Q2 Math 6 Ratio and Proportion

2nd Quarter Math 6

by Patricia Diomampo

​ESLR

​Through understanding Ratio and Proportion, Faithians will learn to respect territories and differences knowing that we are all equal in the eyes of God. Faithians will give respect to the minorities even though they are part of a smaller group in our society.

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​BIBLE VERSE:

“Having gifts that differ according to the grace given to us, let us use the: If prophecy, in proportion to our faith.” Romans 12:6

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BIBLE PRINCIPLE: God is glorified when we use our gifts and talents in accordance with our faith.

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​Motivation:

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​Look around your room, what are the things you find inside?

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​Aim:

​I will be able to...

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• ​Express one value as a fraction of another given their ratio and vice versa.

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• Define and illustrate the meaning of ratio and proportion using concrete or pictorial model

​Action:

​Observe the following images

​Analysis

​Compare the number of oranges to the number of apples.

​Compare the number of squares to the number of circles.

​Compare the number of girls to the number of boys.

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How many of each item A is there in item B? How can you express the relationship of these items?

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​With these given examples, can you define what is ratio?

​10/26/21

Ratio

​A ratio is a representation of the relationship between two things.

Open Ended

What is ratio?

​Summary/ Generalization

​How do we compare the quantities of 2 or more sets of objects?

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​Write a ratio for each of the following.

1) 4 wins and two losses in a basketball.

2) 24 girls to 18 boys.

3) 3 cups of sugar for every 5 cups of flour

4)2 men for every 5 cups of rice

5) 1 book for every 2 pupils

​Application

Fill in the Blanks

4 wins and two losses in a basketball

express your answer in colon form

Fill in the Blanks

24 girls to 18 boys. 

express your answer in colon form

Fill in the Blanks

3 cups of sugar for every 5 cups of flour

express your answer in fractional form

Fill in the Blanks

2 men for every 5 cups of rice

express your answer in fractional form

Fill in the Blanks

1 book for every 2 pupils

express your answer in word form

​Assignment:

​Prepare sliced 5pcs calamansi and 1 glass of water for tomorrow.

​10/27/21

Open Ended

What have you learned today?

Poll

Rate today's lesson

Review:

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​How do we find equivalent fractions? Can you give examples of equivalent fractions?

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​2nd Day

Aim:

I will be to...

• Express ratio in its simplest form

• ​Find equivalent ratios

​Motivation:

What is your favorite drinks for snacks?

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​Action

​Mother is preparing Calamansi Juice:

a) For each glass of Calamansi Juice, 5 pieces of Calamansi are needed.

b) If she makes 2 glasses, how many pieces of calamansi are needed?

c) If she makes 3 glasses, how many pieces of calamansi are needed?

​Analysis:

​a) What is asked?

b) What are the given facts?

c.) What strategies may be used to answer the problem?

​Illustration of the problem:

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a) For each glass of Calamansi Juice, 5 pieces of Calamansi are needed.

​b) If she makes 2 glasses, how many pieces of calamansi are needed?

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​c) If she makes 3 glasses, how many pieces of calamansi are needed?

​​What is the ratio of the glass of water to calamansi in letter a? b? c?

• ​1:5

• 2:10

• ​3:15

​Which of these ratio is expressed in lowest/ simplest form?

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​Why?

​Similar Examples

​https://quizlet.com/547622967/flashcards

​https://www.youtube.com/watch?v=5J6wNdD8j64

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​refer to shared screen

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​Content book page 72

​Generalization/ Summary:

How do we find ​equivalent ratios?

​Can we simplify it or find its lowest form? How?

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​Application:

​Reduce the following ratios in lowest term. Choose the letter that corresponds to the ratio in simplest form. 10mins

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​E= 3:4 I=1:2 R = 2:9 T = 15:4 G = 1:6 N = 5:6 S = 1:4

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Fill in the Blanks

What is the hidden message?

Fill in the Blanks

Is 5:6 equivalent to 10:12?

Fill in the Blanks

Is 10:4 equivalent to 5:2?

​Assignment:

​page 72 of Content book Practice Questions Number 1 (A-C) & 2 (A-C)

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​* Prepare square cut outs: 6 blue and 12 red

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Open Ended

What have you learned today?

Poll

Rate today's lesson

Express the following ratio of:

a) stamps to patches

b) bookmark to patches

c) diary to patches

d) bookmark to stamps

e) diary and stamps

11/2/21​

Review:

​Answers:

a) stamps to patches- 10:15

b) bookmark to patches- 20:15

c) diary to patches- 12:15

d) bookmark to stamps- 20:10

e) diary and stamps- 12:10

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​11/2/21

Review

​Give the simplest/ lowest form of these ratios.

