few_shots: 
Example:
Concept/skill: 
Understand a fraction as a number on the number line; represent fractions on a number line diagram.
 Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.

Problem/activity:
Task
 Arrange the fractions in order from least to greatest. Explain your answer with a picture.
 $\frac{1}{5}, \frac{1}{7}, \frac{1}{3} $
 $\frac{2}{5}, \frac{2}{7}, \frac{2}{3} $
 $\frac{5}{6}, \frac{3}{6}, \frac{1}{6} $
 $\frac{5}{12}, \frac{8}{12}, \frac{4}{12} $

Answer: 
No. Completing this task does not involve representing fractions on a number line diagram.

Now, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: im_task_000157_neg_0

3
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: Warm-up
The purpose of this warm-up is for students to reason about powers of positive and negative numbers. While some students may find the numeric value of each expression to make a comparison, it is not always necessary. Encourage students to reason about the meaning of the integers, bases, and exponents rather than finding the numeric value of each expression.
Launch
Display one problem at a time. Give students up to 1 minute of quiet think time per problem and tell them to give a signal when they have an answer and a strategy. Follow with a whole-class discussion.
There may be some confusion about how negative numbers interact with exponents. Tell students that exponents work the same way for both positive and negative bases. In other words,
\((\text- 3)^2 = \text- 3 \boldcdot \text- 3\)
.
Students may also struggle to interpret the notation difference between two expressions such as
\((\text- 4)^2\)
and
\(\text- 4^2\)
. Tell students that the interpretation of the first expression is
\((\text- 4)^2 = \text- 4 \boldcdot \text- 4\)
and the interpretation of the second expression is
\(\text- 4^2 = \text- 1 \boldcdot 4 \boldcdot 4\)
.
Student Facing
Is each statement true or false? Be prepared to explain your reasoning.
\(3^5 < 4^6\)
\(\left(\text- 3\right)^2 < 3^2\)
\(\left(\text- 3\right)^3 = 3^3\)
\(\left( \text- 5 \right) ^2 > \text- 5^2\)
Student Response
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Activity Synthesis
Poll students on their response for each problem. Record and display their responses for all to see. If all students agree, ask 1 or 2 students to share their reasoning. If there is disagreement, ask students to share their reasoning until an agreement is reached. After the final problem, ask students if the same strategies would have worked if all of the bases were 10 to highlight the idea that powers with a base of 10 behave the same as those with bases other than 10.
To involve more students in the conversation, consider asking:
“Do you agree or disagree? Why?”
“Who can restate ___’s reasoning in a different way?”
“Does anyone want to add on to _____’s reasoning?”


aligns: no