MEASUREMENTS

Money - Identifying Currencies Used in Different Countries
Money - Converting Currency from One to Another in Real Life Situations

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

-Identify currencies used in different countries;
-Match currencies with their respective countries;
-Recognize currency symbols;
-Show interest in learning about different currencies.

In groups, learners are guided to:
-Use digital devices to search and print pictures of currencies from: a) Neighboring countries b) Other African countries c) Common currencies used globally;
-Make a collage of different currencies on a piece of carton;
-Match currencies with their respective countries;
-Identify currency symbols (e.g., $, €, £, ¥);
-Display and present their collages to other groups.

Why do different countries use different currencies?

-Mathematics learners book grade 9 page 138;
-Digital devices for research;
-Pictures/samples of different currencies;
-Manila paper or carton;
-Charts showing currencies and their countries.
-Mathematics learners book grade 9 page 141;
-Exchange rate tables from newspapers or online sources;
-Scientific calculators;
-Digital devices for checking current exchange rates;
-Charts showing examples of currency conversions.

-Observation; -Oral questions; -Group presentations; -Assessment of currency collages.

MEASUREMENTS

Money - Converting Currency from One to Another in Real Life Situations
Money - Working Out Export Duties Charged on Goods

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

-Convert Kenyan currency to foreign currency;
-Use exchange rate tables to convert currencies;
-Solve problems involving currency conversion;
-Show interest in understanding international currency exchange.

In groups, learners are guided to:
-Review the concept of exchange rates;
-Understand that the selling rate is used when converting Kenyan Shillings to foreign currency;
-Convert Kenyan Shillings to various foreign currencies using the selling rate;
-Solve problems involving currency conversion;
-Discuss real-life situations where currency conversion is necessary;
-Discuss and share results with other groups.

How do exchange rates affect international trade?

-Mathematics learners book grade 9 page 142;
-Exchange rate tables from newspapers or online sources;
-Scientific calculators;
-Digital devices for checking current exchange rates;
-Charts showing examples of currency conversions.
-Mathematics learners book grade 9 page 143;
-Digital devices for research;
-Charts showing export duty rates;
-Examples of export scenarios.

-Observation; -Oral questions; -Written exercises; -Problem-solving assessment.

MEASUREMENTS

Money - Working Out Import Duties Charged on Goods
Money - Working Out Excise Duty Charged on Goods

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

-Define import duty;
-Calculate import duty on goods;
-Identify goods exempted from import duty;
-Show interest in understanding import duties.

In groups, learners are guided to:
-Use digital devices to search for the meaning of import duty;
-Research the percentage of import duty on different goods and services;
-Identify examples of goods exempted from import duty in Kenya;
-Calculate import duty on goods using the formula: Import Duty = Customs Value × Duty Rate;
-Solve problems involving import duties;
-Discuss and share findings with other groups.

What are import duties and why are they charged?

-Mathematics learners book grade 9 page 143;
-Digital devices for research;
-Scientific calculators;
-Charts showing import duty rates;
-Examples of import scenarios.
-Mathematics learners book grade 9 page 145;
-Charts showing excise duty rates;
-Examples of goods subject to excise duty.

-Observation; -Oral questions; -Written exercises; -Research presentation.

MEASUREMENTS

Money - Determining Value-Added Tax (VAT) Charged on Goods and Services
Approximations and Errors - Approximating Quantities in Measurements

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

-Define Value Added Tax (VAT);
-Identify goods and services that attract VAT;
-Calculate VAT on goods and services;
-Appreciate the role of VAT in government revenue collection.

In groups, learners are guided to:
-Use digital devices or print media to search for information on VAT;
-Research goods that attract VAT;
-Research the percentage of VAT charged on goods and services;
-Study receipts to identify VAT amounts;
-Calculate VAT on various goods and services;
-Discuss and share findings with other groups.

How is VAT calculated and why is it charged?

-Mathematics learners book grade 9 page 145;
-Supermarket receipts showing VAT;
-Digital devices for research;
-Scientific calculators;
-Charts showing VAT calculations.
-Mathematics learners book grade 9 page 148;
-Measuring tapes/rulers;
-Various objects to measure;
-Charts showing conventional and arbitrary units;
-Open space for measuring with strides.

-Observation; -Oral questions; -Written exercises; -Analysis of receipts.

MEASUREMENTS

Approximations and Errors - Determining Errors Using Estimations and Actual Measurements
Approximations and Errors - Determining Percentage Errors Using Actual Measurements

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

-Define error in measurements;
-Determine errors by comparing estimated and actual measurements;
-Calculate absolute errors in measurements;
-Develop genuine interest in understanding measurement errors.

In groups, learners are guided to:
-Estimate the measurements of various items in centimeters;
-Use a ruler to find the actual measurements of the items;
-Find the difference between the estimated and measured values;
-Understand that error = measured value - estimated value;
-Complete a table with estimated values, measured values, and errors;
-Discuss and share findings with other groups.

How do we determine errors in measurements?

