Unit 2:Introduction to Ratios

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Unit 2:Introduction to Ratios

Unit 2:Introduction to Ratios

PRESENTATION

Unit Calendar

"L" stands for Lesson (i.e. L1 = Lesson 1)

Unit Calendar

"L" stands for Lesson (i.e. L1 = Lesson 1)

INDEX

Lesson 3

Lesson 2 & Quiz

Lesson 1

Lesson 5 & Quiz

Lesson 4

Lesson 6

Lesson 8

Lesson 7

Lesson 9

Lesson 12

Lesson 11

Lesson 10 & Quiz

Lesson 15

Lesson 14 & Quiz

Lesson 13

Lesson 16

Review

Test

Introducing ratios and ratio language

Monday, September 15th

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HI-SCORE

Vocabulary

Ratio

Definition

A ratio is a way to relate 2 or more quantities. For example, the ratio 3:2 could describe: 1. A recipe that uses 3 cups of flour for every 2 eggs. 2. A boat that moves 3 meteres every 2 seconds. 3. A diagram that has 3 blue squares for every 2 green squares.

Lesson 1: Introducing Ratios and ratio language

Learning Target

I can define ratios and use ratio language.

I can use my understanding of groupings to understand ratios.

Success Criteria

Problem 1

Think of different ways you could sort these figures. What categories could you use? How many groups would you have?

+ Hint

Problem 2 | Part 1

Draw the table in your notebook.

Categorize the collection that you were given, and write down the values for each category. For example,if you're sorting coins, one category name might be "Quarters", and the category amount would be the number of quarters you have in the collection.

Problem 2 | Part 2

Write at least two sentences that describe ratios in the collection. Remember, there aremany ways to write a ratio:

1. The ratio of one category to another category is ______ to ______.
2. The ratio of one category to another category is ______ : ______.
3. There are ______ of one category for every ______ of another category.

+ example

Cool-Down

Write at least two sentences that describe ratios in the collection.

Reminder: quiz tomorrow after the lesson.

Representing Ratios with diagrams

Tuesday, September 16th

Lesson 2: Representing ratios with diagrams

Learning Target

I can use diagrams to represent ratios.

I can write ratio sentences and represent them using diagrams.

Success Criteria

Problem 1

Select all statements that correctly describe this situation.

a. The ratio of cups of white paint to tablespoons of blue paint is 2:6.b. For every cup of white paint, there are 2 tablespoons of blue paint. c. There is 1 cup of white paint for every 3 tablespoons of blue paint. d. There are 3 tablespoons of blue paint for every cup of white paint. e. For each tablespoon of blue paint, there are 3 cups of white paint. f. For every 6 tablespoons of blue paint, there are 2 cups of white paint. g. The ratio of tablespoons of blue paint to cups of white paint is 6 to 2.

Problem 2

Jada mixed 8 cups of corn flour with 2 pints of liquid glue to make play clay. a. Draw a diagram that represents the situation. b. Write at least two sentences describing the ratio of corn flour and glue.

Card sort

You're going to get cards showing diagrams or sentences that describe the items in different pencil cases. In the diagrams: • A circle represents a pencil. • A square represents an eraser. • A triangle represents a paper clip. Work together with your group to match the diagrams to the sentences.

Cool-Down

1. Draw a diagram to represent the ratios between the numbers of erasers, pencils, ad notepads that Lin has. Lin has 3 sets of stationary. Each set has 2 erasers, 4 pencils, and 1 notepad. 2. Use the information about the sets Lin has to fill in the blanks.

Section A Quiz

1. Make sure you have your name at the top of your paper.2. Answer ALL questions. 3. Turn in when you're finished and put your privacy divider away. 4. Silently go on the games in my Google Classroom.

Ratios:1. The value that's talked about first should go first in the ratio. 2. The number of objects mentioned should match or be equivalent tothe number of squares in a diagram.

Recipes

Wednesday, September 17th

Lesson 3: Recipes

Learning Target

I will be able to identify equivalent ratios.

I can use common factors and diagrams to find equivalent ratios.

Success Criteria

Problem 1

How would the taste of Mixture A compare to the taste of Mixture C? Mixture B uses ____ cups of water and ____ teaspoons of drink mix. The ratio of cups of water to teaspoons of drink mix in Mixture B is __:__. Mixture C uses ____ cups of water and ____ teaspoons of drink mix. The ratio of cups of water to teaspoons of drink mix in Mixture C is __:__.

