Mathematics Primary 5 Third Term Lesson Notes

1. Exploring Temperature: Learn to Compare and Convert in Mathematics Primary 5 Third Term Lesson Notes Week 1
2. Lines, Bearing and Angles : How to draw and identify parallel lines and Perpendicular lines Primary 5 Third Term Lesson Notes Mathematics Week 2
3. Properties of plane shapes like Rhombus, Square, Rectangle in relation to real life situations Primary 5 Third Term Lesson Notes Mathematics Week 3
4. Types, Measurement and Sum of Angles Primary 5 Third Term Lesson Notes Mathematics Week 4
5. Real life examples of square base and triangular prism Primary 5 Third Term Lesson Notes Mathematics Week 6
6. Measure the height of some pupils, desk, flowering plants and short distances. use tape to measure the dimensions of the classroom compare heights of pupils in the classrooms Primary 5 Third Term Lesson Notes Mathematics Week 6

Mid Term Test Primary 5 Third Term Lesson Notes Mathematics Week 7

Primary 5 Exam Questions – First Term, Second Term and Third Term Examination Primary 5 (Basic 5) – All Primary 5 Subjects – Edu Delight Tutors

Primary 5 Third Term Examination Mathematics

WEEK 2

PLANE SHAPE

Pupils should be able to

(i) identify parallel and perpendicular lines

 (a) label the diagrams below

appropriately

i

.Triangle Properties

The properties of the triangle are:

The sum of all the angles of a triangle(of all types) is equal to 1800.

The sum of the length of the two sides of a triangle is greater than the length of the third side.

In the same way, the difference between the two sides of a triangle is less than the length of the third side.

The side opposite the greater angle is the longest side of all the three sides of a triangle.

The exterior angle of a triangle is always equal to the sum of the interior opposite angles. This property of a triangle is called an exterior angle property

Two triangles are said to be similar if their corresponding angles of both triangles are congruent and lengths of their sides are proportional.

Area of a triangle = ½ × Base × Height

The perimeter of a triangle = sum of all its three sides

(a) equilateral

-All sides are equal

-All angles are equal

(b) isosceles

-Two opposite side are equal

-Two base angles are equal

(c) scalene

-The three sides are not equal

-The three angles are not equal

d). Right angled:

-Two sides are perpendicular

-One angle is a right angle

 (I). Parallelogram

-Opposite sides are equal

-Opposite sides are parallel

(II). Trapezium

-One pair of opposite sides are Parallel

-No line of symmetry

WEEK 3

PLANE SHAPE

PROPERTIES OF A RHOMBUS, SQUARE AND RECTANGLE.

Pupils should be able to:

(I). State the properties of a Rhombus e.g RHOMBUS, SQUARE, RECTANGLE.

Rhombus

-All sides are equal

-Opposite angles are equal

-Has two lines of symmetry

-Diagonals are perpendicular to Each other

(II). Square

-All sides are equal

-All angles are equal

-Diagonals meet at angles 90Right angle

-Has four lines of symmetry

(III). Rectangle

-Opposite sides are equal and

Parallel

-All angles are equal

-Has two lines of symmetry

WEEK 4

Topic: Angles

Complementary Angle

Two Angles are Complementary when they add up to 90 degrees (a Right Angle).

They don’t have to be next to each other, just so long as the total is 90 degrees.

Examples:

60° and 30° are complementary angles.

5° and 85° are complementary angles.

Supplementary Angles

Two Angles are Supplementary when they add up to 180 degrees.supplementary angles 40 and 140

These two angles (140° and 40°) are Supplementary Angles, because they add up to 180°:Notice that together they make a straight angle. supplementary angles 60 and 120But the angles don’t have to be together.

These two are supplementary because60° + 120° = 180°

Acute angle:

An angle whose measure is less than 90 degrees.

Right angle

 angle whose measure is 90 degrees.

Obtuse angle:

An angle whose measure is bigger than 90 degrees but less than 180 degrees. Thus, it is between 90 degrees and 180 degrees.