-Mathematics learners book grade 9 page 149;
-Measuring tapes/rulers;
-Various objects to measure;
-Weighing scales/balances;
-Scientific calculators.
-Mathematics learners book grade 9 page 151;

-Observation; -Oral questions; -Written exercises; -Practical assessment.

Geometry

Similarity and Enlargement - Similar figures and properties
Similarity and Enlargement - Identifying similar objects

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

Identify similar figures and their properties;
Measure corresponding sides and angles of similar figures;
Appreciate the concept of similarity in real-life objects.

Learners study diagrams of similar cross-sections.
Learners measure the corresponding sides of the cross-sections and find the ratio between them.
Learners measure all the corresponding angles and discover that they are equal.

What makes two figures similar?

-KLB Mathematics Grade 9 Textbook page 203
-Ruler
-Protractor
-Cut-out shapes
-Charts showing similar figures
-Manila paper
-KLB Mathematics Grade 9 Textbook page 204
-Various geometric objects
-Charts with examples
-Worksheets with diagrams

-Oral questions -Observation -Written exercise -Checklist

Geometry

Similarity and Enlargement - Drawing similar figures
Similarity and Enlargement - Properties of enlargement

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

Draw similar figures in different situations;
Calculate dimensions of similar figures using scale factors;
Enjoy creating similar figures.

Learners draw triangle ABC with given dimensions (AB=3cm, BC=4cm, and AC=6cm).
Learners are told that triangle PQR is similar to ABC with PQ=4.5cm, and they calculate the other dimensions.
Learners construct triangle PQR and compare results with other groups.

How do we construct a figure similar to a given figure?

-KLB Mathematics Grade 9 Textbook page 206
-Ruler
-Protractor
-Pair of compasses
-Drawing paper
-Calculator
-Charts with examples
-KLB Mathematics Grade 9 Textbook page 209
-Tracing paper
-Colored pencils
-Grid paper
-Charts showing enlargements
-Diagrams for tracing

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

Geometry

Similarity and Enlargement - Negative scale factors
Similarity and Enlargement - Drawing images of objects

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

Determine properties of enlargement with negative scale factors;
Locate centers of enlargement with negative scale factors;
Appreciate the concept of negative scale factors in enlargements.

Learners trace diagrams showing an object and its image where the center of enlargement is between them.
Learners join corresponding points to locate the center of enlargement.
Learners find the ratio of distances from the center to corresponding points and note that the image is on the opposite side of the object.

What happens when an enlargement has a negative scale factor?

-KLB Mathematics Grade 9 Textbook page 211
-Ruler
-Tracing paper
-Grid paper
-Colored pencils
-Charts showing negative scale factor enlargements
-Diagrams for tracing
-KLB Mathematics Grade 9 Textbook page 214
-Charts showing steps of enlargement
-Manila paper

-Oral questions -Practical activity -Written exercise -Checklist

Geometry

Similarity and Enlargement - Linear scale factor
Similarity and Enlargement - Using coordinates in enlargement

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

Determine the linear scale factor of similar figures;
Calculate unknown dimensions using linear scale factors;
Value the application of linear scale factors in real-life problems.

Learners consider similar cones and find the ratios of their corresponding dimensions.
Learners study similar triangles and calculate the linear scale factor.
Learners use the scale factor to find unknown dimensions of similar figures.

How do we use linear scale factors to calculate unknown dimensions of similar figures?

-KLB Mathematics Grade 9 Textbook page 216
-Ruler
-Calculator
-Similar objects of different sizes
-Charts with examples
-Worksheets
-KLB Mathematics Grade 9 Textbook page 218
-Grid paper
-Colored pencils
-Charts with coordinate examples

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

Geometry

Similarity and Enlargement - Applications of similarity
Trigonometry - Angles and sides of right-angled triangles

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

Apply similarity concepts to solve real-life problems;
Calculate heights and distances using similar triangles;
Value the practical applications of similarity in everyday life.

Learners solve problems involving similar triangles to find unknown heights and distances.
Learners discuss how similarity is used in fields such as architecture, photography, and engineering.
Learners work on practical applications of similarity in the environment.

How can we use similarity to solve real-life problems?

-KLB Mathematics Grade 9 Textbook page 219
-Ruler
-Calculator
-Drawing paper
-Charts with real-life applications
-Manila paper for presentations
-KLB Mathematics Grade 9 Textbook page 220
-Protractor
-Set square
-Charts with labeled triangles
-Colored markers

-Oral questions -Problem-solving -Written exercise -Group presentation

Geometry

Trigonometry - Sine ratio
Trigonometry - Cosine ratio

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

Identify sine ratio from a right-angled triangle;
Calculate sine of angles in right-angled triangles;
Value the use of sine ratio in solving problems.

Learners draw triangles with specific angles and sides.
Learners draw perpendiculars from points on one side to another and measure their lengths.
Learners calculate ratios of opposite side to hypotenuse for different angles and discover the sine ratio.

What is the sine of an angle and how do we calculate it?

