Distribute to Solve
Lesson 1 of 20
Objective: SWBAT distribute integers and other rational numbers to solve equations.
Students enter silently according to the Daily Entrance Routine. Do Nows are already on their desks and students must get to work right away. A timer is set for 6 minutes and started once all students have been seated. There is a message written on the SmartBoard, displayed above the timer:
Click in your answers!
Once you have finished, bring me your paper before time runs out for a chance to receive ACHIEVEMENT POINTS!
Students who bring me their paper before time runs out and get all the answers correct are allowed the choice of two achievement points, a “sweet treat” (misc. candy options), or a positive point on their paycheck. Students who bring me their paper before time runs out, but have incorrect answers will be sent back to their seat to fix any incorrect answers. These students automatically receive a positive point on their paycheck, though I do not let them know this so that they have a reason to fix their mistakes and come back to see me. As we get closer to our Thanksgiving Break it does become difficult to continue motivating students to complete work quickly and to the highest level possible. Offering choices to students who are completing the work correctly motivates others in a positive way by using student role models, rather than nagging from the teacher, a strategy which has had negative effects for me in the past.
Since we will be solving equations which include parentheses and require simplifying before solving, it is important to begin the lesson with a review of simplifying expressions with parentheses. I also included expressions that would require combining like terms after distributing in anticipation of tomorrow’s lesson, solving equations by distributing and combining like terms.
Common misconceptions and feedback given to students are listed below:
After the 5 minutes expire, no other students may line up to have their answers checked, though I will take time to check the papers for any student in line. I call the last person’s name as an indicator of where I will stop checking. During this time, students are completing any incomplete problem, or getting ready for Class Notes by putting away their Do Now.
Class Notes are distributed and students are asked to fill out their headings and copy the aim. One student reads the aim and I explain that students will be putting together various skills learned in the last weeks to solve equations today. I then ask a brave student to read the statement at the top of their “Notes” and fill in the blanks (“By now you have learned how to use thedistributive property to simplify expressions”)
Which property would we use to do something with this expression?
Why are we distributing? (to simplify the expression)
Ask for another brave student to give a first step or all steps to solve the two step equation. For a multi-stepped problem like this one I try to select a student that might need help. I am more interested in a team response rather than one student telling me how to solve the entire equation.
After we’re finished solving the two step equation, I call on two student volunteers. One student will solve the equation if they feel confident that their solution is grounded in what we have reviewed, and the other students will write down the steps taken to solve. Again, strategic pairing of the students is important here as this may present an opportunity for some students who don’t often stand out, to shine. A note taker who would not be able to come up with the steps on his/her own might be able to recognize the steps being taken. The board (or chart paper) is previously set up to allow both students working at the board at once. All other students copy what is on the board.
Before closing out this section, I ask students to consider another way to solve. Is it possible to avoid distribution? This is a good opportunity to try out MP8 as students push themselves to identify shorter paths to a solution by dividing the entire equation by the outside factor. In order to see this solution, students must be able to understand an important detail: the numbers inside the parentheses create a quantity being multiplied by the outside factor. Dividing by the outside factor on both sides is the same as dividing by 2 on both sides to solve 2x = 8
Paired Partner Practice
Class work is distributed along with Senteo Clickers. Students will be advised that they are receiving two grades today: one for completion of the class work (effort) and one for correct or incorrect answers academic).
What I’m doing: Checking answers and registering them into my roster; helping students solve equations by reminding them of the steps they wrote down earlier in their notes.
Common misconceptions I encounter are similar to the ones covered during the do now. The most difficult thing to get done is get them started. Many students freeze up and claim they don’t know what to do. This is why the notes are so helpful. Referring students to the notes empowers them to use them at other times on their own.
What students are doing: Students must enter their answers into their clickers for the academic grade. They are welcome to work in pairs or independently and I try to allow pairs of students to spread out around the room so that there aren’t any clusters or groups off task. Students must come show me their answers to questions #7 – 10 so that I can check them by hand.
Students are asked to return to their seats once there are 10 – 15 minutes left in class. They are given the rest of this time to work silently and independently to finish their class work, click their answers in, and have their last four questions checked by me. The data holds students accountable to the practice and provides me with important information about which students to pull during remediation periods.
Students are given homework before leaving and advised that the grade on this assignment could be used to replace one of their grades in class today.