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

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.

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

MEASUREMENTS

Money - Working Out Excise Duty Charged on Goods
Money - Determining Value-Added Tax (VAT) Charged on Goods and Services

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

-Define excise duty;
-Identify goods and services that attract excise duty;
-Calculate excise duty on goods and services;
-Show interest in understanding taxation systems.

In groups, learners are guided to:
-Use digital devices to search for the meaning of excise duty;
-Research goods that attract excise duty;
-Research percentage of excise duty on goods and services;
-Calculate excise duty on various goods and services;
-Solve problems involving excise duty;
-Discuss and share findings with other groups.

What is excise duty and how is it different from other taxes?

-Mathematics learners book grade 9 page 145;
-Digital devices for research;
-Scientific calculators;
-Charts showing excise duty rates;
-Examples of goods subject to excise duty.
-Supermarket receipts showing VAT;
-Charts showing VAT calculations.

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

MEASUREMENTS

Approximations and Errors - Approximating Quantities in Measurements

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

-Approximate quantities using arbitrary units;
-Use strides, hand spans, and other body measurements to estimate lengths;
-Compare estimated values with actual measurements;
-Show interest in approximation techniques.

In groups, learners are guided to:
-Measure the lengths of their strides in centimeters;
-Measure the length of the classroom using strides;
-Estimate the length of the classroom in centimeters;
-Use hand spans to estimate lengths of various objects;
-Use thumb lengths to estimate smaller lengths;
-Discuss and share findings with other groups.

How do we estimate measurements of different quantities?

-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; -Practical assessment; -Group presentations.

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

Coordinates and Graphs - Plotting points on a Cartesian plane
Coordinates and Graphs - Drawing a straight line graph

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

Plot out points on a Cartesian plane;
Work in groups to locate points on a plane;
Appreciate the use of Cartesian plane in locating positions.

Learners are guided to work in groups and locate the point of intersection of the x-coordinate and the y-coordinates on a Cartesian plane.
Learners plot given points such as P(3,4), Q(4,-2), R(-3,-5) and S(-1,5) on a Cartesian plane.

How do we locate a point on a Cartesian plane?

-KLB Mathematics Grade 9 Textbook page 154
-Graph paper
-Ruler
-Pencils
-Charts with Cartesian plane
-Colored markers
-KLB Mathematics Grade 9 Textbook page 155
-Calculator
-Blackboard illustration

-Oral questions -Observation -Written exercise -Peer assessment

Geometry

Coordinates and Graphs - Completing tables for linear equations

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

Complete tables of values for different linear equations;
Plot points from completed tables on a Cartesian plane;
Enjoy drawing straight line graphs from tables of values.

Learners complete tables of values for given linear equations such as y=2x+3.
Learners plot the points on a Cartesian plane and join them using a straight edge to form a straight line graph.
Learners work in pairs to generate their own tables of values for different equations.

How do we use tables of values to draw straight line graphs?

-KLB Mathematics Grade 9 Textbook page 156
-Graph paper
-Ruler
-Pencils
-Calculator
-Charts with prepared tables

-Oral questions -Peer assessment -Written exercise -Checklist

Geometry

Coordinates and Graphs - Drawing parallel lines
Coordinates and Graphs - Relating gradients of parallel lines

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

Generate tables of values for parallel line equations;
Draw parallel lines on the Cartesian plane;
Appreciate the relationship between parallel lines on a graph.

Learners generate tables of values for equations such as y=x-5 and y=x-3.
Learners use the tables of values to draw the lines on the Cartesian plane.
Learners measure the distance between the two lines at different positions using a set square and discuss their findings.

How can we tell if two lines are parallel by looking at their equations?

-KLB Mathematics Grade 9 Textbook page 157
-Graph paper
-Ruler
-Set square
-Calculator
-Charts showing parallel lines
-KLB Mathematics Grade 9 Textbook page 158
-Manila paper
-Digital devices (optional)

-Oral questions -Group work -Written exercise -Observation

Geometry

Coordinates and Graphs - Drawing perpendicular lines
Coordinates and Graphs - Relating gradients of perpendicular lines

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

Generate tables of values for perpendicular line equations;
Draw perpendicular lines on the Cartesian plane;
Enjoy identifying perpendicular lines from their equations.

Learners generate tables of values for equations such as y=2x+3 and y=-1/2x+4.
Learners draw the lines on the Cartesian plane and measure the angle at the point of intersection.
Learners discuss and share their findings with other groups.