Straight angle

An angle whose measure is 180 degrees.Thus, a straight angle look like a straight line.

Reflex angle:

An angle whose measure is bigger than 180 degrees but less than 360 degrees.

In worksheet on angles you will solve 10 different types of questions on angles.

Classify the following angles into acute, obtuse, right and reflex angle:

(i) 35°

(ii) 185°

(iii) 90°

(iv) 92°

(v) 260°

Measure these angles:

Use your protractor to draw these angles:

(i) 40°

(ii) 125°

(iii) 25°

Identify which of the following pairs of angles are complementary or supplementary?

(i) 70°, 20°

(ii) 20°, 170°

(iii) 50°, 145°

(iv) 125°, 55°

(v) 105°, 75°

(vi) 55°, 35°

Find the complement of each of the following angles:

(i) 40°

(ii) 27°

(iii) 35°

Find the supplement of each of the following angles?

(i) 100°

(ii) 90°

(iii) 110°

(iv) 107°

Draw a pair of supplementary angles such that one of them measures:

(i) 120°

(ii) 90°

Construct the angles of the following measures with the help of a compass:

(i) 150°

(ii) 90°

(iii) 120°

An angle whose measure is less than 90° is called an ……………… .

An angle measure 0° is called a …………….. .

WEEK  5

3 DIMENSIONAL SHAPES

A prism is solid with a uniform cross-section. The top and bottom faces are the same. Cubes,

cuboids and cylinders are prisms.

Triangular prism

In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides. A right triangular prism has rectangular sides, otherwise it is oblique. A uniform triangular prism is a right triangular prism with equilateral bases, and square sides.

to

(Rectangular prism)

a rectangular cuboid, all angles are right angles, and opposite faces of a cuboid are equal.

Cuboid

(Square prism)

Cube

A square prism is a three-dimensional shape cuboid figure whose bases are squares. The opposite sides and angles are congruent to each other. In the given figure, the bases of the prism are square, and therefore, it is called a square prism.

(Circular prism)

cylinder

A pyramid is a solid with a non-uniform cross-section. The top has only one vertex. In a

prism the number of vertices at the top is the same with the number of vertices at the

bottom. Consider the following solids.

Triangular-based pyramid

Square-based

pyramid Rectangular-based pyramid

Circular-based pyramid (cone)

239

Remember:

A vertex is a point where three or more edges meet. It is a corner point of a 3-D shape.

A face is a 2-D shape (known as a plane shape). Examples of 2-D shapes are triangles,

squares, rectangles, parallelograms, kites, circles etc.

An edge is a line where two faces meet.

Lead the class to discover all these from the above drawings of the 3-D shapes.

Solids (3-D shapes)     Faces/surfaces (F)    Edges (E)     Vertices (points where edges meet)

Triangular prism                      5                       9                       6

Triangular-based pyramid            4                      6                     4

Square prism (cube)                     6                     12                    8

Square-based pyramid                   5                    8                      5

Rectangular prism (cuboid)              6                  12                      8

Rectangular-based pyramid             5                    8                       5

Circular prism (cylinder)                  3                    2                           0

Circular-based pyramid (cone)        2                   1                           1

Exercise

Answer the following questions.

How many faces has your mathematics textbook?

Write down two everyday objects which are

a) cuboids b) cubes c)

What shapes are the faces of

a) rectangular prism b) triangular prism?

What shapes are the faces of

a) rectangular-based pyramid b) triangular-based pyramid?

What is the difference between a triangular-based pyramid and a triangular prism?

What shape are the faces of a cylinder?

If F stands for faces, E stands for edges and V stands for vertices, what shapes satisfy the

following equations? Question f) is done for you. Use the table on page 335 to help you.

a) E + F – V = 10 b) E + V – F = 10 c) V + F – E = 2

d) F + V + E = 20 e) F + E – V = 6 f) F + E + V = 26 = cuboid

g) F + E + V = 4 h) V + E – F = 6 i) F + E – V = 5

Use the nets of these shapes you have made to answer questions 1 to 18.

A cube has _____ faces.

A cube has _____ vertices.

