Geometry

Angles - Angles on a straight line

By the end of the lesson, the learner should be able to:
- Identify angles formed on a straight line
- State that angles on a straight line add up to 180°
- Show interest in learning about angles

In groups, learners are guided to:
- Go outside classroom and identify angles made by objects in relation to ground
- Draw line AB and mark point P, measure angle APB using protractor
- Draw lines LP and KP and measure angles APL, LPK, KPB

What is the sum of angles on a straight line?

- Smart Minds Mathematics Learner's Book pg. 184
- Protractors
- Rulers

- Oral questions - Written exercises - Observation

Geometry

Angles - Angles at a point

By the end of the lesson, the learner should be able to:
- Identify angles formed at a point
- State that angles at a point add up to 360°
- Appreciate the relationship between angles at a point

In groups, learners are guided to:
- Trace and cut out diagram with angles ACB, ACD and BCD
- Use protractor to measure each angle
- Find sum of angles and establish they add up to 360°

What is the sum of angles at a point?

- Smart Minds Mathematics Learner's Book pg. 186
- Protractors
- Paper cut-outs

- Written assignments - Class activities - Oral questions

Geometry

Angles - Vertically opposite angles

By the end of the lesson, the learner should be able to:
- Identify vertically opposite angles
- State that vertically opposite angles are equal
- Show confidence in working with vertically opposite angles

In groups, learners are guided to:
- Trace and cut out figure with angles a, b, c and d
- Use protractor to measure each angle
- Compare angles: a = c, b = d (vertically opposite angles are equal)

What are vertically opposite angles?

- Smart Minds Mathematics Learner's Book pg. 187
- Protractors
- Scissors

- Written exercises - Oral questions - Observation

Geometry

Angles - Alternate angles on a transversal

By the end of the lesson, the learner should be able to:
- Define a transversal
- Identify alternate angles on a transversal
- Value the properties of alternate angles

In groups, learners are guided to:
- Draw two parallel lines and a transversal crossing them
- Mark angles d and f, cut them out using scissors
- Place angle f on top of angle d and compare (alternate angles are equal)

What are alternate angles?

- Smart Minds Mathematics Learner's Book pg. 188
- Rulers
- Scissors

- Written assignments - Class activities - Oral questions

Geometry

Angles - Corresponding angles on a transversal

By the end of the lesson, the learner should be able to:
- Identify corresponding angles on a transversal
- State that corresponding angles are equal
- Show interest in properties of corresponding angles

In groups, learners are guided to:
- Draw pair of parallel lines and a transversal
- Mark angles v and r, cut them out
- Compare by placing one on top of the other (corresponding angles are equal)

What are corresponding angles?

- Smart Minds Mathematics Learner's Book pg. 190
- Rulers
- Scissors, protractors

- Written exercises - Oral questions - Observation

Geometry

Angles - Co-interior angles on a transversal

By the end of the lesson, the learner should be able to:
- Identify co-interior angles on a transversal
- State that co-interior angles add up to 180°
- Appreciate the relationship between co-interior angles

In groups, learners are guided to:
- Draw pair of parallel lines and a transversal
- Mark angles n and p, cut them out
- Place two angles on a straight line and observe they add up to 180°

What is the sum of co-interior angles?

- Smart Minds Mathematics Learner's Book pg. 191
- Rulers
- Scissors, protractors

- Written assignments - Class activities - Oral questions

Geometry

Angles - Angles in a parallelogram

By the end of the lesson, the learner should be able to:
- Identify properties of angles in a parallelogram
- State that opposite angles are equal and interior angles add up to 360°
- Show confidence in working with parallelogram angles

In groups, learners are guided to:
- Use 4 straws and string to form rectangular shape
- Push top straw sideways to form parallelogram
- Measure angles a, b, c, d and find that opposite angles are equal

What are the properties of angles in a parallelogram?

- Smart Minds Mathematics Learner's Book pg. 193
- Straws, string
- Protractors

- Written exercises - Oral questions - Observation

Geometry

Angles - Interior angles of triangles, rectangles, squares

By the end of the lesson, the learner should be able to:
- Identify interior angles of triangles, rectangles and squares
- Calculate sum of interior angles
- Value the properties of interior angles

In groups, learners are guided to:
- Trace and draw triangle, cut angles a, b, c and make straight line (sum = 180°)
- Trace rectangle and square, measure interior angles
- Establish sum of interior angles is 360° for quadrilaterals

What is the sum of interior angles of a triangle?

