Area and Circumference in Real Situations
Lesson 18 of 20
Objective: SWBAT calculate area and circumference of circles by solving real world problems.
Students enter silently according to the Daily Entrance Routine. They find Do Now assignments already on their desks, the Skills Quiz. For the past two days students have been given two opportunities to practice these skills to prepare for this quiz. These skills were determined and targeted based on recent quiz scores. We are practicing to prepare for the unit test at the end of the week. Students have 10 minutes to complete the entire quiz. I collect it at the end of ten minutes for a grade.
Students receive Cornell notes including word problems which require circumference and area calculations. The power point is meant to walk students through each step, beginning with writing of the formula. I take a few seconds at each step to walk around to ensure students are copying this work into their notes. When reporting our answers I run through the same line of questioning as the previous day and add on a word problem application question:
- What is the approximate answer rounded to the nearest hundredth? tenth? which is more accurate to the exact answer?
- Why can't we give an exact answer in decimal form? what is the only way we can give an exact answer?
- What does it mean to write an answer in terms of pi?
- In this word problem, which is more useful: the answer in terms of pi or an approximated answer? Why?
I also make sure to review examples of rounding to the “nearest inch, foot, dollar, etc”. These are examples where the wording often trips up students. After reviewing answers and answering student questions, the task is distributed and students are assigned to different areas of the room to work.
Students also receive slides 5 and 6 from the presentation. These slides will provide additional help for the word problems. I ask students to play close attention to the last slide, on the relationship between area and circumference of a circle (7.G.B.4), and that we will talk more about this slide at the end of class.
After reviewing the sample problems in the notes students receive their class worksheet. Once again, groups working together will be determined from the results on the previous day’s skills quiz. Students still struggling with circumference and area will be working with me. All others will be allowed to spread out in the room to work. This is prime time for MP1 as students strive to make sense of the problem situations on their worksheets. Students are advised to pay special attention question in each problem. I use the following questions to guide students:
- Which formula do you need?
- Which formula represents the distance around the crater?
- What information are you given?
- What are you being asked to find? What information will you need?
- For Q3: What measure of a circle is the same as a revolution? The rotating arm is the radius or the diameter of a circle?
The largest misconception students will encounter is relating the parts of a circle or the facts provide to the appropriate parts in the formulas. It is important to continue evaluating student progress and understanding throughout this work time. If most are still struggling to apply, all students may need to be asked to return to their seats to complete the problems through whole class discussion, having students talk with each other about chosen steps and their justification.
I will also need one student to complete an additional activity that involves cutting out a circle. I copy these cut outs (included in the resources section) on color cardstock and ask students to label the radius and circumference before cutting out the wedges of the circles. This will help them identify the parts of the re-configured parallelogram (the radius and half the circumference as the length).
Once there are 10 minutes left in class I have 1 – 2 students who recreated the cut outs of circles’ wedges explain the relationship between circumference and area of circles by displaying the work with literal equations on the board. The rest of the class is responsible for copying the work in their copy of slide 6. Using at least three complete sentences, students must answer the following questions in their journals.
- What is the relationship between area and circumference of a circle?
- How can we prove this relationship?
- How can you calculate the area using a circumference fact?