MATHEMATICS PRIMARY 5 SECOND TERM LESSON NOTE SCHEME OF WORK

**SUBJECT: MATHEMATICS **

**CLASS: BASIC FIVE**

WEEK TOPIC ** **

- RATIO AND PERCENTAGE
- SIMPLE PROBLEMS ON PERCENTAGE
- MONEY: profit and loss
- MONEY: SIMPLE INTEREST
- MONEY: DISCOUNT AND COMMISION
- PERIMETER OF PLANE SHAPES
- AREA OF RIGHT ANGLED TRIANGLE
- VOLUME
- PROBLEM ON WEIGHT
- AVERAGE SPEED
**WEEK ONE **

**RATIO AND PERCENTAGE **

**Meaning of ratio **

The relation between two quantities (both of the same units) obtained by dividing one quantity with another is called ratio. Ratio can be denoted by using the symbol ( : ).

EXAMPLE 1

What is the ratio between the weight two bags of sugar of 4kg and 6kg respectively?

**Solution **

Ratio of weights of bags of sugar = 4kg/ 6kg = 2/3 = 2:3

EXAMPLE 2

A pole of length 165cm is divided into two parts such that lengths are in the ration 7:8. Find the length of each part of the pole?

Total ratio = 7 + 8 = 15

First part = ^{7/}_{15 }, second part = 8/15

Length of first part = 7/15 of 165cm

= 7/15 × 165

= __7 x 11 __ = 77cm

1 x 1

Length of second part = 165cm – 77cm = 88cm

DIRECT PROPORTION

Examples

- A marker costs $18. Calculate the cost of 5 markers.
- A student went to the market to purchase textbooks. He purchased two textbooks for $24

- What is the price of one notebook?
- What would be the price of 5 such note

Solution

- If one marker = $18

5 markers = $18 x 5 = $90

- 2 textbooks = $24

1 textbook = m

2 × m = 1 x $24

2m = $24

M = $24 ÷ 2 = $12. Therefore 1 textbook = $24

(b) Since 1 textbook = $12

5 textbooks = $12 × 5 = $60

Equal and equivalent ratios

- The two ratios below are equal or equivalent.

1/2 = 4/ 8

3/5 = 6/10

- The two ratio below are not equal or equivalent

4/3≠6/10 3/5≠7/15

EVALUATION

- What is ratio?

- Find the ratio of each of the following in its lowest terms:

- 24cm: 72cm
- 425km: 750km
- 75min: 150min
- 85kg: 102kg

- A field is 50m in length and 60m in width. Find the ratio between its width and length.

- A scooter can travel 225km with 5 litres of petrol. How many litres of petrol is needed to travel 675km?

WEEK TWO

SIMPLE PROBLEMS ON PERCENTAGES

Percentages are fractions with 100 as denominator

EXAMPLE 1

Change the following fractions to percentages

^{2/}_{5 }= ^{2}/_{5 }of 100 = ^{2/}_{5 }× 100 = __200 __= 40%

5

EXAMPLE 2

Change these percentage to fractions

- 75% =
__75 __ = __15 __= __3 __

100 20 4

EXAMPLE 3

Change 7 ½% to fractions in their lowest terms

Solution

7 ½ % = 7 ½ out of 100

= 15/2 × 1/100

= (15 × 1) ÷ 200

= 15 ÷ 200 = 3/40

EXERCISE

Change the following fraction to percentage

^{2}_{/5}
^{2/}_{4}
^{3}/_{30}

Change to fractions in their lowest terms

- 66 ½ %
- 12 ¼ %
- 16
^{2}/_{3} %

MEANING OF PROFIT

When the selling price of an article is higher or greater than the cost price, we have a profit or gain.

Profit = selling price – cost price

MEANING OF LOSS

When the selling price is less than cost price we have a loss.

Loss = cost price – selling price