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Introduction to Ratios (What Are Ratios?) | Ratio Examples and Answers

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Understanding the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, the ratio of wings to beaks in a bird house at the zoo was 2:1, because for every 2 wings there was 1 beak. Another example could be for every vote candidate A received; candidate C received nearly three votes.

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RATIO: A comparison between two different quantities.

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An Intro to Ratios | What is a Ratio? | Understanding Ratios | Math with Mr. J

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Improve your math knowledge with free questions in "Write a ratio" and thousands of other math skills.

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Website for Bytelearn Teachers, Students and Parents

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Log in to play review Boddle review game.
Username:  utm11
Password: pot65

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Click here to login and start playing Boddle. Available on the web and iOS

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Intro to ratios (video) | Ratios | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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I <3 Math: What is a Ratio? | PBS LearningMedia

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An introduction to the concept of ratios that provides real world examples. This I <3 Math episode defines ratios, discusses combining ratios, and demonstrates the correct ways to write ratios.

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Let's describe two quantities at the same time.

Learning Targets:

I can write or say a sentence that describes a ratio.

I know how to say words and numbers in the correct order to accurately describe the ratio.

1.1 What Kind and How Many?

1. If you sorted this set by color, how many groups would you have?

2. If you sorted this set by area, how many groups would you have?

3. Think of a third way you could sort these figures. What categories would you use? How many groups would you have?

1.2 The Teacher's Collection

1. Think of a way to sort your teacher's collection into two or three categories. Record your categories in the top row of the table and the amounts in the second row.

category name category amount

Pause here so your teacher can review your work.

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

The ratio of one category to another category is ________ to ________.

The ratio of one category to another category is ________ : ________.

There are _______ of one category for every _______ of another category.

1.3 The Student's Collection

1. Sort your collection into three categories. You can experiment with different ways of arranging these categories. Then, count the items in each category, and record the information in the table.

category name category amount

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

The ratio of one category to another category is ________ to ________.

The ratio of one category to another category is ________ : ________.

There are _______ of one category for every _______ of another category.

Pause here so your teacher can review your sentences.

3. Make a visual display of your items that clearly shows one of your statements. Be prepared to share your display with the class.

Are you ready for more?

1. Use two colors to shade the rectangle so there are 2 square units of one color for every 1 square unit of the other color.

2. The rectangle you just colored has an area of 24 square units.

Draw a different shape that does not have an area of 24 square units, but that can also be shaded with two colors in a ratio. Shade your new shape using two colors.

Lesson 1 Summary

A ratio is an association between two or more quantities. There are many ways to describe a situation in terms of ratios. For example, look at this collection:

Here are some correct ways to describe the collection:

The ratio of squares to circles is .

The ratio of circles to squares is 3 to 6.

Notice that the shapes can be arranged in equal groups, which allow us to describe the shapes using other numbers.

There are 2 squares for every 1 circle.

There is 1 circle for every 2 squares.

Glossary Terms

ratio

A ratio is an association between two or more quantities.

For example, the ratio could describe a recipe that uses 3 cups of flour for every 2 eggs, or a boat that moves 3 meters every 2 seconds. One way to represent the ratio is with a diagram that has 3 blue squares for every 2 green squares.

Lesson 1 Practice Problems

1. In a fruit basket there are 9 bananas, 4 apples, and 3 plums.

1. The ratio of bananas to apples is ________ : ________.

2. The ratio of plums to apples is ________ to ________.

3. For every ________ apples, there are ________ plums.

4. For every 3 bananas there is one ________.

2. Complete the sentences to describe this picture.

1. The ratio of dogs to cats is _______.

2. For every _____ dogs, there are _____ cats.

3. Write two different sentences that use ratios to describe the number of eyes and legs in this picture.

4. Choose an appropriate unit of measurement for each quantity.

1. area of a rectangle

2. volume of a prism

3. side of a square

4. area of a square

5. volume of a cube

5. Find the volume and surface area of each prism.

Prism A: 3 cm by 3 cm by 3 cm

​

Prism B: 5 cm by 5 cm by 1 cm

Compare the volumes of the prisms and then their surface areas. Does the prism with the greater volume also have the greater surface area?

