few_shots: 
Example:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Concept/skill: 
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

Answer: 
Yes. This problem involves understanding fractions and division to divide rational numbers, such as 1, -4, 4, and -1. This problem also involves an understanding of multiplication: if p and q are integers, then -(p/q) = (-p)/q = p/(-q).

Now, does the following problem or activity enable students to learn the full intent of the following concept or skill?

shot_info: fl_problem_001097_pos_0

7
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
The purpose of this activity is for students to order three objects by length. Students line up objects from shortest to longest and longest to shortest. Students need to attend to the language in the question to know which way to order the objects. The language and reasoning students use in this activity helps prepare them to compare the length of objects indirectly in future lessons.
Required Materials
Materials to Gather
Materials from a previous activity
Required Preparation
Each group of 4 needs the collection of objects from the previous activity.
Launch
Groups of 4
Give each group 10–12 objects.
Activity
Read the task statement.
5 minutes: small-group work
Monitor for students who line up the endpoints of the objects.
Student Facing
Pick 3 objects.
With your partner, put the objects in order from
shortest
to longest.
Trace or draw your objects.
Pick 3 new objects.
With your partner, put them in order from
longest to shortest
.
Write the names of the objects in order from longest to shortest.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If students appear to order their objects correctly without lining them up, consider asking:
“How did you order your objects from ___ (shortest to longest or longest to shortest)?”
“How could you prove to someone that your objects are ordered correctly?”
Activity Synthesis
Invite previously identified students to demonstrate how they ordered three objects from shortest to longest.
Display the three objects with the endpoints lined up so all students can see.
“What statements can you make to compare the length of their objects?” (The ___ is longer than the ___ and ___.)
As time permits, repeat by inviting a previously identified students to demonstrate how they ordered three objects from longest to shortest.


aligns: no