- Smart Minds Mathematics Learner's Book pg. 195
- Protractors
- Polygon cut-outs

- Written assignments - Class activities - Oral questions

Geometry

Angles - Interior angles of rhombus, parallelogram, trapezium, pentagon, hexagon

By the end of the lesson, the learner should be able to:
- Identify interior angles of various polygons
- Calculate sum of interior angles using formula (n-2) × 180°
- Appreciate the relationship between sides and interior angles

In groups, learners are guided to:
- Trace and cut out rhombus, parallelogram, trapezium
- Measure interior angles and find sums
- Sub-divide pentagon into 3 triangles, hexagon into 4 triangles

How do we calculate sum of interior angles of any polygon?

- Smart Minds Mathematics Learner's Book pg. 197
- Polygon cut-outs
- Protractors

- Written exercises - Oral questions - Observation

Geometry

Angles - Exterior angles of polygons

By the end of the lesson, the learner should be able to:
- Identify exterior angles of polygons
- State that sum of exterior angles of any polygon is 360°
- Show interest in calculating exterior angles

In groups, learners are guided to:
- Trace and cut out quadrilateral, measure exterior angles A, B, C, D
- Find sum of exterior angles (360°)
- Draw and find sum of exterior angles of pentagon, hexagon

What is the sum of exterior angles of any polygon?

- Smart Minds Mathematics Learner's Book pg. 201
- Polygon cut-outs
- Protractors

- Written assignments - Class activities - Oral questions

Geometry

Geometrical Constructions - Measuring angles

By the end of the lesson, the learner should be able to:
- Use a protractor to measure angles accurately
- Draw angles of given sizes
- Show interest in measuring angles

In groups, learners are guided to:
- Trace and draw figures with angles ABC, BAC, ACB, ACD
- Place protractor with centre at vertex, straight edge along one line
- Read angle measure from correct scale

How do we measure angles using a protractor?

- Smart Minds Mathematics Learner's Book pg. 207
- Protractors
- Rulers

- Oral questions - Practical activities - Observation

Geometry

Geometrical Constructions - Bisecting angles

By the end of the lesson, the learner should be able to:
- Define angle bisector
- Bisect angles using a pair of compasses
- Appreciate the use of bisecting angles

In groups, learners are guided to:
- Trace and draw lines, measure angles ABC, ABD and DBC
- With compasses at point L, mark arcs on lines LK and LM at P and W
- With same radius at P and W, draw arcs to intersect at O, join O to L

What is an angle bisector?

- Smart Minds Mathematics Learner's Book pg. 208
- Pair of compasses
- Rulers

- Written assignments - Practical activities - Oral questions

Geometry

Geometrical Constructions - Constructing 90° angle

By the end of the lesson, the learner should be able to:
- Construct an angle of 90° using a pair of compasses and ruler
- Verify the constructed angle using a protractor
- Show confidence in constructing 90° angles

In groups, learners are guided to:
- Draw horizontal line, mark point A
- With compasses at A, make arcs on line at points X and Y
- With centres X and Y, draw arcs above line to intersect at T, join T to A

How do we construct an angle of 90°?

- Smart Minds Mathematics Learner's Book pg. 210
- Pair of compasses
- Rulers, protractors

- Practical exercises - Oral questions - Observation

Geometry

Geometrical Constructions - Constructing 45° angle

By the end of the lesson, the learner should be able to:
- Construct an angle of 45° by bisecting 90°
- Verify the constructed angle
- Value accuracy in geometrical constructions

In groups, learners are guided to:
- Draw horizontal line, mark point K
- Construct 90° angle (MKB = 90°)
- Bisect angle MKB: make arcs at S and R, draw arcs to intersect at O, join O to K

How do we construct an angle of 45°?

- Smart Minds Mathematics Learner's Book pg. 211
- Pair of compasses
- Rulers

- Written assignments - Practical activities - Oral questions

Geometry

Geometrical Constructions - Constructing 60° angle

By the end of the lesson, the learner should be able to:
- Construct an angle of 60° using a pair of compasses and ruler
- Verify the constructed angle using a protractor
- Show interest in constructing angles

In groups, learners are guided to:
- Draw straight line, mark point A
- With A as centre, make arc intersecting line at Y
- With Y as centre and same radius, draw arc to intersect first at K, join K to A

How do we construct an angle of 60°?