A cube has _____ edges.

sss4. A cuboid has _____ vertices.

A cuboid has _____ edges.

A triangular-based pyramid has _____ triangular faces.

A triangular-based pyramid has _____ vertices.

A triangular-based pyramid has _____ edges.

A square-based pyramid has _____ square faces.

A square-based pyramid has _____ vertices.

A square-based pyramid has _____ edges.

A closed cylinder has _____ circular faces.

A closed cone has _____ circular faces.

The curved surface of a cylinder is a _____.

The curved surface of a cone is a _____.

A triangular-based prism has _____ vertices.

The shape of a Bournvita tin is a _____.

Sugar, maggi and dice for playing Ludo game are examples of _____.

WEEK 6

CIRCLE

IDENTIFICATION OF CIRCLE

Identify and state the meaning Of

– radius

– diameter

– circumference of a circle

– chord

– sector (minor and major)

– segment (minor and major)

A path traced from a fixed point such that the same distance from that point is maintained

is called a circle.

O

This is a circle.

The fixed point O is called the centre of the circle

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Parts of a circle

There are special words to describe different parts of a

circle as shown in the diagram of the circle drawn.

The distance round the circle is called the

circumference or perimeter.

A straight line from the centre of a circle to the

circumference of the circle is called a radius.

A straight line across a circle which starts and ends

at two points on the circumference is called a chord.

A chord which passes through the centre of a circle

is called a diameter.

An arc is part of the circumference of a circle.

The area enclosed by two radii and an arc is called a sector.

The area enclosed by an arc and a chord is called a segment.

A straight line which touches the circumference of a circle is called a tangent.

Exercise 1

Use the circle below to answer the questions.

Measure radius OA. Copy and complete: OA = !

Name four other radii. (Radii is the plural of radius.)

Copy and complete: OY = !, OQ = !, OY = !,

OP = !, OX = !

Are all the radii of the same length?

Measure the diameter POQ.

Name another diameter and find its length.

Compare the length of a diameter with the length of a radius. What do you observe?

Copy and complete these statements.

The length of a diameter is the length of a radius.

The length of a radius is that of a diameter.

Measure EF and QY. Record their lengths.

Compare the lengths of EF and QY with the length of POQ and XOY respectively.

What do you observe?

WEEEK 8

Binary numbers

Counting in base two

Counting in tens came from the fact that man has ten fingers. The counting system using ten

as a base was internationally accepted. Other counting system varied over places.

The base ten system is also known as decimal base denary. The digits in base ten are: 0,

1, 2, 3, 4, 5, 6, 7, 8, 9. We can write one hundred and twenty three as 123. The expanded

form is: 123 = (1 × 100) + (2 × 10) + 3.

That is:            H  T  U

                         1   2 3                                Thus 123 = (1 × 102) + (2 × 101) + (3 × 100).

In the expanded index form, 123456 can be written as:

H Th T Th Th H T U

105 104 103 102 101 100

1    2     3    4   5     6

123456 = (1 ××105) + (2 × 104) + (3 × 103) + (4 ×102) + (5 × 101) + (6 ×100).

Here, we shall pay attention to numbers in base two. In base 2, the digits are 0 and 1.

Counting in twos

Base 10    0    1    2    3     4       5       6      7      8       9       10

Base 2       02   12   102    112  1002 1012 1102 1112 1 0002 1 0012 1 0102

.

Examples

7 in base ten = 1112 in base two

1112 is read as ‘one one one, base two’. Please do not read 1112 as ‘one hundred and

eleven base 2’.

The expanded form of: Remember

1012 = (1××22) + (0 × 21) + (1 × 20)                20 = 1        26 = 64

= (1 × 4) + (0 × 2) = (1 × 1)                               21 = 2         27 = 128

= 4 + 0 +1 = 5                                                22 = 4         28 = 256

1112 = (1 × 22) + (1 × 21) + (1 × 2)                      23 = 8         29 = 512

= (1 × 4) + (1 × 2) + (1 × 1)                                24 = 16       210 = 1 024

= 4 + 2 + 1 = 7                                                  25 = 32

10012 means:

10012 = (1 × 23) + (0 × 22) + (2 × 21) + (1 × 20)            23 22 21 20

= 8 + 0 + 0 + 1 = 9                                                  1 0  0   1

Conversion of base 10 to binary numbers

Examples

Here the following numbers are converted to base 2.

