CCSS.Math.Content.6.RP.A.1 Usual Core State Standards Math Grade 6,Ratios and also Proportional Relationships

Cluster: Understand also ratio ideas and usage ratio thinking to fix problems

Standard: Understand the idea of a ratio and use proportion language to define a proportion partnership between two quantities. For instance, “The ratio of wings to beaks in the bird residence at the zoo was 2:1, bereason for eexceptionally 2 wings there was 1 beak.” “For eincredibly vote candidate A got, candidate C obtained virtually 3 votes.”

Learning Domain: Ratios and Proportional Relationships

Standard: Understand also ratio ideas and usage proportion thinking to resolve problems

Indicator: Understand also the idea of a proportion and usage ratio language to describe a ratio connection between 2 quantities. For instance, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak."ť "For eincredibly vote candiday A got, candidate C got nearly 3 votes."ť

Learning Domain: Ratios and Proportional Relationships

Standard: Understand also ratio principles and use ratio thinking to fix problems.

You are watching: A comparison of two amounts using division

Indicator: Understand also the idea of a ratio and usage proportion language to describe a ratio connection in between two amounts.

Ratios Comparing Numbers with Ratios Comparing Numbers with Ratios This leskid formally introduces and specifies a proportion as a way of comparing numbers to one one more.

Key Concepts

A ratio is characterized by the complying with characteristics:

A proportion is a pair of numbers (a:b).Ratios are offered to compare 2 numbers.The value of a ratio a:b is the quotient a ÷ b, or the result of dividing a by b.

Other important features of ratios incorporate the following:

A proportion does not constantly tell you the worths of quantities being compared.The order of worths in a proportion matters.Goals and Learning ObjectivesIntroduce a formal interpretation of proportion.Use the meaning of proportion to settle troubles regarded comparing quantities.Understand that ratios perform not constantly tell you the worths of the amounts being compared.Understand also that the order of worths in a proportion matters.
Overview to Ratios
Lesboy Guide

In this leskid, students learn the formal interpretation of a proportion and then use it to resolve troubles. The start of the leschild introduces the principle of a ratio as a method of comparing numbers of objects making use of division, which is an alternative to comparing numbers using subtractivity. Have students look at the picture of stars and also triangles and then read the message.

The ratio of triangles to stars is 3:10. What is the proportion of stars to triangles? (Answer: 10:3)

ELL: Keep in mind that some students may not feel comfortable analysis aloud. Be ready to support them in this task.

Opening

Summary to Ratios

Look at the image of stars and also triangles and read the complying with indevelopment.

One way that you deserve to compare the variety of stars and also the number of triangles is to say that tbelow are 7 even more stars than tbelow are triangles. This comparichild looks at the difference in between 2 quantities; it supplies the operation of subtractivity.Another way that you deserve to compare the variety of stars and also the number of triangles is to say that for eexceptionally 3 triangles tbelow are 10 stars. You can say that the ratio of triangles to stars is 3 to 10 or 3:10. This comparichild uses the procedure of department.The value of the ratio of triangles to stars is 310, or 0.3. Ratio of Egginess
Lesboy Guide

Have a volunteer review the definition of a ratio aloud.

Resee the definition of ratio: A proportion is a comparichild of two numbers by department.

The value of a proportion is the quotient that outcomes from dividing the 2 numbers. For instance, the value of the proportion 35:7 is 5, which you find by computing 35 ÷ 7 = 5.

Have students review the video of the egginess problem from the previous lesson. Discuss the ratio in the egginess difficulty. Demonstprice how to compose the proportion. Talk about the fact that the ratio can be flour to eggs or eggs to flour. The proportion of flour to eggs is 3:2; the ratio of eggs to flour is 2:3.

ELL: When mirroring the video, be sure that ELLs are following the explacountries. Pausage the video at essential times to permit ELLs time to process the indevelopment. Ask students if they need to watch it a second time. Remind students that they are finding the ratio in the egginess problem.

Opening

Ratio of Egginess

A ratio is a comparichild of 2 numbers by department.

The value of a proportion is the quotient that results from splitting the 2 numbers. For instance, the worth of the ratio 35:7 is 5, which you uncover by computer 35 ÷ 7 = 5.

In the previous leschild, you looked at just how to solve the egginess in a mixture. Watch the EgginessPart 2 video.