6. Which figure is a triangular prism? Select all that apply.

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Grade 6 Mathematics, Unit 2.1 - Open Up Resources

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Let's describe two quantities at the same time. I can write or say a sentence that describes a ratio. I know how to say words and numbers in the correct order to accurately describe the ratio. If you sorted this set by color, how many groups would you have?

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Notice and Wonder Warm-up

Students love notices and wonders. This activity will give students the opportunity to notice parts and wholes of ratios without even knowing it! Display slide `1` of the teacher slideshow. Ask students to jot down a few noticings and a few wonderings before sharing with their neighbor.

Here are some things you might hear:

Notices:

There are `4` suns.

There are `3` lightning bolts.

There are `5` moons.

There are more suns than lightning bolts.

There are more moons than suns and lightning bolts.

There are `12` total shapes.

Wonders:

Why are there more moons than there are suns and lightning bolts?

What is the comparison between each figure?

Warm-up discussion

The warm-up is a good intro into this lesson as it allows for students to start using ratio language by identifying how many of each shape there are and understanding that there is a total as well. Share with students that we have parts and a whole in this example. Explain to students that they are going to use this concept to describe ratios.

What is a ratio?

On slide `2`, discuss with the class the definition of a ratio, as well as different representations of ratios, such as using the word "to", using a colon, or writing as a fraction. Give students some time to write down the definition as well as the three forms of representation we'll talk about today.

Writing a part to part ratio from images

This first example contains the same images from the warm-up. Since students are already a bit familiar, allow them some time to try writing the ratio on their own. If students need help getting started, ask, "How many suns are there? How many moons are there?". They can consult with a partner to check their answers. You'll want to make sure students write all three forms of the ratio. While discussing students' answers, be sure to verbally explain the ratio, like the sentence at the bottom of the slide. "For every `4` suns, there are `5` moons." This helps students to understand what the ratio representations really mean.

Congratulate students for writing their first set of ratios! Explain to students that this type of ratio is a "part to part" ratio because we're comparing a part of the total to another part of the total.

Writing a part to whole ratio from images

For the next set of ratios, we'll use the same images, but this time have students write the ratio of the number of moons to the total number of shapes. Again, since students are familiar with the numbers for this specific example, they should be able to write the ratio in the `3` different forms. Explain to students that this type of ratio is a "part to whole" ratio because we're comparing a part of the total to the total.

After you've gone over the `3` forms of the ratio, ask if anyone can explain verbally what these ratios mean. Hopefully, students will explain that for every `5` moons, there are `12` total shapes. Explain to students that we will write ratios based on images (like these first examples), tables, and tape diagrams.

Write a ratio from a table

Some students will find writing ratios even easier from a table than from images, because they don't have to count! Allow students to look at the table to find the number of students who play soccer and the number of students who play football. Once they find the correct values, they can write their ratio in the `3` forms.

Extend the example

Now ask students, "If I wanted to know the ratio of students who play football to students who play soccer, would anything change?" The idea behind this is to get students to recognize that the order of the ratio matters. Be sure to continuously reinforce this concept for students.

Additional questions to ask

What is the ratio of students who play baseball to the total number of students who play fall sports?
For students who get stuck with this one, remind them that they will need to add all of the numbers to get the total number of students who play a sport.

What is the ratio of students who play baseball to students who play football or soccer?
The key idea here is for students to recognize that they need to add to find the second amount, but they are not adding all the numbers, just the number of students who play football and the number of students who play soccer.

Write a ratio from a tape diagram

This last example shows a tape diagram. We're asking students to write the ratio of cats to dogs. Remind students that the boxes in tape diagrams are all the same size, so they represent the same amount. We can count the number of boxes for cats, `7`, and the number of boxes for dogs, `10`. Once we've counted the necessary values, students should be really familiar with writing the ratios all `3` ways at this point.

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Intro to Ratios Lesson Plan - 6th Grade Math

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Discover an engaging intro to ratios lesson plan 6th grade math that helps students master mathematical concepts. Download now and make math easie.