Clicker Quizzes: Multiplicative Inverse in One Step Equations
Lesson 12 of 23
Objective: To solve one step equations using multiplication and the multiplicative inverse by completing clicker quizzes.
Students enter silently according to the Daily Entrance Routine. There are Do Now assignments (Clicker Quiz) at their desks. Based on data from past assignments, most students seem to be struggling with the representation of word problems through the use of equations. Thus, question 1 on the Do Now will assess students’ ability to identify (DOK1) the correct equation from a list of choices. The translation of this equation is complex because it includes two equivalent expressions which students have to independently identify. If “tracy’s score is 5 point lower than Aleyah’s” and “Tracy scored a 92 on her math test” this means Tracy’s score of a 92 is equal to “5 points lower” than Aleyah’s score.
a – 95 = 92
Since the skill for this problem is rigorous, I need to assess it at a lower DOK level to identify any conceptual misunderstandings and/or develop the understanding of equivalent statements in a word problem. This is why I chose a multiple choice question rather than open response. Additionally, each multiple choice will give me valuable information about the misunderstanding a student may have. Students who choose A or B incorrectly are most likely to be the most confused about this question because there aren't any words in the problem indicating anything needs to be added. Students incorrectly choosing D are likely misunderstanding that Aleyah's score is not lower than Tracy's.
The remaining questions assess student retention of recently learned skills. The last question will assess the same skill as #1, but it is a less rigorous question which allows me to assess at a higher DOK level (construct an equation). This last question as well as the first is also engaging students through MP1.
Everyone will be entering their answers into clickers. These answers will be checked once they are done and the results will be used to put students into homogenous groups.
Students are asked to put their Do Now away and get ready for class notes. The words in red on the notes are left off the page and are written on the board for students to copy into their notes. This continues to be an effort to develop the habit of note-taking. After copying the notes students are asked to complete the three examples labeled a – c. After 3 minutes I ask for attention and ask students “what did you notice about all of the examples?” “All answers were 1” is not enough. I stretch their thinking by following up with “what do you have to multiply by to get 1” and “what about the signs? What do you notice about the signs + and – ?“ By pushing students to think about these ideas I aim to proactively address some common misconceptions when solving equations in this form. For example, if the coefficient is a negative fraction, students often wonder if they should multiply by a positive reciprocal. Negative x as a variable can then be discussed when solving these equations. If we multiply by positive 13/7 in example 3 would results in negative x, not positive x. If time permits, students may ask questions about solving and checking answers.
Worksheets are distributed and students are split into three groups. Groups will be determined using the results to the do now "clicker quiz". Students who are still having a hard time with one step equations will sit at the front to work with me on half of the questions in their worksheet. Students who scored well on the task (above 75% correct) and are trustworthy will sit in booths, and the remainder of students will be allowed to relocate anywhere in the room, including their own seats toward the front of the room.
When reviewing one step equations I will ask students to remind me about the goal when solving equations and some of the basic rules ( i.e. the goal is to isolate the variable, meaning leave the x alone. We do this using opposite operations until the variable has a +1 as a coefficient. When solving equations it is important to make sure that the equation is always balanced, meaning the same opposite operations are being done on both sides of the equation).
Question nine is also another question that is reviewed with the group working with me. I ask students to identify a variable first. What is the unknown? (the width of the flag) Then students are to identify the phrase in the word problem that can be used to represent one of the expressions in the word problem. This question is similar to #1 in the Do Now because students must recognize the equivalent expressions as the length of the flag, 5 ft, and the algebraic monomial that represents the length as a function of the width, (19/10)w . Thus,
(19/10)w = 5
At the end of 20 minutes the clicker assessment is stopped and students are aware of the questions they answered correctly and incorrectly. We review work and answers for the 3 lowest scored questions.
For the closing, students are given a 5 question clicker quiz. At the beginning of class students were made aware of a grade choice for the day. I would need one grade by the end of class: the two opportunities were the Do Now and the Exit Tickets. The aim is for students to be motivated to ask questions and engage in the learning even if their score on the first assignment was not good. They can work to improve their score by asking and answering questions throughout class and performing their best work on the exit ticket. I reinforce check steps throughout the task as their defense against losing points on graded assignments. Students who score above 90% on the first task are engaged to score above 90% again because the incentive is a homework pass. At the end of 10 minutes homework is distributed and students are dismissed.