What is the proportion in the egginess problem? VIDEO: Egginess Part 2

MP4
Egginess Part 2
Math Mission
Lesson Guide

Discuss the Math Mission. Students will define just how ratios are offered to compare amounts.

ELL: Discuss the idea of proportion. Lay out diagrams of the examples so students can make associations with compariboy of amounts. Use manipulatives to demonstrate the comparison of 2 amounts making use of subtractivity and also department. Use illustrations or manipulatives to model efficient finding out to describe ratios. It is essential to emphadimension that you deserve to explain ratios by saying “for every” or “per” since these terms will be offered interchangeably throughout the unit. Underline the 2 quantities so that students understand precisely which quantities you are comparing.

Opening

Exsimple just how ratios are supplied to compare amounts.

Ms. Lee’s Class
Leschild Guide

Have students job-related in pairs on the troubles and also the presentation.

SWD: Aid students through disabilities develop their mathematical vocabulary by continually modeling the usage of brand-new terms in the conmessage of classroom occupational and tasks.

Mathematical Practices

Mathematical Practice 2: Reakid abstractly and quantitatively.

Listen for students that usage the trouble instances to help them make feeling of the worths they are working via.

Mathematical Practice 6: Attend to precision.

Listen also for students that usage the term ratio appropriately or who discuss the correct consumption of the term as they work together to settle the troubles.

Interventions

Student thinks that you compose a ratio as a subtractivity.

Look at your interpretation of ratio. Is it a difference?

Student reverses the boys and girls in the proportion.

What are the two things you are comparing? What is the order that you are comparing them in?AnswersThere are 2 even more girls than boys.The ratio of boys to girls is 15:17.The proportion of girls to boys is 17:15.

Work Time

Ms. Lee's Class

Tright here are 15 boys and also 17 girls in Ms. Lee's math course.

What is the difference between the number of girls and the variety of boys in the class?What is the ratio of boys to girls?What is the proportion of girls to boys?

When you should discover the distinction in between two numbers, what procedure perform you use?For the ratio of boys to girls, what have to the initially number be, ”the number of girls or the number of boys?For the ratio of girls to boys, what should the initially number be, the variety of girls or the variety of boys
A Tennis Game
Mathematical Practices

Mathematical Practice 2: Reaboy abstractly and also quantitatively.

Listen for students who use the trouble situations to help them make sense of the worths they are working via.

Mathematical Practice 6: Attend to precision.

Listen also for students who usage the term ratio appropriately or who talk about the correct usage of the term as they job-related together to deal with the problems.

Interventions

Student thinks tright here are precisely 3 females and 2 males watching the tennis game.

The ratio is 3:2. Here are some possibilities that fit this ratio: 6 females to 4 males, 30 females to 20 males, 300 females to 200 males. How have the right to you tell these all have actually a ratio of 3:2?

Student thinks tright here is1 even more female than male watching the tennis game.

Look at the definition of a proportion at the begin of the leskid. Does a ratio compare by subtraction or by division?You are reasoning of the difference between 3 and 2, but the trouble is around the proportion in between them. Tbelow might be 6 females and also 4 males or 30 females and 20 males.

Student believes the variety of females, males, or human being watching the tennis game can be calculated via just the proportion.

If tbelow were 20 males, just how many type of females would certainly tbelow be? If tright here were 15 females, just how many males would there be? If you don’t understand one of these numbers, can you uncover the other?Possible AnswersNo, the proportion tells you that for every 2 males watching the game, tbelow are 3 females watching the game, but it does not tell you the complete variety of females.No, the ratio of 3 females to 2 males does not tell you the total number of world watching the game. It tells you that for eexceptionally 5 civilization watching, 3 are female and 2 are male.Yes, the proportion tells you tright here are 1.5 times as many kind of females as males watching the game.No, without discovering the actual number of each amount, you can’t find their difference.Yes, the ratio of the variety of males to the variety of females is 2:3.

Work Time

A Tennis Game

The ratio of the variety of females watching a tennis game to the number of males watching the tennis game is 3 to 2. You deserve to compose that as32, or 3:2.

