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Benchmark Analysis
Lesson 7 of 8
Objective: SWBAT review major number sense, ratio/proportion and algebraic topics to prepare for the state exam by analyzing and discussing solutions in a benchmark assessment.
Do Now
Students enter silently according to the daily entrance routine. Do Now assignments will be handed at the door upon entry. The state test will take place in three days, so we are reviewing topics in probability and statistics on this assignment. Students will have 5 minutes to work on the assignment and we will review afterward.
 Question 1 reviews basic probabilityin a multiple choice question. Essential question include:
 Probability must be reported in the form of a ______________ (fraction). Why?
 What does the denominator represent?
 What does the numerator represent?
 What is a favorable event?
 Question 2 reviews percentof whole numbers. Essential questions include:
 What strategies can we use to visualize this problem? i.e. Tape diagrams
 Why is the word “closest” used in this problem? We have to estimate
 Question 3 reviews line plots and using them to calculate/identify measures of center. Some essential question to ask include:
 What test taking strategy can we use in this problem?
 Are there any choices we can eliminate because they do not include measures of center?
 What are measures of center vs. measures of variability?
Additional test taking strategies have been included in the back of the Do Now to facilitate discussion. For some students struggling with confidence, it is important to arm them with multiple testtaking strategies (see previous lesson). These will hopefully help them to feel in control of the assessment, even when they struggle to calculate the answer. As we review the answer choices I am also asking students, “did you use any of the strategies in the back of the paper? Which one?”
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Resources
After reviewing the answers to the Do Now, students are asked to take out their Quiz from last Friday. Each student is given answer sheets for the multiple choice questions only (pages B2 – B4), and asked to check their own answers (5 minutes). If they have extra time, students must read the answer document noticing the explanation of the distractors for each answer choice.
Once all students have checked their multiple choice answers, we review the format of the answer sheet. I point out again that the incorrect choices for each question explain the error the student likely made if this answer was selected. Next, students must take out a blank sheet of paper and partner up. Both names should be written on the paper. They will take 7  10 minutes to discuss, in pairs, their mistakes for at least 3 of the questions. Specific expectations will need to be set:
 Begin by selecting who will listen and speak first.
 If you are listening, you must track your partner without interrupting them as they explain their error to one question. If the error does not match the description in the benchmark, be sure to push your neighbor to explain why they selected the incorrect answer choice. It is ok if the answer is simply “I guessed”.
 After your partner is done explaining their error you will ask, “do you know how to get the right answer?”
 If the answer is YES, you will ask your partner to explain how to calculate the correct answer while YOU write down the work and correct solution on a blank sheet of paper.
 If the answer is NO, you will try your best to explain how to calculate the right answer while your partner writes down the correct work and solution on their paper. If neither is sure how to solve, raise your hand so I can help you.
 Then, you will switch roles and it will be your turn to select an incorrect problem on your quiz to discuss.
These expectations will be written on the board so that students can easily view and fulfill the expectations of this segment of class. As I am walking around the room I am vigilant that these expectations are followed, I am answering student questions, and I am also keeping an eye out for students who correctly answered and showed work for the open response items in the last pages of the quiz (QS 9 – 11).
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In the next activity we will need to move the tables in our room to form groups of 6. In the first ten minutes of this section, the following will occur:
 I will ask students who answered at least two of the open response questions correctly (with appropriate work on their paper) to sit together in groups according to the ONE open response question they would like to become “experts” in. This group should include no more than 6 students (2 students per question); I try to select the 6 that I can trust are able to clearly justify, explain, or help other students solve these questions correctly later in this section.
 These students will become experts in ONE of the open response questions. They will take 5 – 7 minutes to discuss with their partner the correct steps for the solution as well as the point values associated for each answer. They must be comfortable using the language in the benchmark to coach other students who were not able to complete these questions correctly.
 The rest of the students can sit at any of the other tables. These are students who did not complete the open response questions, gave wrong answers, or did not show work on their paper to support their answers.

 While the students in the first group are becoming experts, I will be sitting down with this group to explain that the students in the other group will be their coaches for each of the open response questions. In these 10 minutes, this group of students will need to either complete the open response questions if they are not complete (i.e. absent students from Friday), write questions down on their paper to better understand the solutions, or work on some remediation skills with me (i.e. integer operations, rational numbers, simplifying expressions)
After these 10 minutes have passed, my experts will disperse themselves so that there is one expert per table group.
 Experts will be given a sheet of color paper to create a tent with the problem number they will be coaching to label their table group.
 The students in group 2 will be asked to choose the first problem they would like to complete with the expert.
 Expectation: students may NOT bring extra chairs over to form larger groups. There is a limit of 6 students per table group.
Reason: management. When the groups get too large, students get too social or loud and tend to lose motivation.  Experts must teach students how to solve without giving out answers.
 Students must write down solutions, step by step, and will also be expected to ask questions when they do not understand.
 If they finish early and notice an open chair in another group, they may visit that table to complete another problem.
*This "Jigsaw" is one of many cooperative learning, Kagan Strategies. A resource is attached with more ideas.
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Closing
Once there are 10 minutes left in class, all students will be asked to return to their seats. I will be taking a poll, asking students to vote for the most difficult question on this quiz. These will be the types of questions that will appear on our final review the following day.
I will also be asking students to “shout out” experts or other teammates who helped them understand a topic/skill. These shout outs must be specific:
 Who do you want to shout out?
 What question did they help you understand?
 How did they help you understand it?
 What were you struggling to understand?
 What strategy did they teach you?
At the end students will be dismissed. No homework is assigned as I want my students to rest as much as possible this week and have time NOT to think about this test.
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