Problem 2

A recipe for one batch of cookies calls for 5 cups of flour and 2 teaspoons of vanilla. 1. Draw a diagram that shows the amount of flour and vanilla needed for two batches of cookies. 2. How many batches can you make with 15 cups of flour and 6 teaspoons of vanilla? Show the additional batches by adding more ingredients to your diagram. 3. How much flour and vanilla would you need for 5 batches of cookies?

Problem 3

A recipe for two batches of cookies calls for 4 eggs and 2 cups of flour. What is the ratio of eggs to cups of flour? What would the ratio of eggs to cups of flour be if you only made one batch?

Cool-Down

When Elena makes lemonade, she usually mixes 9 scoops of lemonade powder with 6 cups of water. Today, she doesn’t have enough ingredients. Think of a recipe that would give a smaller batch of lemonade but still taste the same. Explain or show your reasoning.

Color Mixtures

Thursday, September 18th

Lesson 4: Color Mixtures

Learning Target

I will be able to identify equivalent ratios.

I can use common factors and diagrams to find equivalent ratios.

Success Criteria

Problem 1

A batch of dark orange paint uses 4 ml of red paint and 2 ml of yellow paint. What is the ratio of red paint to yellow paint for 1 batch? For 2 batches? For 3 batches?

Problem 2 | Part 1

The recipe for Perfect Purple Water says, “Mix 8 ml of blue water with 3 ml of red water.” Jada mixes 24 ml of blue water with 9 ml of red water. Andre mixes 16 ml of blue water with 9 ml of red water. 1. Which person will get a color mixture that is the same shade as Perfect Purple Water? Explain or show your reasoning.

Problem 2 | Part 2

The recipe for Perfect Purple Water says, “Mix 8 ml of blue water with 3 ml of red water.” 2. Find another combination of blue water and red water that will also result in the same shade as Perfect Purple Water. Explain or show your reasoning.

Cool-Down

A recipe for orange water says, “Mix 3 teaspoons of yellow water with 1 teaspoon red water.” For this recipe, we might say: “The ratio of teaspoons of yellow water to teaspoons of red water is 3:1.” 1. Write a ratio for 2 batches of this recipe. 2. Write a ratio for 4 batches of this recipe. 3. Explain why we can say that any two of these three ratios are equivalent

Defining equivalent ratios

Friday, September 19th

9192025

HI-SCORE

Vocabulary

Equivalent Ratios

Definition

Two ratios are equivalent if each of the numbers in the first ratio can be multiplied by the same factor to get the numbers in the second ratio. For example, 8:6 is equivalent to 4:3 because 8÷2=4 and 6÷2=3.

Lesson 5: Defining Equivalent Ratios

Learning Target

I will be able to identify equivalent ratios.

I can use common factors and diagrams to find equivalent ratios.

Success Criteria

Problem 1

The ratios 5:3 and 10:6 are equivalent ratios. 1. Is the ratio 15:12 equivalent to these? 2. Is the ratio 30:18 equivalent to these? 3. Give two more examples of ratios that are equivalent to 5:3. 4. How do you know when ratios are equivalent and when they are not equivalent?

Problem 2

Identify if the following ratios are equivalent or not: 1. 18:12 and 9:6 2. 3:2 and 9:6 3. 18:15 and 9:6

Cool-Down

1. Write another ratio that is equivalent to the ratio 4:6. 2. How do you know that your new ratio is equivalent to 4:6? Explain or show your reasoning. After you're finished with your cool-down, turn it in and get a privacy divider. Make sure your name is on your paper before you turn it in!

Section A Quiz

Equivalent Ratios:When multiplying or dividing, make sure that you're using the same number to multiply or divide both parts of the ratio by. For example, 2:3 is equivalent to 10:15 because both 2 and 3 were multiplied by 5.

1. Make sure you have your name at the top of your paper.2. Answer ALL questions. 3. Turn in when you're finished and put your privacy divider away. 4. Silently go on the games in my Google Classroom.

Introducting double number line diagrams

Tuesday, September 23rd

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HI-SCORE

Vocabulary

Double Number Line Diagram

Definition

A double number line diagram uses a pair of parallel number lines to represent equivalent ratios. There is one number line for each quantity in the ratio. The tick marks for equivalent ratios line up.