- Smart Minds Mathematics Learner's Book pg. 213
- Pair of compasses
- Rulers, protractors

- Practical exercises - Oral questions - Observation

Geometry

Geometrical Constructions - Constructing 30° angle

By the end of the lesson, the learner should be able to:
- Construct an angle of 30° by bisecting 60°
- Verify the constructed angle
- Appreciate the relationship between 30° and 60° angles

In groups, learners are guided to:
- Draw straight line, mark point Y
- With Y as centre, make arc at D, with D as centre make arc at F
- Join F to Y (angle FYD = 60°), then bisect to get 30°

How do we construct an angle of 30°?

- Smart Minds Mathematics Learner's Book pg. 214
- Pair of compasses
- Rulers

- Written assignments - Practical activities - Oral questions

Geometry

Geometrical Constructions - Constructing 120° angle

By the end of the lesson, the learner should be able to:
- Construct an angle of 120° using a pair of compasses and ruler
- Verify the constructed angle
- Show confidence in constructing obtuse angles

In groups, learners are guided to:
- Draw straight line, mark point M
- With centre M, make arc at C, with centre C make arc at E
- With centre E and same radius, make arc at F, join E to M (angle EMB = 120°)

How do we construct an angle of 120°?

- Smart Minds Mathematics Learner's Book pg. 215
- Pair of compasses
- Rulers, protractors

- Practical exercises - Oral questions - Observation

Geometry

Geometrical Constructions - Constructing 105° and 75° angles

By the end of the lesson, the learner should be able to:
- Construct angles of 105° and 75°
- Combine construction of 90° and 60° to get 105°
- Value the application of angle constructions

In groups, learners are guided to:
- Draw line MN, mark point T
- Construct 90° angle (NTO = 90°), then construct 60° on other side (angle KTO = 60°)
- Bisect angle KTO to get 30°, thus angle PTN = 90° + 15° = 105°

How do we construct an angle of 105°?

- Smart Minds Mathematics Learner's Book pg. 216
- Pair of compasses
- Rulers

- Written assignments - Practical activities - Oral questions

Geometry

Geometrical Constructions - Constructing equilateral triangles

By the end of the lesson, the learner should be able to:
- Construct equilateral triangles using compasses and ruler
- Verify that all sides and angles are equal
- Appreciate properties of equilateral triangles

In groups, learners are guided to:
- Draw straight line, mark point Y, mark point X 6 cm away
- With Y as centre and radius 6 cm, draw arc above line
- With X as centre and same radius, draw arc to intersect at Z, join Z to Y and X

How do we construct an equilateral triangle?

- Smart Minds Mathematics Learner's Book pg. 218
- Pair of compasses
- Rulers

- Practical exercises - Oral questions - Observation

Geometry

Geometrical Constructions - Constructing isosceles triangles

By the end of the lesson, the learner should be able to:
- Construct isosceles triangles given side measurements
- Verify that two sides and two angles are equal
- Show confidence in constructing triangles

In groups, learners are guided to:
- Draw straight line, mark point M, mark point N 5 cm away
- With M as centre and radius 7 cm, draw arc above line
- With N as centre and radius 5 cm, draw arc to intersect at P, join points

How do we construct an isosceles triangle?

- Smart Minds Mathematics Learner's Book pg. 219
- Pair of compasses
- Rulers

- Written assignments - Practical activities - Oral questions

Geometry

Geometrical Constructions - Constructing scalene triangles

By the end of the lesson, the learner should be able to:
- Construct scalene triangles given three side measurements
- Verify that all sides and angles are different
- Value accuracy in triangle constructions

In groups, learners are guided to:
- Draw straight line, mark point A, mark point B 6 cm away
- With A as centre and radius 5 cm, draw arc
- With B as centre and radius 8 cm, draw arc to intersect at C, join points

How do we construct a scalene triangle?