How can you determine if two lines are perpendicular from their equations?

-KLB Mathematics Grade 9 Textbook page 159
-Graph paper
-Ruler
-Protractor
-Set square
-Calculator
-Charts showing perpendicular lines
-KLB Mathematics Grade 9 Textbook page 160
-Charts with examples of perpendicular lines

-Oral questions -Observation -Written exercise -Checklist

Geometry

Coordinates and Graphs - Applications of straight line graphs

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

Apply graphs of straight lines to real-life situations;
Interpret information from straight line graphs;
Value the use of graphs in representing real-life situations.

Learners work in groups to generate tables of values for parking charges in two different towns.
Learners draw graphs to represent the information on the same Cartesian plane.
Learners find the gradient of the two lines drawn and determine whether they are parallel.

How can straight line graphs help us solve real-life problems?

-KLB Mathematics Grade 9 Textbook page 165
-Graph paper
-Ruler
-Calculator
-Charts showing real-life applications
-Manila paper for presentations

-Oral questions -Group discussion -Written exercise -Presentation

Geometry

Scale Drawing - Compass directions
Scale Drawing - Compass bearings

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

Identify compass and true bearings in real-life situations;
Draw and discuss the compass directions;
Appreciate the use of compass in navigation.

Learners carry out an activity outside the classroom where a member stands with hands spread out.
Learners draw a diagram showing the directions of the right hand, left hand, front, and back, labeling them in terms of North, South, East, and West.
Learners discuss situations where knowledge of compass direction is used.

How do we use compass directions to locate positions?

-KLB Mathematics Grade 9 Textbook page 168
-Magnetic compass
-Plain paper
-Colored pencils
-Charts showing compass directions
-Maps
-KLB Mathematics Grade 9 Textbook page 170
-Protractor
-Ruler
-Charts showing compass bearings
-Manila paper

-Oral questions -Practical activity -Written exercise -Observation

Geometry

Scale Drawing - True bearings
Scale Drawing - Determining compass bearings

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

Identify true bearings in real-life situations;
Draw and measure true bearings;
Appreciate the difference between compass and true bearings.

Learners trace diagrams showing true bearings.
Learners measure angles from North in the clockwise direction.
Learners draw accurately true bearings such as 008°, 036°, 126°, etc.

What is the difference between compass bearings and true bearings?

-KLB Mathematics Grade 9 Textbook page 171
-Protractor
-Ruler
-Plain paper
-Charts showing true bearings
-Diagrams for tracing
-KLB Mathematics Grade 9 Textbook page 173
-Charts with bearing examples
-Manila paper for group work

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

Geometry

Scale Drawing - Determining true bearings

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

Determine true bearings in different situations;
Measure angles to find true bearings;
Value the use of true bearings in navigation.

Learners consider a diagram showing points C and D.
Learners identify and determine the bearing of D from C by measurement.
Learners measure the bearing of various points in different diagrams.

How do we determine the true bearing of one point from another?

-KLB Mathematics Grade 9 Textbook page 175
-Protractor
-Ruler
-Plain paper
-Worksheets with diagrams
-Charts with bearing examples

-Oral questions -Practical activity -Written exercise -Checklist

Geometry

Scale Drawing - Locating points using compass bearing and distance
Scale Drawing - Locating points using true bearing and distance

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

Locate a point using bearing and distance in real-life situations;
Create scale drawings showing relative positions;
Appreciate the use of scale drawings in real-life situations.

Learners consider two markets U and V such that the distance between them is 6 km and U is on a bearing of N56°E from V.
Learners mark point V on paper, draw the bearing of U from V, and use a scale of 1 cm represents 1 km to locate U.
Learners display and discuss their constructions.

How do we use compass bearings and distances to locate positions?

-KLB Mathematics Grade 9 Textbook page 178
-Protractor
-Ruler
-Plain paper
-Drawing board
-Charts with examples
-Worksheets
-KLB Mathematics Grade 9 Textbook page 182
-Manila paper for presentations

-Oral questions -Practical activity -Written exercise -Peer assessment

Geometry

Scale Drawing - Angle of elevation

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

Identify angles of elevation in real-life situations;
Make and use a clinometer to measure angles of elevation;
Appreciate the application of angles of elevation in real-life situations.

Learners perform an activity outside the classroom where they stand next to a flag pole and mark points at eye level and above.
Learners observe how the line of sight forms an angle when looking at higher objects.
Learners make a clinometer and use it to measure angles of elevation of objects in the school environment.

