The document presents a lesson plan focused on visualizing and understanding ratios through activities involving students counting and comparing numbers of boys and girls in their classes. It includes instructions for reducing fractions to their lowest terms, defining ratios, and demonstrating how to simplify them. Additionally, it covers methods for expressing proportions and practical examples of direct proportion problems.

1. Lesson 49: Visualizing
the Ratio of 2 Given
Numbers
ANNALICE R. QUINAY
MASTER TEACHER 1
SAN JOSE ES
SAN PABLO CITY

2. Reduce the ff. fractions
to lowest terms
12/15 4/5

3. Reduce the ff. fractions
to lowest terms
10/55 2/11

4. Reduce the ff. fractions
to lowest terms
18/50 9/25

5. Reduce the ff. fractions
to lowest terms
35/50 7/10

6. Reduce the ff. fractions
to lowest terms
35/50 7/10

7. Reduce the ff. fractions
to lowest terms
14/42 1/3

8. Reduce the ff. fractions
to lowest terms
21/84 1/4

9. Reduce the ff. fractions
to lowest terms
9/81 1/9

10. Write the total
number of male
and female on
the board.

11. What is the ratio
of male to
female?
Female to male?

12. Male to total
number of pupils?
Female to the total
number of pupils?

13. Using Actual
Pupils in
Naming
Ratio

14. Mechanics:
•Let the pupils count the number
of girls and boys in their
respective column.
•Let the pupils write their
answers on the board.
•Tabulate the data on the board
as follows:

15. Column
number
Number of
Boys
Numbe
r of
Girls
Number of
Pupils in a
Column
1 12 6 18
2 10 5 15

16. •Ask the following questions:
•How many pupils are there
in each column?
•How do you compare the
number of boys to the
number of girls in Column 1?
Column 2?

17. Ratio is the
comparison of
two quantities.

18. Compare the number of
boys in Rows 1 and 2.
Compare the number of
girls in Rows 3 and 4.
Compare the number of
pupils in Rows 1 and 5.

19. There are 7 boys
and 8 girls
playing volleyball.
Problem Opener:

20. What is the
ratio of boys to
girls?
What is the

21. What is the ratio of
boys to players?
What is the ratio of
girls to players?
How do we express
ratio of 2 numbers?

22. Count the number
of objects in each
set and write your
answers on the
board.

23. Set 1 – 2
notebooks, 3
pencils
Set 2 – 5 crayons,
10 sheets of paper

24. How will you compare the
number of notebook with
the number of pencils?
What is the ratio of
notebooks to pencils?

25. Crayons to sheets of paper?
Define the ratio.
Can we interchange the
terms in ratio? Why or Why
not?
Write the ratios in two
ways.

26. a. pencils to notebooks
b. notebooks to pencils
c. pencils to total numbers of things
d. notebooks to total number of

27. a.eggs to baskets
b.baskets to egg
c.eggs to total number of things
d.basket to total number of

28. Ratio
and
Proportion

29. Ratio
A ratio compares the sizes of parts or quantities to each other.
What is the ratio of red counters to
blue counters?
red : blue
= 9 : 3
= 3 : 1
For every three red counters there is one blue counter.

30. What is the ratio of red counters
to yellow counters to blue
counters?
Ratio
red : yellow : blue
= 12 : 4 : 8
= 3 : 1 : 2
For every three red counters there is one yellow counter and two blue counters.

31. Simplifying ratios
Ratios can be simplified like fractions by dividing each part by the highest common
factor.
21 : 35
= 3 : 5
÷ 7 ÷ 7
For a three-part ratio all three parts must be divided by the same number.
6 : 12 : 9
= 2 : 4 : 3
÷ 3 ÷ 3

32. Dividing in a given ratio
A ratio is made up of parts.
We can write the ratio 2 : 3 as:
2 parts : 3 parts
The total number of parts is:
2 parts + 3 parts = 5 parts
Divide £40 in the ratio 2 : 3.
£40 ÷ 5 = £8
We need to divide £40 by the total number of parts.

33. Proportion
There are many ways to express a proportion.
We can express this proportion as:
12 out of 16 3 in every 4
3
4
0.75 or 75%
Proportion compares the size of a part to the size of a whole.
What proportion of these counters
are red?

34. Direct proportion problems
3 packets of crisps weigh 90 g.
How much do 6 packets weigh?
3 packets weigh 90 g.
× 2
6 packets weigh
× 2
180 g.
If we double the number of packets then we double the weight.
The number of packets and the weights are in direct proportion.

35. Now try these:
Divide:

36. Answers:
1. 6:4 2. 16:4 3. 10:4 4. 18:6 5. 15:3
6. 16:12 7. 10:6 8. 50:20 9. 35:10 10.
50:40
11. 35:15 12. 33:44 13. 6:15 14. 16:24 15. 36:3
16. 8:8:4 17. 6:4:2 18. 25:20:5 19. 15:10:5
20. 15:9:3 21. 42:21:7 22. 56:24:16 23. 60:36:24
24. 35:28:21 25. 60:24:24 26. £80, £60 27. 6:9:12
28. 6:8:10 29. 60:150:210 30. 2.5:10:12.5

37. ANNALICE R. QUINAY
Master Teacher 1