Today's lesson builds off the work students did in the previous class, Solving Systems Using Elimination Day 1 of 2. Students will return to the shopping scenarios presented in Shopping for Cats and Dogs and translate those problems into algebraic equations.
I start class by reading the introduction to Can You Get to the Point Too together and walk students through the first scenario together. I try to elicit from students how to translate the shopping receipt from Question 1 into algebra and then we reflect on the work we did in the previous class. Students should remember the argument we used previously was that if we bought the same amount of Tidbits on both shopping trips, the difference in our total costs should be a result of the difference in the amount of Flakes we bought.
Once we have the two equations written on the board and our rationale from the previous class, I ask students how we could get to the same answer using algebra.
The equations from the first problem might look like this:
3T + 6F = 54
3T + 4F = 43
I try to elicit from students that when we think about buying the same amount of the T variable, we are essentially crossing out the 3Ts from the equations. How can we do this using algebra? Also, when we find the difference in the cost of the Flakes, what are we doing with the Fs and the difference in total price? From here, I show students how we can use elimination to solve this problem.
Next, students get to work in small groups on the rest of the problems. Question #4 can be tricky for students because it involves a negative number in front of a variable for the first time. Let students wrestle with this problem before intervening. See if they can build from their argument in the previous class to make the algebra work.
For the discussion section of class today, I have different groups share out their methods for the five different problems from Shopping for Cats and Dogs. Then I have groups that went on share out their answers to the graphing section in Part 2 of the task. Finally, we look at different strategies for dealing with more complicated systems like the ones that show up in the unit problem (Pampering, Feeding, Space, and Cost constraints).
To close today's class, I like to have students write out the steps they would use to solve a system of equations using elimination. Many of my students will need to refer to these steps as we move forward.
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