This document contains materials for a mathematics lesson on ratios and proportions. It includes examples of writing ratios using fractions and colons, forming proportions, and finding missing terms in proportions. Activities guide students to form ratios, write proportions, solve word problems involving ratios, and evaluate their understanding through questions and applications using visual representations. Cooperative learning strategies and using various tools like charts and presentations are suggested for instruction.

1. Demonstration
Teaching in
Mathematics VI
GLENDA D. MATEO
ES Teacher I

3. Drill/Review
Read the following fractions on the
flashcards and tell the reciprocal of each
fraction.
4/5
15/12 4/12
9/3 7/5
Remember: Reciprocal means two fractions whose
product is one.

4. Checking of Assignments
Find the quotient of the given fractions.
1/8 ÷ 3/10
2/3 ÷ 3/4
2 1/3 ÷
2/5
3/9 ÷ 2
5 ÷ 7/2

5. Guess the wordles…

6. What is that word?
Square
Root

7. Guess the word…
x

8. Guess the word…
Multiplication
Table

9. Guess the word…
HIJKLMNO

10. Guess the word…
H O 2

11. Water as H O
2
The ratio of
hydrogen atoms to
oxygen atoms is two
is to one.

12. Did you know that…
Water is the most common
chemical compound that makes
up the lakes, rivers and oceans.
A molecule of water contains
2 atoms of hydrogen
and 1 atom of oxygen.

13. Think About this…
What is the importance of
water in our life?
As a pupil, how do you
conserve water at home
and in school?

14. Study this!
Allan the eldest
brother went to the
market to buy
something for
Alice, Remy and
Nena, her three
stunning sisters.
Iwant to give
these mangoes
to the girls.

15. Answer the following questions…
How many girls are there?
How many mangoes are there?
How do you relate the number of
girls to the number of mangoes?
How many quantities were
compared?
What do you call if we are comparing
two or more quantities?

16. Ratio means…
Ratio- is the
comparison of two
numbers or quantities.

17. Two Ways in Writing Ratio
Using a
colon
Fraction
Form

18. Write ratios Using a colon/ Fraction Form

19. Write ratios Using a colon/ Fraction Form

20. Write ratios Using a colon/ Fraction Form

21. Let’s Have Fun
is to
is to
as
_____
A B C D

22. Read the Problem
Allan bought 6 ripe
mangoes for his three
sisters Alice, Remy and
Nena. How many
mangoes did each
receive?

23. Answer these questions.
How can we express the
number of girls to the number
of mangoes?
How many mangoes
did each receive?
Is 3:6 and 1:2 has the
same value?

24. Draw/Illustrate
How many ratios are there?
3:6
1:2
Are they equal?

25. Cross Product Method
(Cross product method)
3/6 = ½ 3 x 2 = 6, 6 x 1= 6
6=6
3 1
6 2
3 x 2 = 6 x 1
6 = 6

26. Since they are equal…
They can become a
proportion.
What is a
proportion?

27. Proportion
Proportion-
A statement that two
ratios are equal.

28. Form a proportion using this picture.

29. Form a proportion using this picture.

30. Parts of a Proportion
extremes
means
3 : 6 = 1 : 2
1st term 2nd term 3rd term 4th term
What do you observe?

31. How do we form a proportion?
Step 1. Express the
pattern as a proportion.
Step 2. Prove that the
ratios are equal.

32. Observe this equation.
3:6 = 1:n

33. How do we find the missing term in a proportion?
3:6= 1:n
6 x 1 = 3 x n
6 ÷ 3 = n
2 = n or n= 2

34. Formulating the steps
Make the steps on how to
find the missing term in a
proportion. Write your
answer in the chart.

35. Find the missing term in a
proportion
1. Multiply the known
terms.
2. Divide the product by
partner with the
missing term.
The cross
products of
a proportion
are equal.

36. How do we find the missing term in a proportion?
3 kids is to 12
books
1 kid is to n books
3:12= 1: n
12 x 1 = 3 x n
12 ÷ 3 = n
4= n

37. Fixing Skills
Activity 1- Form the ratio of the following
objects.
1.
2.
3.
4.
5.

38. Fixing Skills
Activity 2- Write the ratio in fraction and
using a colon.
19 8 12 1 16
23 17 14 25 21
_______even
numbers to
odd
numbers
__prime
numbers to
composite
_____number
less than 20
to numbers
greater than
20

39. Fixing Skills
Activity 3-
Which two
ratios form a
proportion?
Check the
blank before
the number of
the two ratios
that form a
proportion and
cross- out that
are not.
__1. 1:2=2:4
__2. 6:5 =30:25
__3. 5:4=10:4
__4. 5:2=10:4
__5. 5:3=9:15

40. Fixing Skills
Activity 4- Solve for n.
1. 5/6= n:18
2. 1/8=7:n
3. 3/10=9:n
4. 9:n=3:4
5. 4:7=n:21

41. Application
Group A- Write a
case/argument that would
convince your classmates that
the pictures below show a
ratio of 3:4.
Group B- Is the ratio of 15 is
to 2 the same as 7 ½ is to 1?
If yes, show the solution.
Group C- Use the colon and
fraction to show ratio and
proportion. Group D- Make a two-squared
figure with the ratio of
4:12. Use the yellow and white
squared tiles.
1. The
ratio of
3 apples
to 15
oranges
.
2.Two
men for
every 3
cups of
rice.
3.) 2 m
to 5
skirts as
6 m to
15 skirts
4.) 8
girls for
every 7
boys
5.) 35
pieces
of shorts
in 3
days

42. Generalization
Group yourselves into two.
Group A will ask questions
then group B will answer it
and vice- versa)

43. Generalization
Let’s play “Pick a
Stick” then tell
something what is
written on it.

44. Evaluation
•Form ratios and a proportion out
of the pictures that follow.
1. First ratio: __________
Second ratio: _________
Proportion: __________

45. Evaluation
2. First ratio: __________
Second ratio: _________
Proportion: __________

46. Evaluation
3. First ratio: __________
Second ratio: _________
Proportion: __________
P50.00
P100.00

47. Evaluation
Complete the table.
Write the following
in:
Fraction
Form
Using a
Colon
4.) 13 eggs to 5 ducks
5.) One math teacher to 134
pupils
6.) 1 District Supervisor to
18 schools
7.) 35 minutes to 4 hours

48. Evaluation
Find the missing term in a
proportion.
8.) 4:5 = ____ : 20
9.) 3:7 = 21 : ____
10.) ____: 120 = 3:5

49. Assignment
 Read the given problems below. Form ratios in fraction
and using a colon. Find the missing term in each
problem. Write your answer in your notebook.
1. Two out of three booths sell rag dolls. If there are 27
booths, how many of these sell rag dolls?
2. For every eight children, 10 pieces of fried chicken
are ordered. How many pieces of fried chicken will be
ordered for 32 children?

51. Strategies
Cooperative Learning
Brainstorming
Charts/Graphic Organizer
Power Point Presentation

52. Mr. Herminio Jose C. CatudEPS, Elem. Math.
There is no single best way to teach
math, but research shows that using
manipulative in conjunction with other
methods can deepen students’
understanding of abstract concepts.
Appropriate use of manipulative should
be one component of a comprehensive
mathematics curriculum.

53. www.themegallery.com