As usual, I try to launch this lesson with tasks that allow my students to access some prior knowledge and prepare them for the work they will engage in today. These Launch problems motivate an important problem solving strategy when learning to solve equations, working backwards. (I often teach my students to think about equation solving as reversing the order of operations).
For the Launch today, I encourage students to work with partners and discuss the best way of arriving at the answer in each of the three cases. I walk around listening to students' conversation, asking that they not write anything. I want them to try to figure out how to answer each question mentally, before they begin taking steps on paper. I find that this helps some students to realize that working backwards using opposite, or inverse, operations, is a possible strategy.
Once students are done, I will call on volunteers to share how they solved each of the problems. Then, before moving on to the next section of the lesson, I write the following number puzzle on the board:
I'm thinking of a number
I multiply the number by 4.
I add 6 to that answer
I divide by 2.
I subtract 5.
The number I end up with is 21
Tell me the number I started with.
This activity usually gets students working backwards. Without fully realizing it, most use inverse operations to quickly find that my number was 12. Once we agree on the answer, I will ask students to try this process once with any partner. In the context of solving a number puzzle, I find that they are always eager to give it a try.
Before handing out the Two step equations Activity Sheet, I project The X Story.docx on the board and ask the class to follow along as a student volunteer reads this task. After the work completed during today's Launch, this task should be quite simple. The reason I show it is so students have an idea of what they are going to do in the following activity.
I then ask my student volunteer to come up to the board and complete the table. After completing the table, we should find that x was equal to 2. At this point, I want to make sure that all students see that inverse operations was used at each step to get to x = 2. I demonstrate that when entering information in the left column (writing what happened to x), we use order of operations, but when "unraveling" or solving the equation (the right column), we proceed by reversing the order of operations.
Now, I introduce the main activity for this section of the lesson by distributing Activity Sheet Two step equations. The reversal of the order of operations must be considered in answering equations 3 and 5, especially, because the value being added or subtracted appears first in the equation from left to right. Question 6 is left blank intentionally. I will ask students to write their own equation and "story" about x for Question 6.
I will let the students work together on this task, intervening with questioning and scaffolding. A common intervention in this lesson is "The Cover Up Technique". See the Grappling with Complexity reflection on this teaching strategy for more details about how I employ this during the lesson.
Closing this lesson involves having students show their work for all 6 equations from the Activity Sheet on the board. As students finish working at their desks, I will call on volunteers. After the work is done on the board, I open discussion for questions or comments on the handout making sure students know what to do for the homework assignment.
Tonight's homework is Homework Two Step Equations 1.
Something that might be worth pointing out about tonight's homework:
Although not seen in the lesson, a couple of HW problems contain equations where the coefficient of x is negative; ex) -9x + 1 = -80
Students will make the mistake of adding 9 when they see -9x. This is a major mistake and I always watch for this. It may be a good idea to let students know before the lesson ends that -9x means x is being multiplied by -9, and therefore, to undo this, we must divide by -9: