standard_description: Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.
problem_activity: Optional activity
In this optional activity, students use colored pencils (or pens or highlighters) to label the radius and height on different pictures of cylinders. Then they sketch their own cylinders and label the radius and heights of those. The purpose of this activity is for students to practice identifying the radius and height of various cylinders, some of which are in context.
This activity can also be abbreviated if students demonstrate prior understanding of how to draw or label cylinders and only need a brief refresh.
Launch
Distribute colored pencils. Give students 1–2 minutes of quiet work time followed by a whole-class discussion.
Student Facing
For cylinders A–D, sketch a radius and the height. Label the radius with an
\(r\)
and the height with an
\(h\)
.
[IMG]
Earlier you learned how to sketch a cylinder. Sketch cylinders for E and F and label each one’s radius and height.
Student Response
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Anticipated Misconceptions
In diagrams D and E, some students might mistake the diameter for the height of the cylinder. Some students may mark a height taller than the cylinder due to the tilt of the figure.
Activity Synthesis
Select students to share where they marked the radius and height and the cylinders sketched for images E and F. Discuss examples of other cylinders students see in real life.
Speaking, Listening: MLR3 Clarify, Critique, Correct.
Present an incorrect drawing that reflects a possible misunderstanding from the class about the height of a cylinder. For example, draw a cylinder with the diameter incorrectly placed at its height and the height at its diameter. Prompt students to identify the error, (e.g., ask, “Do you agree with the representation? Why or why not?”), correct the representation, and write feedback to the author explaining the error. This helps students develop an understanding and make sense of identifying the heights of differently-oriented cylinders.
Design Principle(s): Support sense-making; Maximize meta-awareness


aligns: no