2 14

             2    7 rem 0

             2    3 rem 1

             2    1 rem 1

                    0 rem 1     ” 14ten = 1110two

2 27

               2   13 rem 1

               2    6 rem 1

               2    3 rem 0

               2    1 rem 1

                     0 rem 1     ” 27ten = 11011two

2 33

             2    16 rem 1

             2      8 rem 0

             2        4 rem 0

            2        2 rem 0

           2        1 rem 0

                    0 rem 1       ” 33ten = 100001two

2 44

          2     22 rem 0

          2    11 rem 0

          2     5 rem 1

          2     2 rem 1

          2     1 rem 0      ” 44ten = 101100two

Exercise

Convert the following numbers in base ten to numbers in base 2.

19 2. 37 3. 20 4. 41 5. 60

39 7. 47 8. 29 9. 38 10. 57

Unit 3

Conversion of binary numbers to base 10

The binary number will be expressed as the sum of the power of 2.

Examples

The following numbers have been converted to base 10.

Method 1

Using place value: 26 25 24 23 22 21 20

24 23 22 21 20

               1 1 1  0  1

11101two = (1 ××24) + (1 × 23) + (1 × 22) + (0 × 21) + (1×20)

= (1 × 16) + (1 ×8) + (1 × 4) + (0 × 2) + (1 × 1)

= 16 + 8 + 4 + 0 + 1

= 29ten

26 25  24  23  22  21  20

        1  0  1  0  1   0   0

1010100two = (1 × 26) + (0 × 25) + (1 × 24) + (0 × 23) + (1 × 22) + (0 ×21) + (0 × 20)

= 64 + 0 + 16 + 0 + 4 + 0 + 0

= 84ten

265

Exercise

Convert the following binary numbers to base ten.

1011two 2. 11110two 3. 11101two 4. 10111two 5. 10011two

11001two 7. 11010two 8. 11100two 9. 101111two 10. 110111two

100111two 12. 111010two 13. 111001two 14. 111100two 15. 101011two

Examples

Unit 4 Addition of binary numbers

1 0 1 1two

+ 1 1 1two

1 0 0 1 0two

1 + 1 = 2ten = 10two

1 + 1 + 1 = 3ten = 11two

1 1 0 1 1two

+ 1 0 1 1two

1 0 0 1 1 0two

1 + 1 = 2ten = 10two

1 + 1 + 1 = 3ten = 11two

1 0 1 1 0two

+ 1 0 0 1two

1 1 1 1 1two

0 + 1 = 1ten = 1two

1 1 0 0 1two

+ 1 1 1 1two

1 0 1 0 0 0two

1 + 1 = 2ten = 10two

0 + 1 = 1ten = 1two

Exercise

Work out these totals.

1110two + 100two 2. 10101two + 1001two 3. 11100two + 1011two 4. 10111two + 1001two

11010two + 1001two 6. 11001two + 1111two 7. 11011two + 1010two

10011two + 1010two 9. 10011two + 1001two 10. 11101two + 1010two

Revision exercise 36                   

Convert the following numbers in base ten to numbers in base 2.

61 2. 44 3. 28 4. 25 5. 49

Convert the following binary numbers to base ten.

1101two 7. 10110two 8. 10001two 9. 111001two

100100two 11. Add 10110two to 1011two 12. Add 10111two to 1010two

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WEEK 9&10

TALLY MARKS

Exercise 2

Write these figures in tally marks.

13 2. 22 3. 19 4. 25 5. 31 6. 4

29 8. 24 9. 36 10. 43

Mode

Mode is the item or number that occurs most frequently in a given data. To find the mode of

a given data, arrange the numbers in order of magnitude, then count the number of times

each number occurs.

