Sign in to view assessments and invite other educators
Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.
Think of different ways you could sort these figures. What categories could you use? How many groups would you have?
If students struggle to create their own categories, prompt them to consider a specific attribute of the figures, such as the size, color, or shape.
Invite students to share their categories and record their responses for all to see. After students explain how they sorted the figures, solicit additional ways of seeing the collection until several different ways of seeing the figures have been shared.
Emphasize that the important thing is to describe the way they sorted the figures clearly enough that everyone agrees that it is a reasonable way to sort them. Tell students we will be looking at different ways of seeing the same set of objects in the next activity.
This activity introduces students to ratio language and notation through examples based on a collection of everyday objects. Students learn that a ratio is an association between quantities, and that this association can be expressed in multiple ways.
After discussing examples of ratio language and notation for one way of categorizing the objects in the collection, students write ratios to describe the quantities for another way of categorizing objects in the collection.
As students work, circulate and monitor for those who:
Have a collection of objects ready to display for the Launch. Make sure that there are different ways in which the collection can be sorted.
For example, the dinosaurs in this picture can be categorized by color (green, orange, and purple), by the number of legs they stand on (standing on 4 legs or on 2 legs), or by the features along their backs (crest, white stripe, or nothing).
Familiar classroom objects such as binder clips or pattern blocks can also be used to form collections. This picture shows a collection of binder clips that could be categorized by size (small, medium, and large) or by color (black, green, and blue).
Display a collection of objects for all to see. Give students 2 minutes of quiet time to think of as many different categories for sorting the collection as they can.
Ask students to share their categories. Record the categories for all to see. Sort the collection into one of the student-suggested categories and count the number of items in each. Record the number of objects in each category and display for all to see. For example:
| category A: green | category B: orange | category C: purple |
|---|---|---|
| 3 | 2 | 4 |
Explain that we can talk about the quantities in the different categories using something called ratios. Tell students: “A ratio is an association between two or more quantities.” We use a colon, or the word “to,” between two values that we are associating.
Share the following examples (adapt them to suit your collection) and display them for all to see. Keep the examples visible for the duration of the lesson.
Explain that we can also associate two quantities using the phrase “for every of these, there are of those.” Add the following examples to the display.
Finally, find two categories whose items can be rearranged into smaller groups, for example, 4 purple dinosaurs to 2 orange dinosaurs. Point out that in some cases we can associate the same categories using different numbers. Share the following example and add it to the display.
For every 2 purple dinosaurs, there is 1 orange dinosaur.
Have students write two or three sentences to describe ratios between the categories they suggested.
Invite several students to share their categories and sentences. Display them for all to see, attending to correct ratio language. Be sure to include students who express the same categories in reverse order, in different words, or with a different set of numbers (which students will later call an equivalent ratio). Leave several sentences displayed for students to see and use as a reference while working on the next task.
This lesson is all about how to use ratio language and notation to describe an association between two or more quantities. Wrap up the lesson by drawing a diagram for all to see of, for example, 6 squares and 3 circles.
Say, “One way to write this ratio is, there are 6 squares for every 3 circles. What are some other ways to write this ratio?” Some correct options might be:
Display, somewhere in the classroom, this diagram and the associated sentences that the class comes up with so students can refer back to the correct ratio and rate language during subsequent lessons.
Consider posing some more general questions, such as:
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:
Notice that the shapes can be arranged in equal groups, which allow us to describe the shapes using other numbers.
Think of a way to sort your teacher’s collection into two or three categories. Count the items in each category, and record the information in the table.
| category name | |||
|---|---|---|---|
| category amount |
Pause here so your teacher can review your work.
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.
Students may write ratios with no descriptive words. Although is a good start, part of writing a ratio is stating what those numbers mean. Draw students’ attention to the sentence stems in the Task Statement and encourage them to use those words.