The purpose of this Warm-up is for students to consider some common errors that happen when calculating the volume of a sphere. This work will help prepare students for the Information Gap in this lesson.
Monitor for students who use the formula for a cylinder or cone, who use r2 instead of r3, or who forget to include π as a factor in the computation.
Arrange students in groups of 2. Give students 1–2 minutes of quiet work time followed by time to discuss their responses with their partner.
Four students each calculated the volume of a sphere with a radius of 9 centimeters, and they got four different answers.
Do you agree with any of them? Explain your reasoning.
Mai’s calculation is correct. Sample explanation: The volume of a sphere is found with the formula V=34πr3. Using 9 for the radius, the volume is 34π(93)= 34π(729)=972π.
For each answer, ask students to indicate whether or not they agree. Display the number of students who agree with each answer all to see. Invite someone who agreed with 972π to explain their reasoning. Ask students if they think they know what the other students did incorrectly to get their answers. (To get 108, Han and Jada likely used r2 instead of r3, and Tyler may have forgotten to write π as part of his answer.)
All skills for this lesson
No KCs tagged for this lesson
The purpose of this Warm-up is for students to consider some common errors that happen when calculating the volume of a sphere. This work will help prepare students for the Information Gap in this lesson.
Monitor for students who use the formula for a cylinder or cone, who use r2 instead of r3, or who forget to include π as a factor in the computation.
Arrange students in groups of 2. Give students 1–2 minutes of quiet work time followed by time to discuss their responses with their partner.
Four students each calculated the volume of a sphere with a radius of 9 centimeters, and they got four different answers.
Do you agree with any of them? Explain your reasoning.
Mai’s calculation is correct. Sample explanation: The volume of a sphere is found with the formula V=34πr3. Using 9 for the radius, the volume is 34π(93)= 34π(729)=972π.
For each answer, ask students to indicate whether or not they agree. Display the number of students who agree with each answer all to see. Invite someone who agreed with 972π to explain their reasoning. Ask students if they think they know what the other students did incorrectly to get their answers. (To get 108, Han and Jada likely used r2 instead of r3, and Tyler may have forgotten to write π as part of his answer.)