Writing Ratios the Right Way!

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SWBAT relate one quantity to another quantity and be able to describe how ratios are used in everyday life.

Big Idea

Students will write ratios using a variety of formats.


20 minutes

Students will be using the real world ratios they found for homework the other night.  If students did not complete this homework, have some index cards ready showing ratios in real life.  You could use measuring ( For every 1 cup of sugar, you need 3 cups of flour).  You could use  1 in = 2.5 cm.  

In this activity, the students will be working in groups of 3.  To get the students in groups of 3, take the number of students in your class and divide by 3.  Then have students count off by the number found.  For example:  if you have 27 students in class, divide 27 by 3 and get 9.  Count by 9’s.  Then tell 1’s to form a group, 2’s to form a group, 3’s and so on. Each person in the group will share with their group, their real life ratio.  Once students have verbally shared their ratio, have them choose one that they want to share with the class.  Students should come to the board to share their ratio.  Student 1 reads the example and records it on the board.  Student 2 tells which notation to use in the written ratio and Student 3 explains the meaning of the ratio and any inferences that can be made. 

This activity will help to review the prior day’s learning as well as set them up for today’s lesson.

Writing Ratios

30 minutes

During this part of the lesson, I’m going to have the students writing ratios while looking at several different representations.  Students should be aware that ratios can be found in a multiple of representations and they should be able to write ratios in part:whole, part:part, whole:part relationships. (SMP 4:  Students will model real-life situations with mathematics) Additionally, students will be asked to notate the ratios as x:y, x/y, x to y which supports SMP 2 because they are figuring out what the numbers mean and how to represent them.  Be sure to watch how students are writing the ratios.  They may not realize that order matters when writing ratios.  To point this out, you could say, if I write a ratio of boys to girls as 4 to 5 is this the same ratio as 5 to 4?  As a rule of thumb, I have students label each of their ratios.  It's a good habit to start and will help when solve ratio problems. 

Each slide of the power point will have students writing ratios using a variety of problems. 

Independent Work

20 minutes

The students will be working alone on this worksheet.  I want them to use their notes and apply it to these questions as they work on their own.(SMP 1)  There are two problems that students may have difficulty with.  These problems are asking students to make equivalent ratios when they alter the original amount.  I would encourage students to make a table or a visual to help them figure this out (This supportsSMP 5 because students will need to decide what tool to use to help them figure out the problem.) Once the students have finished, I’m going to have them partner up to share responses.  During this time, students should use mathematical reasoning for their answers and be able to justify their answer if they have different answers (SMP 3).  Have students do a HUSUPU to get into groups of two.  Once there, have them compare the answers from their independent work.


Resource:  Massachusetts DOE (2012)


15 minutes

Write your own ratio problem.  Your problem needs to include pictures, a question to solve and the way in which you want the solution written.  Once the students write their own problem, have them switch papers with a partner and allow them to solve each other’s question.

I'm looking for students to do something like this:

They will draw a picture of 5 red circles and 3 blue circles.  There question might be, "what is the ratio of red circles to the total amount of circles?"  Write this ratio as a fraction.


They will draw a picture of 2 bubble gum pieces and 6 jaw breakers.  There question might be, "what is the ratio of jaw breakers to bubble gum pieces?  Write this ratio with a colon.  "is there another way to represent this ratio?"