9232025

HI-SCORE

Vocabulary

Per

Definition

The word per means "for each". For example, the price is $5 per ticket. This means $5 must be paid for each ticket. Buying 4 tickets costs $20, because 4x5=20.

Lesson 6: Introducing Double Number Line Diagrams

I will be able to read and use double number lines to find equivalent ratios.

Learning Target

I can use my understanding of equivalent ratios and represent them on a double number line.

Success Criteria

Problem 1 | Part 1

A drink recipe says to mix 4 teaspoons of powdered drink mix for every cup of water. Here are two ways to represent multiple batches of this recipe:

1. How can we tell that 4:1 and 12:3 are equivalent ratios? 2. How are these representations the same? How are these representations different?

Problem 1 | Part 2

3. How many teaspoons of drink mix should be used with 3 cups of water? 4. How many cups of water should be used with 16 teaspoons of drink mix? 5. What numbers should go in the empty boxes on the double number line diagram? What do these numbers mean?

Problem 2

1. Complete the double number line diagram to show the amounts of white paint and blue paint in different-sized batches of light blue paint.2. How many cups of white paint should Elena mix with 12 tablespoons of blue paint? How many batches would this make? 3. How many tablespoons of blue paint should Elena mix with 6 cups of white paint? How many batches would this make?

Double Number Line

Cool-Down

A recipe for one batch of cookies uses 5 cups of flour and 2 teaspoons of vanilla. 1. Complete the double number line diagram to show the amount of flour and vanilla needed for 1, 2, 3, 4, and 5 batches of cookies. 2. If you use 20 cups of flour, how many teaspoons of vanilla should you use? 3. If you use 6 teaspoons of vanilla, how many cups of flour should you use?

How much for one?

Wednesday, September 24th

9242025

HI-SCORE

Vocabulary

Unit Price

Definition

The unit price is the cost for 1 item or for 1 unit of measure. For example, 10 feet of fencing costs $150. The unit price is 150÷10, or $15 per foot.

Lesson 8: How much for one?

I will be able to calculate unit price.

Learning Target

I can use my understanding of ratios, multiplication, and division to find unit price.

Success Criteria

Problem 1

Eight avocados cost $4. a. How much do 16 avocados cost? b. How much do 20 avocados cost? c. How much do 9 avocados cost?

Problem 2

Four bags of chips cost $6. a. What is the cost per bag? b. At this rate, how much will 7 bags of chips cost?

Problem 3

At a used book sale, 5 books cost $15. a. What is the cost per book? b. At this rate, how many books can you buy for $21?

Cool-Down

Here is a double number line showing that it costs $3 to buy 2 bags of rice: 1. At this rate, how many bags of rice can you buy for $12? 2. Find the cost per bag. 3. How much do 20 bags of rice cost?

constant speed

Thursday, September 25th

9252025

HI-SCORE

Vocabulary

Constant Speed

Definition

When an object moves at a constant speed, it moves at the same speed at all times. It does not move faster or slower at any time. So, the ratios of distance trabeled to elapsed time are always equivalent.

9262025

HI-SCORE

Vocabulary

Same Rate

Definition

The phrase "same rate" is used to describe two situations that have equivalent ratios. For example, a sink is filled at a rate of 2 gallons per minute. A tub is also filled at a rate of 2 gallons per minute. So, the sink and the tub are filled at the same rate.

Lesson 9: Constant speed

I can use ratios to compare how fast things move and different situations.

Learning Target

I can compare speeds by using my understanding of equivalent ratios.

Success Criteria

Problem 1

Lin and Diego both ran for 10 seconds, each at their own constant speed. Lin ran 40 meters and Diego ran 55 meters. 1. Who was moving faster? 2. How far did each person move in 1 second? 3. Han ran 100 meters in 20 seconds at a constant speed. Is this speed faster, slower, or the same as Lin's? What about Diego's?

Problem 2

1. Mai and Jada ran on treadmils. Each person ran at a constant rate. Mai ran 3 miles in 24 minutes. Jada ran 3 miles in 30 minutes. Who was running faster? 2. Han and Tyler also ran on treadmills. Han ran 3.5 kilometers in 15 minutes. Tyler ran 7 kilometers in 30 minutes. Each person ran at a constant rate. Were Han and Tyler running at the same rate?