Example

The following are the scores of fifteen pupils in a mathematics test: 100%, 84%, 92%, 84%,

67%, 88%, 84%, 45%, 35%, 84%, 24%, 20%, 54%, 64% and 10%. Study the solution to find

the mode of the score.

Solution

Arrange the scores in order of magnitude to enable you to note the mode clearly.

100%, 92%, 88%, 84%, 84%, 84%, 84%, 67%, 64%, 54%, 45%, 35%, 24%, 20%, 10%

The mode of the scores = 84%.

We can also prepare a table as follows.

Scores %   Number of times     Scores %     Number of times

100                       1                     45                       1

92                         1                     35                        1

84                          6                    24                        1

67                          1                    20                        1

58                           1                  0                             1

Unit 1

255

Exercise 1

Find the mode of each set of data.

1, 6, 7, 5, 8, 9, 6, 3, 2 2. 3, 7, 8, 4, 0, 0, 0, 6, 5, 9, 10

5, 2, 5, 6, 8, 6, 2, 2 4. 4, 5, 6, 7, 7, 0, 2, 1, 7, 6, 8

4, 7, 6, 7, 5, 9, 5, 7, 8 5 6. 2, 5, 7, 6, 8, 3, 8, 9, 7, 8

9, 3, 4, 5, 9, 6, 7, 8, 0, 2 8. 10, 2, 4, 6, 8, 7, 9, 10, 10, 0

7, 5, 6, 4, 5, 6, 3, 8, 7 10. 4, 6, 9, 7, 9,

MEAN

Mean is the average of a given set of numbers. To find the mean, add up all the numbers,

then divide by how many numbers that are in the set.

Mean = Sum of the numbers/Numbers in the set

Example

The mean of the following set of numbers has been calculated:

36, 59, 54, 20, 82, 61, 48, 42, 58 and 40

Solution

Mean = 36 + 59 + 54 + 20 + 82 + 61 + 48 + 42 + 58 + 40/10

= 500/10

       = 50

256

Exercise

Find the mean of each set of the following scores.

50%, 85%, 70%, 45%, 90%, 68%, 98%, 25%, 63%, 39%

14%, 91%, 40%, 73%, 88%, 60%, 55%, 59%

32%, 24%, 53%, 68%, 92%, 81%, 47%, 76%, 40%, 87%, 61%, 23%

Answer these questions.

The pulse rates of six patients are as follows: 59, 36, 48, 51, 62, 68. Find the mean of

the pulse rate.

The following are the scores of fifteen pupils in a mathematics test out of 10

5, 8, 6, 9, 7, 4, 10, 2, 5, 8, 9, 0, 1, 6, 9.

Find the mean score.

The ages of eight pupils are shown below. Find their mean age:

13 years, 14 years, 12 years, 10 years, 11 years, 9 years, 15 years, 8 years

The allowances of ten students are as follows: 􀎏800.00, 􀎏1000.00, 􀎏2000.00, 􀎏1500.00,

􀎏700.00, 􀎏1800.00, 􀎏2200.00, 􀎏1700.00, 􀎏2500.00, 􀎏600.00. What is the mean

allowance?

The distance covered by eight cars are 120 km, 200 km, 350 km, 150 km, 250 km, 90 km,

500 km, 420 km. Find the mean of the distance covered.

Median

The median of a set of numbers is that number that is exactly at the middle of the set of

numbers when they are arranged in order of size.

To find the median, arrange the numbers in order of size, from the largest to the smallest.

The median is then the middle number.

Examples

Here the median of each of the following sets of numbers has been found.

20, 30, 10, 90, 80, 100, 70

Solution

Arrange the numbers in order of size.

100 90 80 |70| 30 20 10

The median = 70

We have three numbers to the left and three to the right and 70 is at the middle.

18, 20, 14, 15, 12, 16, 24, 28, 30, 25

Solution

Arrange the numbers in order of size

30 28 25 24 |20 18| 16 15 14 12

Since there is no middle number the median is the mean of the two middle numbers.