What is an angle of elevation and how do we measure it?

-KLB Mathematics Grade 9 Textbook page 186
-Protractor
-String
-Weight (about 25g)
-Cardboard
-Straight piece of wood
-Charts showing angles of elevation

-Oral questions -Practical activity -Written exercise -Project assessment

Geometry

Scale Drawing - Determining angles of elevation
Scale Drawing - Angle of depression

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

Determine angles of elevation in different situations;
Use scale drawings to find angles of elevation;
Value the use of scale drawings in solving problems involving elevation.

Learners consider a flag pole AB that is 8 m high with point C on level ground 18 m from the foot of the pole.
Learners make a scale drawing showing A, B, and C using a scale of 1 cm represents 2 m.
Learners measure the angle between AC and CB and display their drawings.

How can we use scale drawings to determine angles of elevation?

-KLB Mathematics Grade 9 Textbook page 187
-Protractor
-Ruler
-Plain paper
-Drawing board
-Calculator
-Charts showing examples
-KLB Mathematics Grade 9 Textbook page 190
-Clinometer (made in previous lesson)
-String
-Weight
-Charts showing angles of depression
-Diagrams

-Oral questions -Scale drawing -Written exercise -Presentation

Geometry

Scale Drawing - Determining angles of depression
Scale Drawing - Application in simple surveying

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

Determine angles of depression in different situations;
Use scale drawings to find angles of depression;
Enjoy solving problems involving angles of depression.

Learners consider a stationary boat (B) that is 120 m away from the foot (F) of a cliff of height 80 m.
Learners make a scale drawing showing the positions of A, F, and B using a scale of 1 cm represents 20 m.
Learners measure the angle between the horizontal line passing through A and line AB to find the angle of depression.

How can we use scale drawings to determine angles of depression?

-KLB Mathematics Grade 9 Textbook page 192
-Protractor
-Ruler
-Plain paper
-Drawing board
-Calculator
-Charts with examples
-KLB Mathematics Grade 9 Textbook page 195
-Drawing paper
-Set square
-Pencil
-Field book (notebook)
-Charts with survey examples

-Oral questions -Scale drawing -Written exercise -Assessment rubrics

Geometry

Scale Drawing - Survey using bearings and distances

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

Survey an area using bearings and distances;
Create scale drawings from bearing and distance data;
Appreciate the application of bearings in surveying.

Learners study a sketch of a piece of land with positions given in terms of bearings and distances from point A.
Learners mark point A and use the bearings and distances to locate other points.
Learners create scale drawings of areas described by bearings and distances from given tables.

How do surveyors use bearings and distances to map areas?

-KLB Mathematics Grade 9 Textbook page 199
-Protractor
-Ruler
-Plain paper
-Drawing board
-Field book
-Charts with examples

-Oral questions -Scale drawing -Written exercise -Presentation

Geometry

Scale Drawing - Complex surveying problems
Scale Drawing - Project work on scale drawing

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

Solve complex surveying problems involving bearings and distances;
Create scale drawings of multiple points and features;
Show interest in scale drawing applications in real-life.

Learners study problems involving multiple points with bearings and distances between them.
Learners create scale drawings to determine unknown distances and bearings.
Learners discuss real-life applications of scale drawing in surveying and navigation.

How do we determine unknown distances and bearings using scale drawing?

-KLB Mathematics Grade 9 Textbook page 202
-Protractor
-Ruler
-Drawing paper
-Calculator
-Maps
-Charts with examples
-Measuring tape
-Compass
-Colored pencils
-Manila paper
-Drawing instruments

-Oral questions -Scale drawing -Written exercise -Assessment rubrics

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

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

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

Geometry

Similarity and Enlargement - Properties of enlargement
Similarity and Enlargement - Negative scale factors

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

Determine properties of enlargement of different figures;
Locate the center of enlargement and find scale factors;
Value the application of enlargement in real-life situations.

Learners trace diagrams showing an object and its enlarged image.
Learners draw lines through corresponding points to find where they intersect (center of enlargement).
Learners find the ratios of corresponding lengths to determine the scale factor.

How do we determine the center and scale factor of an enlargement?