- Smart Minds Mathematics Learner's Book pg. 220
- Pair of compasses
- Rulers

- Practical exercises - Oral questions - Observation

Geometry

Geometrical Constructions - Constructing scalene triangles

By the end of the lesson, the learner should be able to:
- Construct scalene triangles given three side measurements
- Verify that all sides and angles are different
- Value accuracy in triangle constructions

In groups, learners are guided to:
- Draw straight line, mark point A, mark point B 6 cm away
- With A as centre and radius 5 cm, draw arc
- With B as centre and radius 8 cm, draw arc to intersect at C, join points

How do we construct a scalene triangle?

- Smart Minds Mathematics Learner's Book pg. 220
- Pair of compasses
- Rulers

- Practical exercises - Oral questions - Observation

Geometry

Geometrical Constructions - Constructing scalene triangles

By the end of the lesson, the learner should be able to:
- Construct scalene triangles given three side measurements
- Verify that all sides and angles are different
- Value accuracy in triangle constructions

In groups, learners are guided to:
- Draw straight line, mark point A, mark point B 6 cm away
- With A as centre and radius 5 cm, draw arc
- With B as centre and radius 8 cm, draw arc to intersect at C, join points

How do we construct a scalene triangle?

- Smart Minds Mathematics Learner's Book pg. 220
- Pair of compasses
- Rulers

- Practical exercises - Oral questions - Observation

Geometry

Geometrical Constructions - Constructing circles

By the end of the lesson, the learner should be able to:
- Construct circles given radius or diameter
- Measure and verify the dimensions of constructed circles
- Appreciate the application of geometrical constructions in real life

In groups, learners are guided to:
- Use pair of compasses to draw circles with different diameters
- Measure diameter of circles drawn
- Calculate radius from diameter (radius = diameter ÷ 2)

How do we construct circles with given measurements?

- Smart Minds Mathematics Learner's Book pg. 221
- Pair of compasses
- Rulers

- Written assignments - Practical activities - Oral questions

Geometry

Geometrical Constructions - Constructing circles

By the end of the lesson, the learner should be able to:
- Construct circles given radius or diameter
- Measure and verify the dimensions of constructed circles
- Appreciate the application of geometrical constructions in real life

In groups, learners are guided to:
- Use pair of compasses to draw circles with different diameters
- Measure diameter of circles drawn
- Calculate radius from diameter (radius = diameter ÷ 2)

How do we construct circles with given measurements?

- Smart Minds Mathematics Learner's Book pg. 221
- Pair of compasses
- Rulers

- Written assignments - Practical activities - Oral questions

Data Handling and Probability

Data Handling - Meaning of data and data collection
Data Handling - Frequency tables

By the end of the lesson, the learner should be able to:
- Define data as information gathered by observation, questioning or measurement
- Collect data through simple activities
- Show interest in collecting data

In groups, learners are guided to:
- Use digital device to find meaning of data
- Select favourite fruit from options (banana, watermelon, orange, mango)
- Write favourite fruit on paper and drop in basket, count responses

What is data?

- Smart Minds Mathematics Learner's Book pg. 222
- Pieces of paper
- Basket
- Smart Minds Mathematics Learner's Book pg. 223
- Class registers
- Frequency table templates

- Oral questions - Written exercises - Observation

Data Handling and Probability

Data Handling - Determining suitable scale

By the end of the lesson, the learner should be able to:
- Explain the importance of choosing appropriate scale
- Determine suitable scale for vertical and horizontal axes
- Show confidence in selecting scales for graphs

In groups, learners are guided to:
- Compare Anne's and Josephine's graph scales
- Observe that congested scales make graphs hard to interpret
- Use multiples of 2 or 5 to make divisions easy to plot

Why is it important to choose a suitable scale for graphs?

- Smart Minds Mathematics Learner's Book pg. 225
- Graph papers
- Rulers

- Written exercises - Oral questions - Observation

Data Handling and Probability

Data Handling - Drawing pictographs

By the end of the lesson, the learner should be able to:
- Define a pictograph
- Draw pictographs to represent data
- Value the use of pictures in representing data

In groups, learners are guided to:
- Study chart showing wild animals at Masai Mara National Park
- Trace and cut out animals, stick under suitable category
- Use symbols to represent quantities (key: 1 symbol = specific value)

What is a pictograph?

