standard_description: Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.
problem_activity: Narrative
The purpose of this True or False is for students to demonstrate strategies and understandings they have for interpreting a fraction as division of the numerator by the denominator and vice versa. These strategies help students deepen their understanding of the relationship between division and fractions where the unknown is the numerator, denominator, or the value of the quotient.
Launch
Display one statement.
“Give me a signal when you know whether the statement is true and can explain how you know.”
1 minute: quiet think time
Activity
Share and record answers and strategy.
Repeat with each statement.
Student Facing
Decide if each statement is true or false. Be prepared to explain your reasoning.
\(5 \div 2 = \frac{5}{2}\)
\(\frac{5}{2} = 5\frac{1}{2}\)
\(\frac{6}{2} = 3\)
Student Response
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Activity Synthesis
Display:
\(5\frac{1}{2}\)
\(\frac{5}{2}\)
“How are these expressions the same? How are they different?” (They both have 5 and 2 in them. They both show halves.
\(5\frac{1}{2}\)
means 5 wholes plus one half and
\(\frac{5}{2}\)
means 5 groups of one half.)


aligns: no