​a.) 10:15 d.) 20:10

​b.) 20:15 e.) 12:10

​c.) 12:15

​Answers:

​a.) 2:3

​b.) 4:3

​c.) 4:5

​d.) 2:1

​e.) 6:5

​Review

Give 3 equivalent ratio of the following:​​

a.) 2:3

​b.) 4:3

​c.) 4:5

​d.) 2:1

​e.) 6:5

​Answers:

​a.) 4:6, 6:9. 8:12

​b.) 8:6, 12:9, 16:12

​c.) 8:10, 12:15, 16:20, 20:25

​d.) 4:2, 6:3, 8:4, 10:5

​e.) 12:10, 18:15, 24:20, 30:25

​Checking of assignment

Multiple Select

Which of the given ratios are equivalent to 1:3?

• A. 9:81

• B. 16:48

• C. 200:600

Open Ended

Find any 4 equivalent ratios for each given ratio: 

2:7

Open Ended

Find any 4 equivalent ratios for each given ratio: 

5 to 8

Open Ended

Find any 4 equivalent ratios for each given ratio: 

3:6

11/3/21

Aim:

I will be able to

• solve real life situation problems involving ratio and expressing it into its simplest form

​Action:

​Bring out your square cut outs.

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Ask: What is the ratio of the number of blue cubes to the number of red cubes?

​Place the square cut outs in groups of 2

• What is the ratio of the blue squares to the red squares?

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​​Place the square cut outs in groups of 3

• What is the ratio of the blue squares to the red squares?

​Place the square cut outs in groups of 6

• What is the ratio of the blue squares to the red squares?

​Analysis:

​What are the ratios? What are they called?

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​Which one is in the simplest or lowest form?

​Discussion

​In a Grade VI Mathematics class, there are 27 boys and 21 girls.

​a) Write the ratio of boys to girls.

b) Write the ratio of girls to boys.

c) Write the ratio of girls to the whole class.

d) The ratio of boys to the whole class.

​11/3/21

Open Ended

What have you learned today?

Poll

Rate today's lesson

​Equivalent ratio

​answer workbook B8 S2

​Aim:

I will be able to...

Differentiate ratio from rate​

​Action

​YES

​NO

​Analysis

​How do you differentiate the two given columns?

​What can you say about the examples in the yes column? No column?

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​Ratio is the comparison of two quantities.

​Rate is the comparison of two measurements with different units.

​Give an example of ratio

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​Give an example of rate

​Example:

​Joshua scored 168 points in 7 basketball games. Express in lowest terms, the average rate of the number of points that Joshua scored in every game.

​11/10/21

​11/10/21

​Problem

​Sheena and Nikka joined the ladies’ basketball tryout. Sheena scored 34 points in her two games while Nikka scored 51 in her three games. Whose average point per game is higher?

 

Determine the following.

a) Sheena’s Average Point in Lowest Term.

b) Nikka’s Average Point in Lowest Term.

c) Compare Sheena’s Average Point to Nikka’s Average Point.

​Sheena and Nikka joined the ladies’ basketball tryout. Sheena scored 34 points in her two games while Nikka scored 51 in her three games.

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​a) Sheena’s Average Point in Lowest Term.

​* Determine the ratio of Sheena's points to the number of games she had

​The average of Sheena's game is 17 points per game.

​​Sheena and Nikka joined the ladies’ basketball tryout. Sheena scored 34 points in her two games while Nikka scored 51 in her three games.

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b) Nikka’s Average Point in Lowest Term.

​Determine the ratio of Nikka's score to the game she had.

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​​​Sheena and Nikka joined the ladies’ basketball tryout. Sheena scored 34 points in her two games while Nikka scored 51 in her three games.

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​c) Compare Sheena’s Average Point to Nikka’s Average Point.

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Sheena and Nikka have the same average point.

​Application

Answer B8 S3 of your workbook

​Question:

​Victoria walks 60 miles in 3 hours and her sister walks 45 miles in 2 hours. Who walks faster?

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​How can we find out?

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​Find the rate:

 

a) If Luisa can type 440 words in 8 minutes, what is her rate of typing?

 

b) If 30 green oranges cost Php100, at what rate are the oranges sold?

​Aim

​Forming ratio and proportion

 Using colon (:) and fractions in writing ratios and proportions

​Action

​Find the ratio/proportion of the following. Use 2 different ways in writing them.

1) There are 10 buses at a station. If each bus has 6 wheels, what is the ratio of buses to

wheels?

2) Every quarter each student submits 2 projects in EPP. Give the ratio of projects to quarters.

3) There are 3 caimito trees and 4 mango trees in Mang Tino’s orchard. While in Mr. Muñoz’

orchard, there are 6 caimito trees and 8 mango trees. Give the ratio of the mango to caimito

trees in each orchard then write a proportion.

​Aim:

We will be able to identify ratios in proportion

​Action

5:12, ​15:36, 20:24

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​Are the given ratios equivalent?

​What do you understand about proportion?

​Are the given ratios proportional to each other?

​Action

5:12 is equivalent to 15:36

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​Equivalent ratios are in proportion to each other.

​Thus 5:12 and 15:36 are in proportion.

​Application

​Aim:

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