standard_description: Use square root and cube root symbols to represent solutions to equations of the form x^(2) = p and x^(3) = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that Ö2 is irrational.
problem_activity: Narrative
This activity prompts students to compare multiple fractions and put them in order by size. The work gives students opportunities to look for and make use of structure (MP7) in each set of fractions and make comparisons strategically. For instance, rather than comparing two fractions at a time and in the order they are listed, students could first classify the given fractions as greater or less than
\(\frac{1}{2}\)
or 1, look for fractions with a common numerator or denominator, and so on.
If time is limited, consider asking students to choose two sets of fractions to compare and order.
Representation: Internalize Comprehension.
Synthesis: Invite students to identify which details were most useful when putting fractions in order. Display the sentence frame, “The next time I put fractions in order, I will pay attention to . . . .”
Supports accessibility for: Memory
Launch
Groups of 2
Activity
“Work independently on two sets. Then, discuss your work with your partner and complete the rest together.”
10 minutes: independent work time
Monitor for students who look for and make use of structure. Ask them to share during lesson synthesis.
3–4 minutes: partner discussion
Student Facing
Put each set of fractions in order, from least to greatest. Be prepared to explain your reasoning.
\(\frac{3}{12} \qquad \frac{2}{4} \qquad \frac{2}{3} \qquad \frac{1}{8}\)
\(\frac{8}{5} \qquad \frac{5}{6} \qquad \frac{11}{12} \qquad \frac{11}{10}\)
\(\frac{21}{20} \qquad \frac{9}{10} \qquad \frac{6}{5} \qquad \frac{101}{100}\)
\(\frac{5}{8} \qquad \frac{2}{5} \qquad \frac{3}{7} \qquad \frac{3}{6}\)
Student Response
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Advancing Student Thinking
Some students may try to write equivalent fractions with a common denominator for all four fractions in each set before comparing them but may be unable to do so. Encourage them to try reasoning about two fractions at a time, and to use what they know about the fractions to determine how they compare (to one another or to familiar benchmarks).
Activity Synthesis
See lesson synthesis.


aligns: no