Objectives Write objectives in IWBAT form. Evaluation Questions (at least one open-ended) Each question should match the written objective. You may use one of your sample TAKS/STAAR problems as a guiding template for your evaluation questions. Note: these should be the SAME questions you are utilizing in the evaluation section. Include answers to all questions. Include 1 real-world, 1 griddable, and 1 explanation question 1 I will be able to measure the circumference and diameter of a circle. Use your ruler and string to measure the diameter and Circumference of the circular objects you are provided (in centimeters). 2 I will be able to use a or graph of data to identify the relationship between the circumference of a circle and its diameter. After collecting the measurements of the circular objects in the bag, what relationship do you notice between the circumference and the diameter of all of the circles you measured? Did your partner get the same results? Did your classmates get the same results? 3 I will be able to determine the diameter of a circle given the circumference of the circle. The tallest tree in the is believed to be the Mendicino Tree, a redwood near Ukiah, California, that is 112 meters tall! Near the ground the circumference of this tree is about 9.85 meters. The age of a redwood can be estimated by comparing its diameter to trees with similar diameters. What is the diameter of the Mendicino tree? Resources, Materials, Handouts, and Equipment List in the form of a table: ITEM (Specify worksheets) Quantity (How many do you need?) Source (Who is responsible?) List who this is for (teacher, student, group) Ziploc® Gallon size Bags 1 per pair Teacher Student Pairs Tablet Computer 1 per student Teacher Student Circular items (cans, lids, Frisbees, rolls of tapes, CDs) 4-6 items per pair Teacher Student Pairs Tennis balls in a can 1 can Teacher Whole Class Yarn or String 1, 2-ft section per student Teacher Student 1 box assorted markers 1 per pair Teacher Student Pairs Rulers 1 per student Teacher Student Recording Sheet 1 per student Teacher Students Advanced Preparations: Prepare a gallon Ziploc® bag of materials for each student pair. The bag should contain the following: 4-6 circular items
supply station and pick up a Ziploc® bag and two recording sheets.” Hold up the bag and the recording sheet. Instruct students to take their supplies out of their bags when they get them back to their desks. Review the following directions with the students: Using the ruler and string in the bag, each person will need to measure the diameter and the circumference of the circular objects in your Ziploc® bag. This means all of the objects will be measured twice – once by you and once by your partner. Don’t simply copy your partner’s measurement. You have to actually measure the circumference of each circle – do not use your formula for circumference. Record your measurements on the recording as you go along. Once you are finished measuring, you will submit your measurements using the Google Form, My Measurements. If you finish early, you and your partner can look over your recording sheets. Begin looking for patterns in the data you collected. Once everyone is finished submitting their data, you How we start looking for a pattern? Try adding, subtracting, multiplying, or dividing the diameters and the circumferences to look for a repeated result…. Look at a change between the diameters of two circles and see if there is corresponding change in the circumferences. Graph the data. What relationships are you finding in the data on the table? The circumference is approximately three times the length of the diameter. The diameter is approximately one-third of the length of the diameter. What patterns do you notice when you plot your data points? They appear to form a straight line. Students may find it helpful to plot their data points using the Google spreadsheet functions.
Transition Statement Now that we know what π represents. Let’s look at how we can use this relationship to answer a real-world question. ELABORATION 1 Time: 5 Minutes What the Teacher Will Do Probing/Eliciting Questions and Student Responses What the Students Will Do Send the following prompt to the students on their tablets: The diameter of the Earth at the equator is approximately 12,756 km. Explain how you could use what you just discovered about to find the distance around the Earth at the equator. Use the guiding questions to have students determine what information is provided in the prompt and how they might find a solution to the prompt. It might help to take an extra tennis ball and cut it in half so students visualize what the cross-section of the Earth would look like if it were sliced in half at the equator. [Interesting fact: The is not a perfect sphere. The diameter of the Earth at the equator is 12, 756 km, but the diameter of the Earth measured at its poles is 12,713 km.] What information are we given in the prompt? The diameter of the Earth is approximately 12,756 km. What are they asking us to find? The distance around the at the equator. What geometric shape is the Earth? A sphere (like the tennis balls). If we were to slice the Earth in half at its equator, what shape would we have at the cross-section? A circle. How would the distance around the Earth’s equator be related to this circle? The distance around the Earth’s equator would be the circumference of this circle. How could we use what we discovered about to help use find the distance around the Earth? Since is the ratio of the circumference of a circle to its diameter, we can write If we multiply by 12,756, we can find C. Students will utilize their tablets to access the Google Doc, Equator Distance. Students will highlight important information in the prompt. Using their stylus, students will write a response to how they would find a solution to the question.