-KLB Mathematics Grade 9 Textbook page 222
-Ruler
-Protractor
-Calculator
-Drawing paper
-Charts showing sine ratio
-Manila paper
-KLB Mathematics Grade 9 Textbook page 223
-Charts showing cosine ratio
-Worksheets

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

Geometry

Trigonometry - Tangent ratio
Trigonometry - Reading tables of sines

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

Identify tangent ratio from a right-angled triangle;
Calculate tangent of angles in right-angled triangles;
Appreciate the importance of tangent ratio in problem-solving.

Learners draw triangle ABC with specific angles and mark points on BC.
Learners draw perpendiculars from these points to AC and measure their lengths.
Learners calculate ratios of opposite side to adjacent side for different angles and discover the tangent ratio.

What is the tangent of an angle and how do we calculate it?

-KLB Mathematics Grade 9 Textbook page 225
-Ruler
-Protractor
-Calculator
-Drawing paper
-Charts showing tangent ratio
-Manila paper
-KLB Mathematics Grade 9 Textbook page 227
-Mathematical tables
-Worksheets
-Chart showing how to read tables
-Sample exercises

-Oral questions -Practical activity -Written exercise -Checklist

Geometry

Trigonometry - Reading tables of cosines and tangents

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

Read tables of cosines and tangents for acute angles;
Find cosine and tangent values using mathematical tables;
Enjoy using mathematical tables to find trigonometric ratios.

Learners study parts of the tables of cosines and tangents.
Learners use the tables to find cosine and tangent values of specific angles.
Learners find values of angles with decimal parts using the 'SUBTRACT' column for cosines and 'ADD' column for tangents.

How do we use mathematical tables to find cosine and tangent values?

-KLB Mathematics Grade 9 Textbook page 229-231
-Mathematical tables
-Calculator
-Worksheets
-Chart showing how to read tables
-Sample exercises

-Oral questions -Practical activity -Written exercise -Observation

Geometry

Trigonometry - Using calculators for trigonometric ratios
Trigonometry - Calculating lengths using trigonometric ratios

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

Determine trigonometric ratios of acute angles using calculators;
Compare values obtained from tables and calculators;
Value the use of calculators in finding trigonometric ratios.

Learners use calculators to find trigonometric ratios of specific angles.
Learners compare values obtained from calculators with those from mathematical tables.
Learners use calculators to find sine, cosine, and tangent of various angles.

How do we use calculators to find trigonometric ratios?

-KLB Mathematics Grade 9 Textbook page 233
-Scientific calculators
-Mathematical tables
-Worksheets
-Chart showing calculator keys
-Sample exercises
-KLB Mathematics Grade 9 Textbook page 234
-Ruler
-Drawing paper
-Charts with examples

-Oral questions -Practical activity -Written exercise -Checklist

Geometry

Trigonometry - Calculating angles using trigonometric ratios
Trigonometry - Application in heights and distances

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

Use trigonometric ratios to calculate angles in right-angled triangles;
Apply inverse trigonometric functions to find angles;
Enjoy solving problems involving trigonometric ratios.

Learners consider right-angled triangles with known sides.
Learners calculate trigonometric ratios using the known sides and use tables or calculators to find the corresponding angles.
Learners solve problems involving finding angles in right-angled triangles.

How do we find unknown angles in right-angled triangles using trigonometric ratios?

-KLB Mathematics Grade 9 Textbook page 235
-Scientific calculators
-Mathematical tables
-Ruler
-Drawing paper
-Charts with examples
-Worksheets
-KLB Mathematics Grade 9 Textbook page 237
-Charts with real-life examples
-Manila paper

-Oral questions -Group work -Written exercise -Observation

Geometry

Trigonometry - Application in navigation
Trigonometry - Review and mixed applications

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

Apply trigonometric ratios in navigation problems;
Calculate distances and bearings using trigonometry;
Appreciate the importance of trigonometry in navigation.

Learners solve problems involving finding distances between locations given bearings and distances from a reference point.
Learners calculate bearings between points using trigonometric ratios.
Learners discuss how pilots, sailors, and navigators use trigonometry.

How is trigonometry used in navigation and determining positions?

-KLB Mathematics Grade 9 Textbook page 238
-Scientific calculators
-Mathematical tables
-Ruler
-Protractor
-Maps
-Charts with navigation examples
-KLB Mathematics Grade 9 Textbook page 240
-Drawing paper
-Past examination questions

-Oral questions -Problem-solving -Written exercise -Assessment rubrics

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
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;
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
-KLB Mathematics Grade 9 Textbook page 251
-Colored markers

-Oral questions -Written exercise -Group presentations -Checklist

Data Handling and Probability

Data Interpretation - Median of grouped data
Data Interpretation - Calculating median using formula

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

-Oral questions -Written exercise -Group presentations -Observation

Data Handling and Probability

Data Interpretation - Median calculations in real-life situations
Probability - Equally likely outcomes

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

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

Data Handling and Probability

Probability - Range of probability
Probability - Complementary events

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

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

Data Handling and Probability

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

-Oral questions -Group discussions -Written exercise -Observation

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

Probability - Complex tree diagrams

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