3D Solids UnitLesson Six – Review of Circle Formulas

Time: Shortened 33-minute period

Objectives: Students use algebra to determine “backwards” formulas for circles, solving for components like radius. Students can explain that radius, diameter, circumference, and area can all be found knowing just 1 of the 4. Students will apply the formulas for components of a circle to solve realistic problems.

Common Core Standard(s) Addressed: 8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world

and mathematical problems.

Materials: Overhead transparencies Computer with internet connection and television screen for display

Procedure:Time Task

0:00-5:00 Warm-up: What is the area of the red space on this bullseye? (see next page)

5:00-7:00 Distribute homework folders for students to turn in their work.

7:00-17:00Provide students will all possible circle formulas, based on the known variable.Encourage them to copy these onto the back of their formulas checklist because they will probably want to add these to their notecards. (see two pages ahead for full list)

17:00-28:00

Bring up the website h ttp://illuminations.nctm.org/ActivityDetail.aspx?ID=116 on a television or Promethean Board.

On the “intro” tab, drag the circle slider to demonstrate how the circumference changes along with the radius.

Have students calculate the circumference of a circle with radius 4, then adjust the slider so that the radius is 4 and read the answer for circumference. Click the movie icon (right side) to demonstrate how the circumference can be “unraveled” to be measured.

Click the “d” button to toggle to diameter instead of radius. Have students calculate the circumference if the diameter is 6. Now adjust the slider till the diameter is 6 and check the answer. Click the movie icon once more.

Now click the “Problems” tab. (Get ready for the music. You can click the purple icon to turn it off.) Discuss the listed problem with students. Which variable do we know? Which are we looking for? Ask them to find the appropriate formula to use and substitute the given value.

Once a student volunteers an answer, ask if there are any different answers. Allow all students to offer their unique responses if they are confident.

Check students’ responses by dragging the radius slider until the variable listed in the problem matches what is shown in the upper right corner. Does the value of the unknown variable match students’ responses?

Whichever student gets the problem correct gets to choose the color of the goat before proceeding to the next problem.

Continue this game until there are approximately six minutes of class left. (Sometimes clicking “next” again is necessary if the same types of problems keep popping

up. Try to provide students with a good variety of problems.)

28:00-33:00

Distribute 3” x 5” notecards, explaining that each student will get to use one of these notecards (front and back) to help them during the unit test on Friday. The test will not provide any formulas needed to solve the problems, therefore it is important to transfer everything from the checklists onto the notecard. If a student is absent tomorrow, the day before the test, it is still his or her responsibility to complete their notecard and bring it on Friday!

Differentiation: (higher) During the game, stop providing clues as to which variable is known and which must be found.

Assessment: Are students’ responses to the goat game problems correct? Are students using the new formulas effectively to find unknown variables from the one provided?

CIRCLES WARM-UP

What is the area of just the RED space on this bullseye?

Full listing of Circle Formulas