Bell Ringer: Use the student activity task from day one (Proportional Candy Gate Day 1) for the bell ringer as well as the graphs from day 2 (Proportional Candy Gate Day 2). As students walk in the room instruct them to take out their student activity sheet and coordinate grids from day one of the lesson. Students will use their activity sheet to find the constant change of the x and y axis from the tables. Students will need to figure out on their own how to determine the equation the tables represent. Do not instruct students beforehand on how to determine the equation, this will come during the whole group discussion time. The question at the start of the bell ringer for the students will be “Does the data in the tables have a proportional relationship, and how can we use the equation to prove or disprove?” Allow students to engage in mathematical practice 1 and 2. Students will appreciate investigating this on their own and not be given the correct response. The bell ringer also lends itself to MP 4, 5, and 6.
Students may struggle with finding the constant change between values. Many students will try to find the relationship between the x values to the y value. One other struggle students may have is once they find the constant change between the y values they may not know what to do with the constant change to determine the equation.
Before you begin the whole group discussion, have students discuss their thinking with a partner. This will lend itself to MP3. Instruct students to compare their equations with their graphs from day 2. Students should discuss 1) how they determined the constant changes 2) how they know the changes are constant 3) if the changes are not constant how does that affect the line that was graphed 4) what they did with the constant change to determine the equation 5) is there a correlation between the graphs and the equations or constant changes and if so what is it. Students should discuss their thinking with a partner for 10 minutes.
Once students have been afforded 10 minutes to discuss their thinking with a partner, go over their discussions as a whole group discussion. Points of interest to hit with students are, what is a constant change, what is the relationship between the x values and y values when determining the equation, what happens if there is not constant change, how do we use the constant change to determine the equation, will there be a scenario where we will need to add or subtract in addition to multiplying the constant change by the x value, how do we determine if we need to do more than just multiply the constant change by the x value, how do we know the equation is accurate, how do we know the equation represents a proportional relationship. Students should be able to recognize patterns between the x and y values which is a practice of MP 8. It is important that students lead the discussion. You will affirm correct thinking, correct mistakes, and guide students toward the correct process in determining the equation that represents proportional relationships between two quantities.
Have students pair up with a partner. Students will complete the Student Activity. This may take two days. If the students do not complete the lab sheet today, please open the next day’s lesson with student work time and bypass the bell ringer. This task will lend itself to MP 1,2,3,4,5,6,and 8.