Can you tell from this ratio how many type of females are watching the tennis game? Exsimple.Can you tell from this ratio exactly how many world are watching the tennis game? Explain.Can you tell from this ratio whether more males or even more females are watching the game? Explain.Can you tell from this ratio the difference between the number of males and the number of females watching the game? Explain.Could you usage this proportion to write the proportion of the variety of males watching the tennis game to the number of females watching the tennis game? Exordinary.

Map out a diagram showing several feasible numbers of females and also males watching the game. Can you tell which numbers are correct based upon the ratio?In looking at a ratio, how have the right to you tell which number represents the larger amount?What would you have to understand to find the distinction in between the variety of males and females watching the game?In determining whether the proportion can be rewritten to recurrent males to females, think about the interpretation of a proportion.
Prepare a Presentation
Preparing for Ways of Thinking

Listen and look for the following student reasoning to highlight throughout the Ways of Thinking discussion:

Students who clearly discuss subtractivity and also division as ways of comparing numbersStudents who comment on the borders of what a proportion tells you (e.g., “It doesn’t tell us exactly how many kind of …”)Students who divide 3 by 2 to gain 1.5 and then talk about the meaning of 1.5 through reference to the problem situationChallenge Problem

The statement is always true. A number separated by itself is equal to 1, so if 2 amounts gain closer to each various other, their ratio’s value is closer to a number divided by itself, or 1.

Work Time

Prepare a Presentation

Exsimple what kinds of conclusions you deserve to and cannot make based upon the tennis game proportion.

In your own words, describe what a proportion is.

Challenge Problem

As two quantities acquire closer to each other, the value of the proportion of the amounts philosophies 1.

Is the over statement constantly true, sometimes true, or never true? Explain.
Make Connections
Mathematics

Have students share their presentations. If tbelow are any kind of misunderstandings, facilitate a class conversation that concentrates on the definition of a proportion and also what it does and does not tell us.

What are some examples of numbers of females and males that can be watching the tennis game?

Compare these examples to the situation around the number of boys and also girls in Ms. Lee’s course, in which the actual numbers of students are given fairly than a proportion between numbers. Highlight correct usage of the term ratio, or carry out avenues for students to revise their usage of the term.

Conclude the conversation through a emphasis on whether the proportion tells you whether even more males are watching the game or even more females are watching the game. If tbelow is a student that split 3 by 2 to get 1.5, ask them to share their strategy. Ask the course what 1.5 indicates in this situation:

Does it make feeling for a proportion of numbers of people to have a worth of 1.5?

Check that all students understand also that the order of worths in a proportion matters. The ratio of males to females (2:3) is various from the proportion of females to males (3:2).

Mathematical Practices

Mathematical Practice 2: Reakid abstractly and also quantitatively.

Ask students to talk about how they can use the context of a difficulty instance to help them make feeling of the worths they are working via.

Mathematical Practice 6: Attend to precision.

Call attention to correct provides of the term ratio,or ask for clarifications around its use and also definition as essential as students present their work-related and ask questions of presenters.

Ways of Thinking: Make Connections

Take notes about your classmates' explacountries of the conclusions that deserve to and cannot be made based upon the tennis game proportion, and their explacountries of what a proportion is.

What feasible numbers of females and also males watching the tennis game did you find?How did you recognize these numbers?How did you decide what kinds of conclusions you deserve to and also cannot make based upon the tennis game ratio?Is there anything you can add to your explanation to make it more certain or precise?
A Possible Summary

Ratios permit you to compare quantities, yet by themselves, they perform not tell you the actual worths of the quantities. Using a proportion to compare quantities is different from using subtraction to uncover the distinction between quantities bereason a ratio tells you the worth of one amount for a given value of the other quantity. For instance, for a proportion of 3:2, you know that if the initially quantity has a worth of 6, the second amount has a worth of 4.

SWD: Create a resource for some students that contains this explacountry in much easier language (maybe via visual illustrations). Annotate illustrations that show ratios and what they represent.

Further Discussion Points

If tright here is time, comment on the following:

A summary of different ways to compare numbersA definition of a ratioA summary of what a ratio tells you and also what it doesn’t tell you

Formative Assessment

Summary of the Math: What I Kcurrently about Ratios

Write a summary of what you learned around ratios.

Do you describe what a ratio is?Do you discuss what forms of conclusions deserve to and also cannot be made based upon a ratio?Do you describe exactly how making use of ratios to compare 2 numbers is different from using subtraction to compare two numbers?