few_shots: 
Example:
Problem/activity:
Narrative
The purpose of this activity is for students to create composite shapes and compose new shapes from composite shapes. For example, students may find that a rectangular prism can be made from four triangular prisms or from eight smaller cubes. Students then discover that they can combine two of the composed rectangular prisms to make a new rectangular prism.
Required Materials
Materials to Gather
Geoblocks
Launch
Groups of 4
Give each group geoblocks.
Display a large cube.
“This cube can be built from other shapes. See how many ways you can build a cube using other shapes.”
3 minutes: partner work time
Share responses.
Activity
“Choose a different shape. Try to find smaller shapes you can use to build that shape.”
5 minutes: partner work time
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Display a cube and a composite cube—for example, a cube composed of four small cubes and one rectangular prism.
Demonstrate putting the shapes together.
“What new shape did I make with the cube and the cube I made?”
“Put your shapes together to make a rectangular prism.”
Display a rectangular prism and two triangular prisms.
“Find these shapes. Put them together. What new shape can you make?” (a cube, a rectangular block)


Concept/skill: 
Recognize area as an attribute of plane figures and understand concepts of area measurement.

Answer: 
No. This activity does not teach students area as an attribute of plane figures. Instead, the activity focuses on solid, three-dimensional figures.

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

shot_info: im_lesson_009431_neg_0

1
standard_description: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
problem_activity: Activity
This activity addresses the common misconception that if a figure is dilated by a factor of
\(k\)
, the image’s area also changes by a factor of
\(k\)
. As students decide which response (if either) they agree with, they are critiquing the reasoning of others (MP3).
Launch
Writing, Listening, Conversing: MLR1 Stronger and Clearer Each Time.
Use this routine to help students improve their written responses for the first question. Give students time to meet with 2–3 partners to share and receive feedback on their responses. Display feedback prompts that will help students strengthen their ideas and clarify their language. For example, “How is the area of the triangle affected when it is dilated by a factor of
\(k=0.25\)
?” or “How do you know that the area of the dilated triangle is 6.25 square inches?” Invite students to go back and revise or refine their written responses based on the feedback from peers. This will help students justify their reasoning for why the area of the triangle is multiplied by
\(k^2\)
when dilated by scale factor
\(k\)
.
Design Principle(s): Optimize output (for explanation); Cultivate conversation
Representation: Access for Perception.
Read the task statement aloud. Students who both listen to and read the information will benefit from extra processing time. Check for understanding by inviting students to rephrase the problem in their own words.
Supports accessibility for: Language
Student Facing
A triangle has area 100 square inches. It’s dilated by a factor of
\(k=0.25\)
.
Mai says, “The dilated triangle’s area is 25 square inches.”
Lin says, “The dilated triangle’s area is 6.25 square inches.”
For each student, decide whether you agree with their statement. If you agree, explain why. If you disagree, explain what the student may have done to arrive at their answer.
Calculate the area of the image if the original triangle is dilated by each of these scale factors:
\(k=9\)
\(k=\frac34\)
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Anticipated Misconceptions
Students may believe they can’t calculate the area of the dilated triangle if they don’t have its dimensions. Remind them of the two approaches highlighted in the warm-up and ask if either of those applies here.
Activity Synthesis
Here are some questions for discussion:
“Why didn’t we need the dimensions of the original triangle to calculate the area of the dilated triangle?” (We could multiply
\(k^2\)
by the original triangle’s area.)
“What are some different ways to deal with the scale factor
\(\frac34\)
?” (We can square the fraction to get
\(\left(\frac34 \right)^2 = \frac{9}{16}\)
, then multiply that fraction by the area. Or, we can divide 3 by 4 to get 0.75, square that to get 0.5625, then multiply that by 100.)


aligns: no