few_shots: 
Example:
Concept/skill: 
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Problem/activity:
Task
Cruz and Erica were both getting ready for soccer.
Cruz ran 1 lap around the school.
Erica ran 3 laps around the playground.
Erica said,
I ran more laps, so I ran farther.
Cruz said,
4 laps around the school is 1 mile, but it takes 12 laps around the playground to go 1 mile. My laps are much longer, so I ran farther.
Who is right? Draw a picture to help you explain your answer.


Answer: 
Yes. This task asks students to compare two fractions that are equal. The students need to explain why the two fractions are equal by drawing a picture, which involves using visual fraction models.

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_000212_pos_0

4
standard_description: Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^(2) + y^(2))^(2) = (x^(2 )– y^(2))^(2) + (2xy)^(2 )can be used to generate Pythagorean triples.
problem_activity: Activity
The goal of this activity is to practice applying the definition of rotation. In this activity, students rotate a segment around its endpoint to create an isosceles triangle. By rotating a segment around one endpoint, students can observe that the distance between the center of rotation and a point is the same as the distance between the center of rotation and the image of that point. This observation is later captured in the formal definition of rotation.
Making dynamic geometry software available gives students an opportunity to choose appropriate tools strategically (MP5).
Digital
Launch
Action and Expression: Internalize Executive Functions.
Chunk this task into more manageable parts to aide students who benefit from support with organizational skills in problem solving. For example, present one question at a time and ensure students complete each step correctly before moving on to the next step.
Supports accessibility for: Organization; Attention
Student Facing
Draw a segment. Label the endpoints
\(A\)
and
\(B\)
.
Rotate segment
\(AB\)
clockwise around center
\(B\)
by 90 degrees. Label the new endpoint
\(A’\)
.
Use the Polygon tool to draw triangle
\(ABA'\)
.
What kind of triangle did you draw? What other properties do you notice in the figure? Explain your reasoning.
Draw a segment. Label the endpoints
\(C\)
and
\(D\)
.
Rotate segment
\(CD\)
counterclockwise around center
\(D\)
by 30 degrees. Label the new endpoint
\(C’\)
.
Rotate segment
\(C’D\)
counterclockwise around center
\(D\)
by 30 degrees. Label the new endpoint
\(C’’\)
.
Use the Polygon tool to draw triangle
\(CDC’’\)
.
What kind of triangle did you draw? What other properties do you notice in the figure? Explain your reasoning.
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?
You constructed an equilateral triangle by rotating a given segment around one of its endpoints by a specific angle measure. An equilateral triangle is an example of a
regular polygon
: a polygon with all sides congruent and all interior angles congruent. Try to construct some other regular polygons with this method.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Extension Student Response.
Print
Launch
Briefly demonstrate how to create an angle of a given measure with a protractor and ask students to use their protractors along with you.
Making dynamic geometry software available gives students an opportunity to choose appropriate tools strategically (MP5). You may wish to demonstrate using GeoGebra Geometry in Math Tools.
Action and Expression: Internalize Executive Functions.
Chunk this task into more manageable parts to aide students who benefit from support with organizational skills in problem solving. For example, present one question at a time and ensure students complete each step correctly before moving on to the next step.
Supports accessibility for: Organization; Attention
Student Facing
Draw a segment. Label the endpoints
\(A\)
and
\(B\)
.
Rotate segment
\(AB\)
clockwise around center
\(B\)
by 90 degrees. Label the new endpoint
\(A’\)
.
Connect
\(A\)
to
\(A’\)
and lightly shade in the resulting triangle.
What kind of triangle did you draw? What other properties do you notice in the figure? Explain your reasoning.
Draw a segment. Label the endpoints
\(C\)
and
\(D\)
.
Rotate segment
\(CD\)
counterclockwise around center
\(D\)
by 30 degrees. Label the new endpoint
\(C’\)
.
Rotate segment
\(C’D\)
counterclockwise around center
\(D\)
by 30 degrees. Label the new endpoint
\(C’’\)
.
Connect
\(C\)
to
\(C’’\)
and lightly shade in the resulting triangle.
What kind of triangle did you draw? What other properties do you notice in the figure? Explain your reasoning.
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?
You constructed an equilateral triangle by rotating a given segment around one of its endpoints by a specific angle measure. An equilateral triangle is an example of a
regular polygon
: a polygon with all sides congruent and all interior angles congruent. Try to construct some other regular polygons with this method.
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
Students may not notice any properties other than that rotation preserves distances to the center of rotation. Encourage these students to use tracing paper to make other conjectures about side lengths or angles.
Activity Synthesis
Display an isosceles triangle
\(ABC\)
with base
\(BC\)
.
Here are some key conjectures and observations students should come away from the discussion with:
Rotations preserve the distance to the center of rotation.
The angle bisector of angle
\(A\)
is also the perpendicular bisector of the base (
\(BC\)
) of an isosceles triangle.
The two base angles (angle
\(B\)
and angle
\(C\)
) of an isosceles triangle are congruent.
An isosceles triangle where angle
\(A\)
is 60 degrees is also equilateral.
It is not necessary at this time to formalize the language of these ideas. This will come later as students prove some of these statements in a subsequent unit.


aligns: no