few_shots: 
Example:
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} $

Concept/skill: 
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
 Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.

Answer: 
Yes. By arranging the fractions in this problem, students learn to compare fractions by reasoning about their size.

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

shot_info: im_task_000157_pos_0

3
standard_description: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
problem_activity: Activity
In later lessons, students will encounter situations in which they need to figure out if they have enough information to be sure two triangles are similar, based on angle measure alone. This activity introduces that concept as students grapple with whether the given information is enough to figure out that at least two pairs of corresponding angles are congruent.
Students will need to use their knowledge of the Triangle Angle Sum Theorem to figure out the third angle in each triangle.
Launch
Speaking, Reading: MLR5 Co-Craft Questions.
Use this routine to increase awareness of the language used to talk about the features of similar triangles. Before revealing the questions in this activity, display the image of both triangles. Ask students to write down possible mathematical questions that could be asked about the image. Invite students to compare their questions before revealing the actual questions. Listen for and amplify any questions about the features of both triangles. For example, “Are the triangles similar?”, “What are the values of
\(x\)
and
\(y\)
?”, and “What are the measures of the missing angles?”
Design Principle(s): Maximize meta-awareness; Support sense-making
Student Facing
Here are 2 triangles. One triangle has a 60 degree angle and a 40 degree angle. The other triangle has a 40 degree angle and an 80 degree angle.
[IMG]
Explain how you know the triangles are similar.
How long are the sides labeled
\(x\)
and
\(y\)
?
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?
Under what conditions is there an Angle-Angle Quadrilateral Similarity Theorem? What about an Angle-Angle-Angle Quadrilateral Similarity Theorem? Explain or show your reasoning.
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 are struggling unproductively, ask them to share what’s hard about this problem. (I’m stuck because I don’t have two pairs of corresponding angles.) Then ask them if it’s possible to find another corresponding angle using the information provided. (Yes, using the Triangle Angle Sum Theorem to figure out the third angle and check if the third pair of angles might be congruent.)
Activity Synthesis
The key idea is that the Triangle Angle Sum Theorem allows us to use the Angle-Angle Triangle Similarity Theorem even when we haven’t been given two pairs of congruent corresponding angles. Invite students to explain how they could tell the triangles were similar.


aligns: no