In this lesson, students will learn how to identify proportionality from tables and verbal descriptions through students’ discussion and problem solving. Students will use tables to help them process identifying proportionality. Then, students will practice with other tables and verbal descriptions with a partner or table group. You can expect this lesson with additional practice to take one `45`-minute class period.
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To begin the lesson, provide students with an opportunity to fill in the table of values with context on their own. If students are stuck, it may help to let them know that the table represents a proportional relationship, so they can try to find a pattern in the table.
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Once students have an opportunity to answer the questions independently, they should check their work and discuss their process with a partner or table group. Once students have an opportunity to share their thoughts, ask if anyone worked with someone who solved the problem a different way but got the same answers.
The goal of having students discuss their methods is for students to understand that there are multiple ways they could look at the information given to help solve the proportion. Here are some ways students may look at the information:
It is important that students understand there is more than one way to solve a problem like this. Once the table is completely filled in, ask students if the relationship is proportional and why. If there are any methods that students do not use but are mentioned above, it may be helpful to mention them directly to students. For some students, seeing a different method can help them understand the information, so it is generally best for students to know what options they have to help identify proportionality from tables and verbal descriptions.
With the next example, it may be helpful to reiterate that a proportional relationship means there is a constant ratio. At this point in time, you do not need to focus on students identifying the constant of proportionality. The goal is for students to identify proportionality from tables and verbal descriptions using any mathematically correct method with the information they’re given.
Here are the different ways in which students might prove that this is a proportional relationship:
With this example, you want to emphasize that students need to find the ratio for every row in the table.
Students may set up a ratio for each row and simplify the ratio. Some might divide one column by the other to see if they get the same number. However, some might see right away that while `12\times 2=24, 20\times 2` is not `45`.
By this example, students should be able to identify proportionality from the verbal description, even though this is presented more like a table. Allow students time to work and discuss if the image represents a proportional relationship.
Some students may think the relationship is proportional because the total cost goes up by the same amount every time; however, with the pattern, `0` cucumbers would cost `$1`. Other students may find the ratio of the number of cucumbers to cost or vice versa and recognize that each row has a different unit rate, so it does not represent a proportional relationship.
Allow students to try this example on their own, and then have students check their work with a partner.
Some students may look at the given values and say it is not proportional without recognizing that the units for the amount of fabric was different. There should be some students who recognize that the units were changed, and will convert one of the given fabric lengths to the other unit, such as inches to yards or yards to inches.
After you’ve completed the examples with the whole class, it’s time for some independent practice! ByteLearn gives you access to tons of practice problems for identifying proportionality from tables and verbal descriptions. Check out the online practice and assign to your students for classwork and/or homework!
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