Problem 3

Diego paid $47 for 3 tickets to a concert. Andre paid $141 for 9 tickets to a concert. Did they pay at the same rate?

cool-down

Andre ran 2 kilometers in 15 minutes, and Jada ran 3 kilometers in 20 minutes. Both ran at a constant speed. Did they run at the same speed?

11

representing ratios with tables

Friday, September 26th

Lesson 11: Representing ratios with tables

I will be able to represent ratios using tables.

Learning Target

Success Criteria

I can complete tables using equivalent ratios.

Tables vs. Double Number Lines

Problem 1

Complete the table using equivalent ratios.

Problem 2

Complete the table to answer the questions: 1. Noah bought 4 tacos and paid $6. At this rate, how many tacos could he buy for $15?

Problem 3

Complete the table to answer the questions: 2. Jada’s family bought 50 tacos for a party and paid $72. Were Jada’s tacos the same price as Noah’s tacos?

Cool-Down

Your cool-down is double sided today. Make sure you complete both sides.

13

Tables and double number line diagrams

Monday, September 29th

Lesson 13: Tables and double number line diagrams

I will be able to solve real-world situations using equivalent ratios.

Learning Target

I can use tables and/or double number lines to help me solve problems involving equivalent ratios.

Success Criteria

Problem 1

Han can run 100 meters in 20 seconds. He wonders how long it would take him to run 3,000 meters at this rate. He made a table of equivalent ratios.

1. Do you agree that this table represents the situation? Explain yourreasoning. 2. Complete the last row with the missing number.

Problem 2

1. Priya can bike 150 meters in 20 seconds. At this rate, how long would it take her to bike 3,000 meters? 2. Priya’s neighbor has a dirt bike that can go 360 meters in 15 seconds. At this rate, how long would it take her neighbor to go 3,000 meters?

Cool-Down

In a sprint to the finish line, a professional cyclist travels 380 meters in 20 seconds. At that rate, how far does the cyclist travel in 3 seconds? You can use a table if it is helpful.

Quiz

1a. Dividir 96 por 4.1b. Multiplica tu repuesta de 1a por 60. 2. Dividir 8:6 por 2 y luego multiplica la proporción equivalente por 15.

1a. Divide 96 by 4.1b. Multiply your answer from 1a by 60. 2. Divide 8:6 by 2, then multiply the equivalent ratio by 15.

15

Part-Part-Whole Ratios

Tuesday, September 30th

9302025

HI-SCORE

Vocabulary

Tape Diagram

Definition

A tape diagram is a group of rectangles put together to represent a relationship between quantities. This tape diagram shows a ratio of 30 gallons of yellow paint to 50 gallons of blue paint.

Lesson 6: Introducing Double Number Line Diagrams

I will be able to read and use double number lines to find equivalent ratios.

Learning Target

I can use my understanding of equivalent ratios and represent them on a double number line.

Success Criteria

Quiz

1a. Divide 96 by 4.1b. Multiply your answer from 1a by 60. 2. Divide 8:6 by 2, then multiply the equivalent ratio by 15.

When you're done:Go on the games in my Google Classroom, complete any missing assignments, or read silently.

16

Solving More ratio problems

Wednesday, October 1st

Lesson 6: Introducing Double Number Line Diagrams

I will be able to read and use double number lines to find equivalent ratios.

Learning Target

I can use my understanding of equivalent ratios and represent them on a double number line.

Success Criteria

End of Unit

Test in Illuminate

Thursday, October 2nd

232323

HI-SCORE

summary

With Genially templates, you can include visual resources to leave your audience speechless. You can also highlight a specific phrase or data that will be etched into your audience's memory, and even embed external content that surprises: videos, photos, audios... Whatever you want!

© 20XX GENIALLY ESCAPE GAMES

Usean image

Need more reasons to create dynamic content? Well: 90% of the information we assimilate comes to us through sight, and we retain 42% more information when the content is in motion.

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Write a subtitle

Write a subtitle

Structureyour content

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WRITE A GREAT TITLE

Describe the problem you are going to solve and, above all, the reason why your idea is interesting

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CAROUSEL

Animate your content and take it to the next level

Including citations always reinforces our presentation. It breaksthe monotony.

Always cite the author

Structureyour content

Sections like this will help you organize

Structureyour content

WRITE A SUBTITLE

Structureyour content

WRITE A SUBTITLE

RELEVANT DATA

75%

of our brain is involved inthe processing of visual stimuli.

