For today's Entry Ticket students work on an estimation problem, and, on the skill of critiquing the reasoning of another person (MP.3).
I like this problem because it gives students an opportunity to estimate, yet is concrete enough so that it is relevant and makes sense (for example, Sam won't have enough money to buy the tickets because she underestimated). Having to make a guess at how Sam came to the estimate pushes students to engage in perspective-taking without the added pressure of interacting with their peers.
Extension: This problem provides an entry point for a conversation about managing money, budgeting, and other functional skills where mathematical reasoning and estimation can be applied.
The class then turns to an active note-taking session where students take Two-Column Notes on calculating levels of accuracy and significant figures.
During this section of class, I am leading the discussion using Class Notes: Measurement, Estimation and Significant Figures. I plan for students to engage in several Turn and Talks to discuss the concepts with a classmate.
Overall, the ideas presented during the class notes provide an overview of significant figures and their applications. I like to think that the class notes and 2-column notes, especially on the topic of significant figures, provides an excellent opportunity for students to attend to precision (MP.6). The very of significant figures lends itself to precision, as the number of significant figures increases, the precision of the measurement increases.
Students then form small groups (this activity can also be completed in pairs or individually without additional prep).
I have students use an ipad (any device with web access will work just fine) to access an online Significant Figure Quiz from Thurston High School in Springfield, OR. I ask students to discuss one problem at a time in groups, and write down the answer that the group agrees upon (this encourages conversations, especially when different group members feel different answers are correct). I also ask students to provide a rationale to each of their answers (see Guided Practice: Template for Online Quiz on Significant Figures in this section as one way to structure this activity).
After writing down all the answers to the quiz, I have each group check and revise their work by clicking the answer on the quiz. I like this online quiz because after clicking a response, the website provides immediate feedback about whether the answer is correct and why.
It is helpful to stress to students that the intent of the assignment is practice and not mastery. I let students know that I am more interested in seeing evidence of the process rather than the number of initially correct answers. The more I can stress and reward effort and perseverance over correctness I try to. Research suggests that students who receive encouragement around effort over grades take more academic risks and persevere more.
After completing the practice problems online, I have students work on creating their own significant figures quiz (see Collaborative Work: Create Your Own Significant Figure Quiz in this section).
I like this assignment as it encourages students to think about what we are working on in class today. By asking students to create an answer key to the quiz with explanations/rationales students need to understand each problem beyond simply knowing how to get the answer. I typically have students create quizzes in pairs, but the class can just as easily create quizzes in small groups or individually.
The task of creating their own quiz, provides an opportunity to engage in higher level critical thinking skills on Bloom's taxonomy. I find that this activity also gets students engaged in rich conversations around their opinions on what types of problems should be included on the quiz they create. For many groups, these conversations lead to consideration of other points of view and do hit on math practice 3 (MP.3).
To conclude the lesson, I have each pair of students switch the quiz they created with another pair. Students then take the quiz created by their peers and check their answers based on the answer key created by their peers.
If time allows: After the quiz students can meet with the group of peers that created the quiz and have a conversation about any outstanding clarifying questions/differing opinions on correct answers and/or explanations.
For homework I assign students to get 5 questions correct on the Khan Academy Website for Practice with Significant Figures.
I also show students how to access overview videos on Khan Academy about significant figures if they need a refresher/additional review on the topic at home. The video is here: