Intro to Ratios Lesson Plan

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.