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: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
problem_activity: Activity
The purpose of this activity is for students to compare the possible ways of constructing equilateral triangles. Look for student work that illustrates a variety of methods and sizes of triangles.
Making dynamic geometry software available gives students an opportunity to choose appropriate tools strategically (MP5).
Launch
Encourage students to construct the equilateral triangles using different methods rather than repeating the same method twice.
Student Facing
Use straightedge and compass moves to construct at least 2 equilateral triangles of different sizes.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Student Facing
Are you ready for more?
[IMG]
[IMG]
Examine the figure carefully. What different shapes is it composed of? Be specific.
Figure out how to construct the figure with a compass and straightedge.
Then, cut it out, and see if you can fold it up into a container like this.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Extension Student Response.
Anticipated Misconceptions
If students get stuck, ask them to refer to the warm-up to see whether they can spot equilateral triangles. Then encourage them to do the compass and straightedge moves required to make those equilateral triangles.
Activity Synthesis
Display several student responses for all to see. Ask students to explain their methods for producing equilateral triangles and justify how they know each triangle is equilateral. If not mentioned by students, conjecture that, in some of these constructions, the entire construction remains the same even when rotated
\(\frac13\)
of a full turn (120 degrees) around the center. This means that each side can be rotated onto the other sides, and each angle can be rotated onto the other angles. This plants ideas about symmetry that will be explored in later lessons.
Speaking, Representing: MLR8 Discussion Supports.
Use this routine to help students prepare for the whole-class discussion. Arrange students in groups of 2. Invite students to take turns explaining their method for constructing equilateral triangles of different sizes. This will provide all students with additional opportunities to clarify their thinking and to produce language.
Design Principle(s): Support sense-making; Cultivate conversation
Action and Expression: Develop Expression and Communication.
Invite students to talk about their ideas with a partner before writing them down. Display sentence frames to support students when they explain their strategy and ideas. For example, “First, I _____ because _____. Then, I....” and “I know _____ because….”
Supports accessibility for: Language; Organization


aligns: no