In this lesson, students will learn how to graph a proportional relationship. Students will review proportional relationships and how to create graphs. Then, students will work with a partner to create a graph for one proportional scenario. Then, students will do a gallery walk with the graphs that are created to determine the characteristics of a graph of a proportional relationship. You can expect this lesson with additional practice to take two `45`-minute class periods, or one `90`-minute class period.
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Before starting the lesson, it is beneficial to review a problem that uses proportional relationships.
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With this problem, encourage students to make a table to help them organize the values and help them process the information. If needed, you could also allow students to work with a partner or table group to determine how to answer the given questions. When reviewing the answers, it is important for students to recognize the ratio was always the same.
For this lesson, students will need to review how to create graphs and how they relate to independent and dependent variables. This review will be essential for helping students with the activity later, so make sure students understand the importance of understanding the information. It may be beneficial to give students guided notes for graphing so they have something to reference later.
It is essential that students can relate independent and dependent variables to the `x`- and `y`-axis respectively. It may be helpful to see if students can come up with examples for independent and dependent variables, like buying shirts and the total cost if all of the shirts were the same price. Students can practice writing a sentence that makes sense to them, such as, total costs depends on the number of shirts.
Determining the axes scales can be difficult for students (and for many adults!!). The purpose of this slide is to give students a reference to help them determine the scales of axes.
The guided notes include two examples: “`$38` and `8` spaces” to determine the dollars per space; “`6` roses and `25` spaces” to determine the number of spaces per rose. Again, it may be helpful to have students recognize the importance of scaling on a graph and how it will help them when they make their graphs later.
For this activity, students will need to work with a partner. If there is an odd number of students, there can be a group of `3`. Let students know that the graphs they complete together will be used during the next class period (or later in the class if you have longer periods). The proportional relationship scenarios includes six different scenarios for student groups to work on, so some pairs will be working on the same scenario. Give a scenario and a piece of graph paper to every pair of students.
Students should write their names at the top of the paper. They should also rewrite or attach the given information on the paper.
With their partner, students will:
Once students have completed that, they can graph the proportional relationship with the appropriate labels. You can let students know that their graphs will be used for discussion, so they should try and make them as neat as possible.
For the second day (or second half of class), organize students’ graph papers so that you can create a gallery walk with stations for different scenarios. Before students begin the gallery walk, make sure they have their own paper that they can record their thoughts for each station. Students should start on a station that has a different problem than what they already graphed with their partner.
Most stations should have at least two graphs from different groups from the previous activity. If there are stations with only one graph, encourage students to write down the similarities and differences between the given graph and the other graphs students have worked with (either from previous stations or from their previous work).
Once students have gone through all of the stations, have a class discussion for students to share what they noticed. Students will see many differences in the graphs - the scale, the titles, the `x`- and `y`-axis labels, the slantiness of the graph. At least a few, if not most students will recognize the following similarities:
Students should note these similarities of the graphs because they represent how to identify proportional relationships from a graph.
By allowing students to explore graphing proportional relationships through experience, students should be able to easily recognize proportional relationships. You can do a quick check with students using the general graphs shown on the last slide.
Although it does not have context, students should still recognize that only A represents a proportional relationship because it is a line that goes through the origin.
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 graphing proportional relationships. Check out the online practice and assign to your students for classwork and/or homework!
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