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
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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: 
Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Students do not need to learn formal names such as “right rectangular prism.”)

Answer: 
Yes. This activity asks students to compose three-dimensional shapes, using geoblocks, to create composite shapes.

Now, assess whether the following problem or activity is 'aligned' with the given Common Core standard in Mathematics.

shot_info: im_lesson_009431_pos_0

1
standard_description: Recognize and represent proportional relationships between quantities.
problem_activity: Activity
In general,
\(P\%\)
of something is
\(\frac{P}{100}\)
times that thing. The purpose of this activity is to make this explicit. In this activity, students are asked to find 80% of several different values, generalize their process, and express their generalization in different ways. As they make repeated calculations, students look for and express regularity in their work (MP8) and see more explicitly that
\(P\%\)
of a number is
\(\frac{P}{100}\)
times that number. Once they arrive at one or more generalizations, students practice articulating why each generalization always works (MP3).
Launch
Give students quiet think time to complete the activity and then time to share their explanation with a partner.
Representation: Internalize Comprehension.
Activate or supply background knowledge about equivalent fractions. Incorporate explicit opportunities for review and practice if necessary. Allow students to use calculators to ensure inclusive participation in the activity.
Supports accessibility for: Memory; Conceptual processing
Writing, Speaking, Listening: MLR1 Stronger and Clearer Each Time.
Use this with successive pair shares to give students a structured opportunity to revise and refine their own strategies to determine 80% of any value to find a sale price. Make sure students include a table as well as an expression in their explanations. Ask each student to meet with 2–3 other partners in a row for feedback. Provide students with prompts for feedback that will help them strengthen their ideas and clarify their language (e.g., “Can you explain how…”, “Will this expression always work? How do you know?”, etc.). Students can borrow ideas and language from each partner to refine and clarify their original explanation. This will help students refine their own strategies and learn about other ways to find the sale price of an item.
Design Principles(s): Optimize output (for explanation); Maximize meta-awareness
Student Facing
During a sale, every item in a store is 80% of its regular price.
If the regular price of a T-shirt is
$
10, what is its sale price?
The regular prices of five items are shown here. Find the sale price of each item.
|               | item 1 | item 2 | item 3 | item 4 | item 5 |
|---------------|--------|--------|--------|--------|--------|
| regular price |        |        |        |        |        |
|  sale price   |        |        |        |        |        |
You found 80% of many values. Was there a process you repeated over and over to find the sale prices? If so, describe it.
[IMG]
Select
all
of the expressions that could be used to find 80% of
\(x\)
. Be prepared to explain your reasoning.
\(\frac{8}{100} \boldcdot x\)
\(\frac{80}{100} \boldcdot x\)
\(\frac{8}{10} \boldcdot x\)
\(\frac{4}{10} \boldcdot x\)
\(\frac85 \boldcdot x\)
\(\frac45 \boldcdot x\)
\(80 \boldcdot x\)
\(8 \boldcdot x\)
\((0.8) \boldcdot x\)
\((0.08) \boldcdot x\)
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
Make sure students have the correct values in the table for the second question. Then, discuss the expressions, starting with
\(\displaystyle \frac{80}{100} \boldcdot x.\)
Guide students to see that if we know the value of 100%, dividing that value by 100 (or equivalently, multiplying it by
\(\frac{1}{100}\)
) tells us the corresponding value for 1%. We can then multiply that value by the desired percentage. Consider using a table to organize this argument, as shown below:
| percentage |         regular price          |
|------------|--------------------------------|
|    100     |             \(x\)              |
|     1      | \(\frac{1}{100} \boldcdot x\)  |
|     80     | \(\frac{80}{100} \boldcdot x\) |
After everyone understands where this expression comes from, ask students to discuss the remaining expressions with a partner. This is a good opportunity for just-in-time review on equivalent fractions, if needed.


aligns: no