and Graphs - Graphical solution of simultaneous linear equations (2)
4.3 Scale Drawing - Representing length to a given scale (2)

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

-Solve simultaneous linear equations graphically
-Appreciate the use of graphs in real life

-Generate the values in a table of the simultaneous linear equations and draw the graphs
-Read the point of intersection as solution for the equations

Where do we use linear graphs in real life?

MENTOR mathematics Learner's Book Grade 8 pg. 186
-Graph paper
-Ruler
MENTOR mathematics Learner's Book Grade 8 pg. 189

-Observation -Written assignments

Geometry

4.3 Scale Drawing - Representing length to a given scale (2)
4.3 Scale Drawing - Converting between actual length and scale length (2)

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

-Represent length to a given scale
-Appreciate the use of scale drawing in daily life

-Measure and represent length of different objects from immediate environment in work book
-Share work with other learners in class

How do we determine scales in real life?

MENTOR mathematics Learner's Book Grade 8 pg. 191
-Ruler
MENTOR mathematics Learner's Book Grade 8 pg. 193

-Observation -Written assignments

Geometry

4.3 Scale Drawing - Converting between actual length and scale length (2)

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

-Convert scale length to actual length
-Enjoy working with measurements

-Practice converting scale length to actual length
-Share work with other learners in class

Where do we use scale drawing in real life situations?

MENTOR mathematics Learner's Book Grade 8 pg. 194
-Ruler

-Observation -Written assignments

Geometry

4.3 Scale Drawing - Linear scales in statement form (2)

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

-Interpret linear scales in statement form
-Appreciate the use of scale drawing in daily life

-Read, discuss and interpret given linear scales in statement form
-Share findings with other learners in class

How do we determine scales in real life?

MENTOR mathematics Learner's Book Grade 8 pg. 195
-Ruler
MENTOR mathematics Learner's Book Grade 8 pg. 196

-Observation -Written assignments

Geometry

4.3 Scale Drawing - Linear scales in ratio form (2)

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

-Interpret linear scales in ratio form
-Appreciate the use of scale drawing in maps

-Read, discuss and interpret given linear scales in ratio form
-Share findings with other learners in class

Where do we use scale drawing in real life situations?

MENTOR mathematics Learner's Book Grade 8 pg. 198
-Ruler
MENTOR mathematics Learner's Book Grade 8 pg. 199

-Observation -Written assignments

Geometry

4.3 Scale Drawing - Converting between statement form and ratio form (1)
4.3 Scale Drawing - Making scale drawings (1)

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

-Convert linear scale from statement form to ratio form
-Convert linear scale from ratio form to statement form
-Appreciate the use of scale drawing in maps

-Discuss and carry out conversions of scales from one form to another
-Share findings with other learners in class

How do we determine scales in real life?

MENTOR mathematics Learner's Book Grade 8 pg. 200
-Ruler
MENTOR mathematics Learner's Book Grade 8 pg. 202

-Observation -Written assignments

Geometry

4.4 Common Solids - Identifying common solids (3)

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

-Identify common solids from the environment
-Appreciate the use of common solids in real life

-Identify and collect common solids such as cubes, cuboids, cylinders, pyramids and cones from the immediate environment
-Share findings with other learners in class

What are common solids?

MENTOR mathematics Learner's Book Grade 8 pg. 209
-Various solid objects

-Observation

Geometry

4.4 Common Solids - Identifying common solids (3)

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

-Identify common solids from the environment
-Appreciate the use of common solids in real life

-Identify and collect common solids such as cubes, cuboids, cylinders, pyramids and cones from the immediate environment
-Share findings with other learners in class

What are common solids?

MENTOR mathematics Learner's Book Grade 8 pg. 210
-Various solid objects
MENTOR mathematics Learner's Book Grade 8 pg. 211

-Observation

Geometry

4.4 Common Solids - Sketching nets of common solids (3)

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

-Sketch nets of cubes and cuboids
-Enjoy working with geometric shapes

-Discuss, open and sketch the nets of hollow cubes and cuboids
-Share sketches with other learners in class

How do we use common solids in real life?

MENTOR mathematics Learner's Book Grade 8 pg. 212
-Various hollow solids

-Observation -Written assignments

Geometry

4.4 Common Solids - Sketching nets of common solids (3)

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

-Sketch nets of pyramids
-Enjoy working with geometric shapes

-Discuss, open and sketch the nets of hollow pyramids
-Share sketches with other learners in class

What are common solids?

v Learner's Book Grade 8 pg. 214
-Various hollow solids
MENTOR mathematics Learner's Book Grade 8 pg. 215

-Observation -Written assignments

Geometry

4.4 Common Solids - Surface area of solids from nets (4)

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

-Work out surface area of cubes from nets
-Enjoy working with geometric shapes

-Work out the surface area of cubes from nets
-Share findings with other learners in class

How do we use common solids in real life?

MENTOR mathematics Learner's Book Grade 8 pg. 216
-Nets of cubes
MENTOR mathematics Learner's Book Grade 8 pg. 217
-Nets of cuboids

-Observation -Written assignments

Geometry

4.4 Common Solids - Surface area of solids from nets (4)

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

-Work out surface area of cylinders from nets
-Enjoy working with geometric shapes

-Work out the surface area of cylinders from nets
-Share findings with other learners in class

What are common solids?

MENTOR mathematics Learner's Book Grade 8 pg. 219
-Nets of cylinders

-Observation -Written assignments

Geometry

4.4 Common Solids - Surface area of solids from nets (4)
4.4 Common Solids - Distance between points on a solid (2)

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

-Work out surface area of pyramids from nets
-Enjoy working with geometric shapes

-Work out the surface area of pyramids from nets
-Share findings with other learners in class

What are common solids?

MENTOR mathematics Learner's Book Grade 8 pg. 221
-Nets of pyramids
MENTOR mathematics Learner's Book Grade 8 pg. 224
-Various solid objects

-Observation -Written assignments

Geometry

4.4 Common Solids - Distance between points on a solid (2)
4.4 Common Solids - Making models of solids (3)

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

-Determine the distance between two points on the surface of a solid
-Show interest in properties of solids

-Discuss and practice measuring the distance between any two points on the surface of the solids
-Share findings with other learners in class

How do we use common solids in real life?

MENTOR mathematics Learner's Book Grade 8 pg. 225
-Various solid objects
MENTOR mathematics Learner's Book Grade 8 pg. 226
-Stiff paper
-Scissors
-Glue

-Observation -Written assignments

Geometry

4.4 Common Solids - Making models of solids (3)

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

-Make models of cuboids
-Enjoy working with geometric shapes

-Make models of hollow and compact cuboids using locally available materials
-Share models with other learners in class

What are common solids?

MENTOR mathematics Learner's Book Grade 8 pg. 227
-Stiff paper
-Scissors
-Glue
MENTOR mathematics Learner's Book Grade 8 pg. 228

-Observation

Geometry

4.4 Common Solids - Making models of solids (3)

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

-Make models of cylinders, pyramids and cones
-Enjoy working with geometric shapes

-Make models of hollow and compact cylinders, pyramids and cones using locally available materials
-Share models with other learners in class

How do we use common solids in real life?

MENTOR mathematics Learner's Book Grade 8 pg. 229
-Stiff paper
-Scissors
-Glue

-Observation