Median = 20 + 18/2

                    = 38/2

                     = 19

Exercise

Find the median of each of the following sets of numbers:

9, 12, 14, 20, 15, 32, 41, 35, 40

218, 314, 420, 117, 510, 250, 340, 480, 550, 180, 390

10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180

8.2, 3.5, 9.7, 10.1, 13.4, 5.5, 17.6, 12.3, 11.4

40, 20, 80, 60, 100, 140, 120, 180, 160, 200, 240, 220

170, 230, 190, 150, 130, 250, 240, 300, 330

111, 222, 333, 414, 515, 616, 720, 820, 920, 1120

8 cm, 10 cm, 14 cm, 18 cm, 22 cm, 24 cm, 12 cm, 26 cm, 11 cm, 17 cm, 25 cm

27 kg, 30 kg, 14 kg, 32 kg, 45 kg, 54 kg, 23 kg

40 litres, 30 litres, 53 litres, 26 litres, 64 litres, 70 litres, 82 litres, 90 litres, 100 litres

Frequency tables can be drawn from your experiments of:

􀁏rolling dice

􀁏tossing coins several times.

Examples

Bisola tossed a coin 20 times and recorded his results as follows. Study the solutions.

H   T   T  H     H

T     T  H   T    H         

T       H T T           H

H T H T T

a) Draw a frequency table to show the experiment.

b) How many times did heads appear?

c) How many times did tails appear?

d) Express b) and c) as fraction of total outcomes.

Solution

a) Face Tally Frequency

      H       //// /////         9

      T       //// //// /        11

Total 20

b) Heads appears 9

c) Tails appears 11

d) i) The fraction of heads appearing is 9/20

ii) The fraction of tails appearing is 11/20

Bar Graph Examples

To understand the above types of bar graphs, consider the following examples:

Example 1: In a firm of 400 employees, the percentage of monthly salary saved by each employee is given in the following table. Represent it through a bar graph.

Savings (in percentage)                Number of Employees(Frequency)

20           105

30           199

40           29

50           73

Total      400

Solution: The given data can be represented as

Bar graph – Vertical

This can be also represented using a horizontal bar graph as follows:

Bar Graph – Horizontal

Example 2: A cosmetic company manufactures 4 different shades of lipstick. The sale for 6 months is shown in the table. Represent it using bar charts.

Month  Sales (in units)

Shade 1                Shade 2                Shade 3                Shade 4

January                4500       1600       4400       3245

February              2870       5645       5675       6754

March   3985       8900       9768       7786

April      6855       8976       9008       8965

May       3200       5678       5643       7865

June      3456       4555       2233       6547Swipe left

Solution: The graph given below depicts the following data

Bar Graph

Example 3: The variation of temperature in a region during a year is given as follows. Depict it through graph (bar).

Month  Temperature

January                -6°C

February              -3.5°C

March   -2.7°C

April      4°C

May       6°C

June      12°C

July        15°C

August  8°C

September         7.9°C

October               6.4°C

November          3.1°C

December           -2.5°C<

Solution: As the temperature in the given table has negative values, it is more convenient to represent such data through a horizontal bar graph.

Bar Graph Example

Uses of Bar Graphs

Bar graphs are used to match things between different groups or to trace changes over time. Yet, when trying to estimate change over time, bar graphs are most suitable when the changes are bigger.

Bar charts possess a discrete domain of divisions and are normally scaled so that all the data can fit on the graph. When there is no regular order of the divisions being matched, bars on the chart may be organised in any order. Bar charts organised from the highest to the lowest number are called Pareto charts.

Bar Graph Question

Question: A school conducted a survey to know the favourite sports of the students. The table below shows the results of this survey.

Name of the Sport          Total Number of Students

Cricket.                                45

Football.                             53

Basketball                         99

Volleyball                         44

Chess                                 66

Table Tennis                       22

Badminton                          37

From this data,.   

Draw a graph representing the sports and the total number of students.

Calculate the range of the graph.

Which sport is the most preferred one?

Which two sports are almost equally preferred?

List the sports in ascending order.