Resources  Testimonials
Plans
Resources  Testimonials
Plans  Lesson plan

# Ratio Table Strategies Lesson Plan

## Overview

In this lesson students will learn different strategies for finding missing values in a ratio table. We’ll start by reviewing equivalent ratios before looking at tables and discussing different methods. We’ll finish up with some ByteLearn independent practice for students to use those new strategies!

Ratios And Rates
6.RP.A.3

## Objective

Students will be able to find missing values in ratio tables.

## Materials

• Teacher slideshow
• Student notesheet
• Online Practice

## How to Teach Ratio Table Strategies

### Warm-up

Start students off by writing a ratio based on these images of flowers and stars. The idea behind the warm up is to have students count that there are 6 flower and 9 stars, which would lead to a ratio of 6:9. However, once simplified the ratio becomes 2:3.  ### Equivalent ratios

The images are purposely placed so we can discuss equivalent ratios. On the next slide circle the first group of 2 flowers and 3 stars and write the simplified ratio of 2/3. Then erase that circle so you can circle a group of 4 flowers and 6 stars and write the ratio 4/6. Lastly, erase that circle and circle all the flowers and stars and write the ratio of 6/9. The slide will now display the 3 ratios.

Ask students if these ratios are equivalent and why. Students might explain things in different ways, such as:

• Each ratio simplifies to 2/3.
• Every time you circled more flowers and stars, you added 2 more flowers and 3 more stars, so it stayed equivalent.
• If we divide all the images into 3 equal groups, they would each have 2 flowers and 3 stars.

### Student notesheet

Give each student a copy of the student notesheet. These contain the same examples as the slideshow, but it will be helpful for students to be able to draw arrows and fill in missing values as you go through the examples as a class.

### Strategy 1: Column multipliers

Show students the first example and tell them we’re looking for the column multiplier. Ask, “what can we do with 3 to get to 9?”. Be careful for if any students respond that we can add 6. Tell them that the rule for going from left to right needs to be the same for all rows. If we do 20 + 3, we get 23. But 3:9 and 20:3 are not equivalent ratios. Ultimately, we want students to recognize that we are multiplying by 3.

### Using the “rule”

Explain to students that we can use the “rule” of multiplying by 3 from left to right to find the missing values in the second row and the fourth row. Students should multiply 20 by 3 and 50 by 3 and fill in those missing values.

### “Rule” in reverse

We still have two other missing values, but they’re on the left side of the table. Go to the next slide and ask students, “if we multiplied by 3 to go from 3 to 9, what do we need to do to go from 9 to 3?” The key is for students to recognize that now we need to use the inverse operation and divide by 3. Let students divide 66 and 240 by 3 to fill in the last two missing values.

### Strategy 2: Row multipliers

The next strategy deals with rows but works a little differently than the column “rule”. Show student the next example and ask them how we can go from 12 to 3. Students should recognize that we can divide by 4. Explain that what we do to one part of the ratio, we have to also do to the other part of the ratio, so we can divide 16 by 4 to get 4. Now we have two completed ratios that we can work from!

You might ask the students if we can do 12-9 to get to 3. Some students might point out that 16-9=7. But 12:16 is not the same ratio as 3:7.

For the next missing value, let’s start from 4 and see how we can get to 100. Students can see what we’ll multiply 4 by 25 to get to 100. So we need to multiply 3 by 25 to get 75.

At this point, students have three completed ratios. Make a point to tell students that they can use any of the ratios to find new equivalent ratios, but that some make it easier than others. You might want to ask students what number on the right side of the completed ratios makes it easiest to get to 200. Hopefully students will answer that from 100 to 200, all you have to do is multiply by 2!

For the last missing value we have 6 in the left column. Allow students to pick whichever ratio they want to use to find the last missing value, 8!

### Strategy 3: Adding rows

For the last strategy we have a new table. Consider going back to the warm up and reminding students that as we added equivalent ratios, we got another equivalent ratio! Like how 2 flowers and 3 stars, combined with 4 flowers and 6 stars, gave us 6 flowers and 9 stars. This can show students how all the ratios are equivalent.

Then ask if they think they can use a similar strategy here. If students need more support getting started, highlight the second and third row and ask how we can use those ratios to find the missing value in the fourth row. We want students to recognize that since 10 + 50 = 60, we can add 6 and 30 to fill in the missing value of 36.

Once students see how this is done, they tend to take off! Allow students to work together to find the rest of the missing values by adding different rows.

## Ratio Table Strategies Practice

Now it’s time for some independent practice! You can assign a ByteLearn online practice to your class using the link below. Students will get immediate feedback and step-by-step help if they need it. Set a due date and allow students to finish the assignment for homework. Once complete, you’ll see detailed reports of students who may need additional support, students who are ready for a challenge, and other interesting insights!  Ratio Table Strategies Practice
Problem 1 of 8
<p>The table shows three pairs of equivalent ratios.</p><selectivedisplay data-props='{"show_in_create":true, "show_in_problem_qa": true}'><TableUIv2 data-props='{ "headers": null, "borders": { "rows": [ 4 ], "cols": [ 3 ] }, "rows": [ [ { "value": 7 }, { "value": 3 } ], [ { "value": 42 }, { "value": "?" } ], [ { "value": "?" }, { "value": 27 } ] ]}'></TableUIv2 ></selectivedisplay><p> Find the missing values in the table.</p>

View this practice  