This lesson is a response to poor results on several equation problems on the unit assessment. While students performed well on the exit tickets from the initial lesson, they did not retain much understanding by the time of the assessment. The problems in this lesson take a similar form to those that were asked of the students on the unit assessment. About 4 days after this lesson, students will take a re-teach assessment specifically on this standard.
This lesson is designed to help students do two things:
1) Find the m, the constant of proportionality, for the equation in form y=mx.
2) Create a table (input/output) to see the pattern that results. They will use this pattern to create the equation (MP8).
Initially, students are given tables, later they will be asked to construct them for themselves.
The middle column of the table is always for the constant of proportionality. Through discussion students will be led to see that the value x is always multiplied by m in order to find y.
i) 8/3 acres per hour or 2 2/3 acres per hour
ii) Number of hours|Constant of proportionality|Acres Harvested
0 | 8/3 | 0
1 | 8/3 | 8/3
2 | 8/3 | 16/3
3 | 8/3 | 24/3
4 | 8/3 | 32/3
x | 8/3 | 40/3
iii) y = 8/3x or any equivalent
iv) The total acres harvested equals the product of 8/3 acres per hour times the number of hours.
I will ask students to do each problem one part at a time, so that I can monitor the progress of the group. Students should have little difficulty finding the unit rate for part i.
Before part iii, I will ask students to discuss the pattern seen in the problem. It also will be important for me to make sure students are paying close attention to the assigned values of the variables. This is something often overlooked by students and variables can sometimes be interchanged. Again, we should conclude that x, the number of shirts, is multiplied by m, the constant of proportionality, in order to find y, the total price. I will then ask students to write the equation.
I will follow the same procedure for problem GP2. The only difference here is that students are required to build their own table. It really does not matter whether x or y are in the far left or far right column, but the constant of proportionality should always be in the middle column. This makes it easier to see the relationship between m, x, and y.
Students will now work independently on seven problems. A table is provided for the first two problems. These are very similar to the two problems in the guided problem solving section. The last five problems require students to build their own tables. I will insist on students building tables, after all this is part of the lesson objective! Some students will say "this is too much" or "I don't need to do it". We talk about a "growth mindset" in my school so this is the perfect opportunity to remind them that we all can use the practice and how helpful a table is to our success with the objective.
The last problem only provides three variables. This will be a good point to discuss what all of the problems have in common - multiplication equations where the constant of proportionality is being multiplied by a number of items.
Before we begin the exit ticket, we will discuss what was common about the equations that we created today. The answers should focus on the fact that all equations are multiplication equations where the constant of proportionality is multiplied by the number of some value to find a total.
I have chosen to give both multiple choice and open response questions on the exit ticket. In fact each problem mirrors a problem from the unit assessment and the type of response required. I will remind students to make sure they are still drawing tables, even on the multiple choice. students often get lazy or sometimes overconfident with multiple choice problems.
Students will need to score 4 out 5 on this exit ticket to show success.