Lesson 10 of 23
Objective: SWBAT show what they know about introductory algebraic concepts and solving one step addition and subtraction equations on Quiz #7. SWBAT show what they know about one step multiplication equations by completing a “Whaddaya Know” survey.
Students enter silently. Quizzes are on their desks and they are to begin as soon as possible. They are allowed to spread out and sit at empty tables and are given the option to use cardboard dividers and noise canceling head phones. Instructions on the board notify students that they will only have 30 minutes to complete this quiz (a timer will be displayed) and that there are available optional “bonus” questions. Incorrectly answered problems will not be held against them.
Once the quizzes are graded, I will be using them to target small groups during our remediation periods through out the week. Each class has at least one "remediation" block during the week. During this time I will be pulling small groups according to their performance on this quiz. The first group will be pulled during remediation early in the week. This group will include students who answered 3 or more questions incorrectly out of the first 5 (basic vocabulary). We will review the definitions with the use of vocabulary cards or notes, and answer more questions like the items on the quiz, justifying our answers with the definitions on the cards. The second group will be pulled toward the end of the week. This group will include students who struggled with solving one-step equations. If this group of students also missed question #10, or missed part of the points, they will have an additional review of simplifying equations during this block or as an assignment for homework.
At the end of the quiz, all students will be asked to turn in their quizzes, bonus questions, and “Whaddaya Know” surveys will be distributed.
Prior Knowledge Survey
Students are instructed to complete the heading and copy the AIM off the SMARTboard on their paper. Then a student volunteer is asked to read the heading in the column on the left and another student reads the heading in the column on the right. Students must choose one column to complete, depending on which heading best describes them. If they complete the column on the left, they must show how they solve. A simple answer is not enough. Eight minutes are projected on the board and students are allowed to work in groups or independently.
After 8 minutes have passed, all students are asked to return to their seats and we review the answers and some steps for solving. I have all students copy the following note:
“When solving an equation you must isolate the variable by using opposite operations. The variable must be positive”
This note is especially important as it describes the solution to equations like –x = 6. Students commonly leave equations like this, thinking it is solved and misunderstanding the coefficient as negative 1. Students who practice and master these types of equations may be more likely to correctly solve two step equations like 9 – x = 2.
I wanted to find a meaningful way to ignite students' prior knowledge about solving equations in the form px = q. Our Friday schedules are shortened and I wanted to ensure students had 30 minutes to complete the quiz. This leaves closer to 25 minutes of class. During this time I wanted to assess where I needed to meet students to move on to multiplication and division equations. As I walked around the room I noticed many students understood the equations as "p times a number x is q" and they knew the answer for x; they just needed to consider how it works when solving using opposite operations. This initial assessment saved me time on reviewing a piece of information they already knew, and gave me time to discuss the relationship between division and multiplication. The equation reading -x = 6 illustrates the relationship and presents an opportunity to identify the coefficient as -1. Students who finally understand that they need to divide to find the answer and understand what the expression -x represents (the opposite of x) are in use of MP2.
Students are asked to complete the check steps for all of their problems. The equation –x = 6 can be further understood when we substitute the answer (–6) for x as follows:
–x = 6
–(–6) = 6
6 = 6
Worksheets must be submitted to me at the end of class for feedback on showing work and as an accountability practice for measuring effort.