The first question will require students to use a proportion or equivalent ratios to find the amount of pool water being leaked per hour. Since the information given is in the form of fractions, I expect some students to struggle putting together the initial ratio of 1/3 gallon : 1/6 hour. For these students I will be prepared with the following feedback:
Next, I can help students by asking them to set up a proportion. If they do not know how to do this, I will ask them to refer back to their notes to figure this out along with the following guiding questions:
The second question asks students to identify the constant of proportionality from a table. This is a great opportunity to shout kids out if they are referring back to their notes from the previous two lessons. The notes from 3 lessons back detail the way to calculate k, the constant of proportionality. I try to wait until a student identifies these notes on their own, shout them out for doing so independently, and ask them to share with the class the date at the top right hand corner of these notes. By doing this I am placing importance on the independent action of referring back to notes, a skill that I try to have students use to get ready for high school.
The last problem asks students to identify the graph which shows a proportional relationship. The answer is letter D, “a straight line that goes through the origin”. When reviewing this answer, I have all students write this phrase next to this problem. We reviewed this concept through homework and classwork in the past three days. Writing and re-writing this phrase will help students remember and study this concept. It is equally important to push students to explain why the graph is a straight line and why it must begin at the origin. One question I use to push this discussion is:
A proportional relationship can be described using the equation y = kx, where k is the constant of proportionality. Explain how this equation justifies the reason why the graph must be a straight line that goes through the origin.
Answer: In the equation y = kx, no matter what k, the constant of proportionality is, if x = 0, y will also equal 0. Which means the graph of the line should always go through the origin, (0,0).
I distribute the guided practice paper to students and begin by explaining that there are two strategies we can use when being asked to solve word problems involving ratios:
I model the use of both of these methods with one problem. The tables completed with red fonts included in the worksheet are meant to be completed and drawn by students with assistance from me and any student identified from the results to the Quiz as available helpers. These students will be asked to walk around the room to help others set up their bar models.
In the second example students we will be filling in values into the table together, and then I will ask students to work on the graph, first by identifying the proper scale to be used as well as the proper locations for the number of cats vs. dogs. This will require students recall the x-axis as the horizontal axis and y-axis as the vertical axis. Once a student or group of students have correctly identified these axes, pairs will be given 3 – 4 minutes to graph the values we determined together in the table and draw a line through the points.
We will come back together as a larger group to recall from our notes (link) the process for writing an equation in the form y = kx.
After reviewing writing an equation in the form y = kx and answering any student questions, all students will be randomly placed in groups of 4 using a random group generator on the SMARTBoard. Each group will receive white boards, dry erase markers, and erasers for a game of Showdown. Here are the rules:
As students work through the showdown game they are using MP3 to discuss and critique each others’ arguments about the solutions to each problem. Fifteen minutes ought to be given to these 4 problems and the game while the remaining 5 minutes can go to answering the 2 multiple choice problems on the back of the Class Work sheet.
As we close out the Task section of class I inform students that they must complete all class work for homework which will be turned in for a grade the following day. After making this announcement and giving students the opportunity to write it down into their agendas, I will distribute exit tickets as a final check for understanding. The results to this Exit Ticket will inform my instruction moving forward on students’ abilities to identify proportional relationships in a table, calculate the constant of proportionality given x and y, and writing an equation to describe a proportional relationship.