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
Geometry
Geometry

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

-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;
-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

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

Geometry

Coordinates and Graphs - Completing tables for linear equations
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:

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

-Oral questions -Peer assessment -Written exercise -Checklist

Geometry

Coordinates and Graphs - Drawing perpendicular lines
Coordinates and Graphs - Relating gradients of perpendicular lines
Coordinates and Graphs - Applications of straight line graphs

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

-Oral questions -Observation -Written exercise -Checklist

Geometry

Scale Drawing - Compass directions
Scale Drawing - Compass bearings
Scale Drawing - True bearings
Scale Drawing - Determining 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
-KLB Mathematics Grade 9 Textbook page 171
-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 -Observation

Geometry

Scale Drawing - Determining true bearings
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:

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

-Oral questions -Practical activity -Written exercise -Checklist

Geometry

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

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
-KLB Mathematics Grade 9 Textbook page 187
-Ruler
-Plain paper
-Drawing board
-Calculator
-Charts showing examples
-KLB Mathematics Grade 9 Textbook page 190
-Clinometer (made in previous lesson)
-Weight
-Charts showing angles of depression
-Diagrams
-KLB Mathematics Grade 9 Textbook page 192
-Charts with examples

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

Geometry

Scale Drawing - Application in simple surveying
Scale Drawing - Survey using bearings and distances
Scale Drawing - Complex surveying problems

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

Apply scale drawing in simple surveying;
Record measurements in a field book;
Value the importance of surveying in mapping.

Learners study a survey of a small island made using a triangle ABC around it.
Learners trace the diagram and draw perpendicular lines from points along the triangle sides to the edge of the island.
Learners measure the lengths of perpendicular lines and record the measurements in a tabular form in a field book.

How do surveyors use scale drawings to create maps?

-KLB Mathematics Grade 9 Textbook page 195
-Drawing paper
-Ruler
-Set square
-Pencil
-Field book (notebook)
-Charts with survey examples
-KLB Mathematics Grade 9 Textbook page 199
-Protractor
-Plain paper
-Drawing board
-Field book
-Charts with examples
-KLB Mathematics Grade 9 Textbook page 202
-Calculator
-Maps

-Oral questions -Practical activity -Written exercise -Field book assessment

Geometry

Scale Drawing - Project work on scale drawing
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:

Apply scale drawing techniques to a real-life situation;
Create a scale map of the school compound or local area;
Appreciate the practical applications of scale drawing.

Learners work in groups to create a scale map of a part of the school compound.
Learners measure distances and determine bearings between key features.
Learners create a detailed scale drawing with a key showing the various features mapped.

How can we apply scale drawing techniques to map our environment?

-KLB Mathematics Grade 9 Textbook page 202
-Measuring tape
-Compass
-Drawing paper
-Colored pencils
-Manila paper
-Drawing instruments
-KLB Mathematics Grade 9 Textbook page 203
-Ruler
-Protractor
-Cut-out shapes
-Charts showing similar figures
-KLB Mathematics Grade 9 Textbook page 204
-Various geometric objects
-Charts with examples
-Worksheets with diagrams

-Project work -Group presentation -Peer assessment -Observation

Geometry

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

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
-KLB Mathematics Grade 9 Textbook page 211
-Charts showing negative scale factor enlargements
-KLB Mathematics Grade 9 Textbook page 214
-Charts showing steps of enlargement
-Manila paper

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

Geometry

Similarity and Enlargement - Linear scale factor
Similarity and Enlargement - Using coordinates in enlargement
Similarity and Enlargement - Applications of similarity

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
-KLB Mathematics Grade 9 Textbook page 219
-Drawing paper
-Charts with real-life applications
-Manila paper for presentations

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

Geometry

Trigonometry - Angles and sides of right-angled triangles
Trigonometry - Sine ratio
Trigonometry - Cosine ratio
Trigonometry - Tangent ratio

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

Identify angles and sides of right-angled triangles in different situations;
Distinguish between the hypotenuse, adjacent side, and opposite side;
Appreciate the relationship between angles and sides in right-angled triangles.

Learners draw right-angled triangles with acute angles and identify the longest side (hypotenuse).
Learners identify the side which together with the hypotenuse forms the angle θ (adjacent side).
Learners identify the side facing the angle θ (opposite side).

How do we identify different sides in a right-angled triangle?

-KLB Mathematics Grade 9 Textbook page 220
-Ruler
-Protractor
-Set square
-Drawing paper
-Charts with labeled triangles
-Colored markers
-KLB Mathematics Grade 9 Textbook page 222
-Calculator
-Charts showing sine ratio
-Manila paper
-KLB Mathematics Grade 9 Textbook page 223
-Charts showing cosine ratio
-Worksheets
-KLB Mathematics Grade 9 Textbook page 225
-Charts showing tangent ratio

-Oral questions -Observation -Written exercise -Checklist

Geometry

Trigonometry - Reading tables of sines
Trigonometry - Reading tables of cosines and tangents
Trigonometry - Using calculators for trigonometric ratios

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
-KLB Mathematics Grade 9 Textbook page 233
-Scientific calculators
-Chart showing calculator keys

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

Geometry

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

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
-KLB Mathematics Grade 9 Textbook page 237
-Charts with real-life examples
-Manila paper

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

Geometry
Data Handling and Probability
Data Handling and Probability

Trigonometry - Application in navigation
Trigonometry - Review and mixed applications
Data Interpretation - Appropriate class width
Data Interpretation - Finding range and creating groups

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
-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 -Problem-solving -Written exercise -Assessment rubrics

Data Handling and Probability

Data Interpretation - Frequency distribution tables
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:

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

-Oral questions -Group presentations -Written exercise -Checklist

Data Handling and Probability

Data Interpretation - Mean of ungrouped data
Data Interpretation - Mean of grouped data
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 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
-KLB Mathematics Grade 9 Textbook page 251
-KLB Mathematics Grade 9 Textbook page 252
-Chart showing cumulative frequency tables

-Oral questions -Written exercise -Observation -Assessment rubrics

Data Handling and Probability

Data Interpretation - Calculating median using formula
Data Interpretation - Median calculations in real-life situations
Probability - Equally likely outcomes

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

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

Data Handling and Probability

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

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

Data Handling and Probability

Probability - Experiments with mutually exclusive events
Probability - Independent events
Probability - Calculating probabilities of independent events
Probability - Tree diagrams for single outcomes
Probability - Complex tree diagrams
Probability - Complex tree diagrams

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
-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
-Chart showing multiplication rule
-KLB Mathematics Grade 9 Textbook page 262
-Chart paper
-Ruler
-Worksheets with blank tree diagrams
-Chart showing completed tree diagrams
-KLB Mathematics Grade 9 Textbook page 263
-Chart showing complex tree diagrams

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