-KLB Mathematics Grade 9 Textbook page 209
-Ruler
-Tracing paper
-Colored pencils
-Grid paper
-Charts showing enlargements
-Diagrams for tracing
-KLB Mathematics Grade 9 Textbook page 211
-Charts showing negative scale factor enlargements

-Oral questions -Practical activity -Written exercise -Observation

Geometry

Similarity and Enlargement - Drawing images of objects

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

Apply properties of enlargement to draw similar objects and their images;
Use scale factors to determine dimensions of images;
Enjoy creating enlarged images of objects.

Learners trace a given figure and join the center of enlargement to each vertex.
Learners multiply each distance by the scale factor to locate the image points.
Learners locate the image points and join them to create the enlarged figure.

How do we draw the image of an object under an enlargement with a given center and scale factor?

-KLB Mathematics Grade 9 Textbook page 214
-Ruler
-Grid paper
-Colored pencils
-Charts showing steps of enlargement
-Manila paper

-Oral questions -Practical activity -Written exercise -Peer assessment

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

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

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

Geometry

Trigonometry - Cosine ratio
Trigonometry - Tangent ratio

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

Identify cosine ratio from a right-angled triangle;
Calculate cosine of angles in right-angled triangles;
Enjoy solving problems involving cosine ratio.

Learners draw triangles with specific angles and sides.
Learners calculate ratios of adjacent side to hypotenuse for different angles and discover the cosine ratio.
Learners find the cosine of marked angles in various right-angled triangles.

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

-KLB Mathematics Grade 9 Textbook page 223
-Ruler
-Protractor
-Calculator
-Drawing paper
-Charts showing cosine ratio
-Worksheets
-KLB Mathematics Grade 9 Textbook page 225
-Charts showing tangent ratio
-Manila paper

-Oral questions -Practical activity -Written exercise -Observation

Geometry

Trigonometry - Reading tables of sines
Trigonometry - Reading tables of cosines and tangents

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

Read tables of trigonometric ratios of acute angles;
Find the sine values of different angles using tables;
Value the importance of mathematical tables in finding trigonometric ratios.

Learners study a part of the table of sines.
Learners use the table to look for specific angles and find their sine values.
Learners find sine values of angles with decimal parts using the 'ADD' column in the tables.

How do we use mathematical tables to find the sine of an angle?

-KLB Mathematics Grade 9 Textbook page 227
-Mathematical tables
-Calculator
-Worksheets
-Chart showing how to read tables
-Sample exercises
-KLB Mathematics Grade 9 Textbook page 229-231

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

Geometry

Trigonometry - Using calculators for 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

-Oral questions -Practical activity -Written exercise -Checklist

Geometry

Trigonometry - Calculating lengths using trigonometric ratios
Trigonometry - Calculating angles using trigonometric ratios

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

Apply trigonometric ratios to calculate lengths of right-angled triangles;
Use sine, cosine, and tangent ratios to find unknown sides;
Appreciate the application of trigonometry in solving real-life problems.

Learners consider a right-angled triangle and find the trigonometric ratio appropriate for finding an unknown side.
Learners find the value of the ratio from tables or calculators and relate it to the expression to find the unknown side.
Learners solve problems involving finding sides of right-angled triangles.

How do we use trigonometric ratios to find unknown sides in right-angled triangles?

-KLB Mathematics Grade 9 Textbook page 234
-Scientific calculators
-Mathematical tables
-Ruler
-Drawing paper
-Charts with examples
-Worksheets
-KLB Mathematics Grade 9 Textbook page 235

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

Geometry

Trigonometry - Application in heights and distances

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

Apply trigonometric ratios to solve problems involving heights and distances;
Calculate heights of objects using angles of elevation;
Value the use of trigonometry in real-life situations.

Learners solve problems involving finding heights of objects like flag poles, towers, and buildings using angles of elevation.
Learners apply sine, cosine, and tangent ratios as appropriate to calculate unknown heights and distances.
Learners discuss real-life applications of trigonometry in architecture, navigation, and engineering.

How do we use trigonometry to find heights and distances in real-life situations?

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

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

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

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
Data Interpretation - Modal class

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
-KLB Mathematics Grade 9 Textbook page 248
-Chart showing frequency distribution tables
-Colored markers

-Oral questions -Written exercise -Group presentations -Observation

Data Handling and Probability

Data Interpretation - Mean of ungrouped data
Data Interpretation - Mean of grouped 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
-KLB Mathematics Grade 9 Textbook page 250
-Graph paper
-Chart with examples

-Oral questions -Written exercise -Observation -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
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

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
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

Probability - Complex tree diagrams

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