+ INFO

write a title here

25%

You can representnumbers in this way

50%

Even if you laterexplain it orally

25%

This is how you will maintain the attention of your audience

timeline

20XX

20XX

20XX

20XX

Communicate

Design

Structure

Plan

Write a subtitle

Write a subtitle

Write a subtitle

Write a subtitle

CHART + TEXT

Use this space to briefly describe your graph and its evolution.

Usean image

Need more reasons to create dynamic content? Well: 90% of the information we assimilate comes to us through sight, and we retain 42% more information when the content moves.

+ INFO

TABLE + TEXT

Here you can put a highlighted title

Describe the problem you are going to solve and, above all, why your idea is interesting

+ INFO

A great presentation...

• Represents data with graphics.
• Uses timelines.
• Is animatedand interactive.
• Excites the brain, through multimedia elements.

• Does NOT overdo it with bullet points.

• Is clear and structured.
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PROCESS

Social beings

Narrative beings

Visual beings

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+ INFO

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+ INFO

Insert a video

In Insert, select video and include your link. Done!

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Generate experiences with your content.

It has a WOW effect. Very WOW.

Engage and amaze your audience.

Measure results and experiment.

icons

PLAYER 1

PLAYER 4

PLAYER 3

PLAYER 2

+ INFO

+ INFO

+ INFO

+ INFO

A GREAT TITLE

AUDIO 3

AUDIO 2

AUDIO 1

Especially with interactivity and animation

They are resources that reinforce the content

We understand images, gifs, videos…

link

link

link

EMBEDDED CONTENT

MAP

SOCIAL MEDIA

MUSIC

INTERACTIVE QUESTION

INTERACTIVE QUESTION

INTERACTIVE QUESTION

INTERACTIVE QUESTION

CONCLUSIONS

Communicate, but do it with interactivity. With Genially you can turn static content into a dynamic and explorable adventure while saving time and resources.Use gamification for your training, visually convey information through infographics, or create a report.

Your content is liked, but it engages much more if it is interactive

Genially

TIMELINE

What are ratios?

Section A

Equivalent Ratios

Section B

Representing equivalent ratios

Section C

Solving Ratio and Rate Problems

Section D

Part-Part-Whole Ratios

Section E

© 20XX GENIALLY PRESENTATION

game over

BUTTON

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WRITE A TITLE

Represent your data in the simplest way: choose your chart, organize the figures and paste them into Genially.

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A GREAT TITLE

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STEP 2

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Hint:

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Represent your data in the simplest way: choose your chart, organize the figures and paste them into Genially.

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Represent your data in the simplest way: choose your chart, organize the numbers, and paste them into Genially.

STEP 1

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STEP 3

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Represent your data in the simplest way: choose your chart, organize the figures and paste them into Genially.

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Represent your data in the simplest way: choose your chart, organize the figures and paste them into Genially.

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Represent your data in the simplest way: choose your chart, organize the numbers, and paste them into Genially.

WRITE A TITLE

Represent your data in the simplest way: choose your chart, organize the figures and paste them into Genially.

WRITE A TITLE

Represent your data in the simplest way: choose your chart, organize the numbers, and paste them into Genially.

With this function...

You can add additional content that excites your audience's brain: videos, images, links, interactivity... Whatever you want!

WRITE A TITLE

Represent your data in the simplest way: choose your chart, organize the figures, and paste them into Genially.

A GREAT TITLE

I am a great subtitle, ideal for providing more context on the topic you are going to address

LINK

WRITE A TITLE

Represent your data in the simplest way: choose your chart, organize the numbers, and paste them into Genially.

WRITE A TITLE

Represent your data in the simplest way: choose your chart, organize the numbers, and paste them into Genially.

WRITE A TITLE

Represent your data in the simplest way: choose your chart, organize the figures and paste them into Genially.

WRITE A TITLE

Represent your data in the simplest way: choose your chart, organize the numbers, and paste them into Genially.

WRITE A TITLE

Represent your data in the simplest way: choose your chart, organize the figures and paste them into Genially.

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Represent your data in the simplest way: choose your chart, organize the numbers, and paste them into Genially.

WRITE A TITLE

Represent your data in the simplest way: choose your chart, organize the figures and paste them into Genially.

WRITE A TITLE

Represent your data in the simplest way: choose your chart, organize the numbers, and paste them into Genially.