- Smart Minds Mathematics Learner's Book pg. 226
- Bloating paper
- Scissors, glue

- Written assignments - Practical activities - Oral questions

Data Handling and Probability

Data Handling - Drawing bar graphs

By the end of the lesson, the learner should be able to:
- Identify components of a bar graph (axes, bars, scale)
- Draw bar graphs to represent data
- Appreciate the use of bar graphs in data representation

In groups, learners are guided to:
- Make boxes of different colours and pile similar colours together
- Draw two axes: vertical (frequency) and horizontal (categories)
- Draw bars of same thickness with heights representing values

How do we draw a bar graph?

- Smart Minds Mathematics Learner's Book pg. 228
- Graph papers
- Rulers, coloured pencils

- Written exercises - Practical activities - Observation

Data Handling and Probability

Data Handling - Interpreting information from bar graphs

By the end of the lesson, the learner should be able to:
- Read and interpret information from bar graphs
- Answer questions based on bar graph data
- Show interest in analyzing data from bar graphs

In groups, learners are guided to:
- Study bar graph showing fruits sold by Bahati in five days
- Identify scale used on vertical and horizontal axes
- Answer questions about highest, lowest values and comparisons

How do we interpret information from bar graphs?

- Smart Minds Mathematics Learner's Book pg. 231
- Bar graph samples
- Worksheets

- Written assignments - Class activities - Oral questions

Data Handling and Probability

Data Handling - Drawing pie charts

By the end of the lesson, the learner should be able to:
- Define a pie chart as a circle divided into sectors
- Calculate angles for each sector
- Draw pie charts to represent data

In groups, learners are guided to:
- Read story of Ndole the bus driver spending salary on fees, savings, food
- Draw circle and shade fractions (1/2, 1/4, 1/4)
- Calculate sector angles: (value ÷ total) × 360°

How do we draw a pie chart?

- Smart Minds Mathematics Learner's Book pg. 233
- Pair of compasses
- Protractors

- Written exercises - Practical activities - Observation

Data Handling and Probability

Data Handling - Interpreting pie charts

By the end of the lesson, the learner should be able to:
- Read and interpret information from pie charts
- Calculate values from pie chart sectors
- Value the use of pie charts in presenting data

In groups, learners are guided to:
- Study pie chart showing how Standa spent monthly salary of sh 30,000
- Calculate values: (sector angle ÷ 360°) × total value
- Answer questions about entertainment, rent, savings, investment

How do we interpret information from pie charts?

- Smart Minds Mathematics Learner's Book pg. 236
- Pie chart samples
- Calculators

- Written assignments - Class activities - Oral questions

Data Handling and Probability

Data Handling - Drawing line graphs

By the end of the lesson, the learner should be able to:
- Define a line graph as showing relationship between two quantities
- Draw line graphs to represent data
- Appreciate the use of line graphs in showing trends

In groups, learners are guided to:
- Study table showing packets of milk and cost in shillings
- Choose appropriate scale, draw and mark axes
- Plot points using table values, join points with straight line

How do we draw a line graph?

- Smart Minds Mathematics Learner's Book pg. 238
- Graph papers
- Rulers

- Written exercises - Practical activities - Observation

Data Handling and Probability

Data Handling - Interpreting travel graphs

By the end of the lesson, the learner should be able to:
- Draw and interpret travel graphs
- Calculate distance, time and speed from travel graphs
- Show interest in using graphs to represent journeys

In groups, learners are guided to:
- Study table showing Lugai's journey from town A to town B
- Draw travel graph with time on horizontal axis and distance on vertical axis
- Calculate distance at specific times, total time and average speed

How do we use travel graphs to show journeys?

- Smart Minds Mathematics Learner's Book pg. 240
- Graph papers
- Calculators

- Written assignments - Class activities - Oral questions

Data Handling and Probability

Data Handling - Interpreting travel graphs

By the end of the lesson, the learner should be able to:
- Draw and interpret travel graphs
- Calculate distance, time and speed from travel graphs
- Show interest in using graphs to represent journeys

In groups, learners are guided to:
- Study table showing Lugai's journey from town A to town B
- Draw travel graph with time on horizontal axis and distance on vertical axis
- Calculate distance at specific times, total time and average speed

How do we use travel graphs to show journeys?

- Smart Minds Mathematics Learner's Book pg. 240
- Graph papers
- Calculators

- Written assignments - Class activities - Oral questions