Area and Circumference
Lesson 17 of 20
Objective: SWBAT calculate area and circumference of circles.
Students enter silently according to the Daily Entrance Routine. They find Do Now assignments and clickers at their desks. Students will be given 10 minutes to answer 10 questions including rational number operations. At the end of 10 minutes, I will ask them to enter their answers into SMARTResponse clickers. Once they are finished (2 – 3 minutes), they will be advised that this type of test will become a quiz for a grade on Wednesday (the next day), thus giving them one more day to practice and improve. I use the data created by the clickers to review the lowest scored question. Students who do not finish in ten minutes will be expected to improve with additional practice the next two days.
Practice sheets are offered once again, reminding students that the quiz takes place tomorrow. Answers are offered to be posted online as well. I keep extra problems in a designated spot in the classroom for students to retrieve on their own. These resources are parts of a Glencoe workbook available online.
I’ve made sure to include questions with fractions and long division on this assignment; these are two skills many of my students are still struggling to master. The “bonus” question is taken from a practice SSAT book to push higher students.
Students receive class notes (#cornellnotes) which include circumference and area questions, without word problem applications. Students need to practice calculating these values as evidenced by their exit tickets from the previous day.
For each problem I ask the following questions:
- 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?
I explain that if a question is not specific about where to round to, it should be done to the hundredths place or reported in terms of pi when appropriate. Then I give students classwork and ask them to pay attention to find out who gets to work in booths today.
Students with 90s and above in the practice quiz from the previous day will be allowed to sit in booths for the remainder of class. All other students will be allowed to pair up to work together or may choose to work with me at the front of the room in a smaller group. Once there are 10 minutes left in class, they will be asked to return to their seats to work independently and silently. It is understood that if at any point students sitting in booths do not meet the expectations of each section of class, they can be removed and the “next student in line can take their opportunity”. These are some way in which I try to cultivate an environment of privileges that must be earned by following directions and working hard.
I will focus my time working with a small group of students at the front of the room. These are students I target based on their results to the Practice Quiz the previous day. I ask them to try and explain what the most difficult part about the quiz was, the time or the content. This will let me know what students need during this time, a new explanation of the concepts or practice to improve speed. I will emphasize to all students that each problem should include the appropriate formula needed for that context in the first step of the solution. Students will also be advised to look out for extra helpful information included in the slides given from the power point.
I make sure to review the concept of accuracy when giving answers in terms of pi or approximated in my small groups. I also take time to review rounding, a skill that often holds back some of the lower students from earning points on these types of questions. Question 4 offers a great opportunity to diagnose knowledge about coordinate planes, a topic we have not explicitly covered in class this year. The 5thproblem is one of the most rigorous because of the multiple and complex steps steps involved. Students must be able to: identify a semi-circle, know to calculate half the area of the semi-circle, know to calculate the area of the rectangle separately, and write an awkward looking answer “in terms of pi” of 70+49/2*pi square meters.
Students are practicing MP7 and MP8 are they repeat the same processes and line of questioning about accuracy in reported answers. By doing this I hope to cement the idea of accurate answers and prepare students to apply these skills to real world problems the next day.
Students who finish early may receive an extra practice sheet (for bonus achievement points) on order of operations.
I ask a couple of students to come to the front of the room and copy their work on the board while all other students return to their seats to complete any unfinished work. After 5 minutes to put up their work these students will be responsible for walking the class through their solutions as well as the possible form of answers:
- in terms of pi
- to the nearest tenth
- to the nearest hundredth
Homework will be distributed at the door as students exit the class.