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Essential Questions for students (objectives): I can use mathematical problem-solving in order to calculate a solution to a question where all information isn’t specifically known. I can use formulas of geometric shapes correctly.
Supplies: Video: https://youtu.be/_XtEAJoUJJE, Help Wanted at Mount Vernon by Holly Young and Cathy Morgan, journal page, scoring rubric, calculators
Common Core Standards: 7.G.4, Mathematical Practice #1 & #5
Prior Knowledge/ Possible Warm-up Activities: Students will need to be familiar with finding the circumference of a circle.
Time needed: 30-45 minutes
Instructional Format: Video, individual or group work
Vocabulary for a Word Wall: Concentric Circles, Circumference
Step by Step Lesson Description:
1) Show video. [Note: you may need to pause the video at the end and replay multiple times for students to gather information]
2) Pass out journal page. Ask students to solve the problem – how far does the flour travel – and write up their solution. It is important that students understand that most real-world problems don’t have exact answers (the circles actually move in a spiral pattern, not perfect concentric circles), and that some pieces of necessary information isn’t always provided (or even available). Students can solve the problem individually or in partners. Note on the rubric how, in order to get full points, students must explain step by step their problem-solving process and why they are doing each individual step.
3) Have students assess one another’s work using the rubric. As a class discuss the “educated estimates” made. What is the range of final answers? Are they close to one another? How would you account for the inconsistencies? What other questions regarding the operation at the Grist Mill came up while working on the problem? [For instance – could the process be improved so that flour doesn’t fall away from the outside circle?]
Exploration: How is an Archimedes spiral used in the process of making flour at George Washington’s Grist Mill? Where else can an Archimedes spiral be used? What mathematics exists in regards to an Archimedes spiral?
Assessment (Acceptable Evidence): Rubric scoring of student work
Cautionary notes/ misconceptions/additional connections: When students explain their work, they have a tendency to write something like the following: first I multiplied by 7, and then I added two, and then I got my answer. I insist that students have to provide the WHY at each step. I coach the students to answer – WHY did you multiply by 7? Why did you add two? I coach them to explain the problem to someone who wouldn’t know how to solve the problem in any way.