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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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)


Standard options: 
A. Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.
B. Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.
C. 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.”)


Your response:
C

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: im_lesson_009431

1
options: Recognize and represent proportional relationships between quantities.

Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
problem_activity: Activity
This activity is intended to build confidence and facility in writing an equation for a proportional relationship. Students build on their understanding that measurement conversions can be represented by proportional relationships, which they studied in an earlier lesson and will revisit in future lessons. Students are expected to use methods developed earlier: organize data in a table, write and solve an equation to determine the constant of proportionality, and use repeated reasoning (MP8) to arrive at an equation. In addition, they are expected to identify the relationship between the constant of proportionality when going from centimeters to meters and vice versa (reciprocals). Since students have already explored a similar relationship (centimeters and millimeters) in a previous lesson, this activity may go very quickly.
As students work, look for students writing an equation like
\(100k = 1\)
(for table 2) as a step to finding the constant of proportionality. Encourage them to say how they would solve the equation. Ask students to say why using this equation makes sense in the scenario.
Launch
Introduce the task: “In a previous lesson, you examined the relationship between millimeters and centimeters. Today we will examine the relationship between centimeters and meters.”
Student Facing
There are 100 centimeters (cm) in every meter (m).
| length (m) | length (cm) |
|------------|-------------|
|     1      |     100     |
|    0.94    |             |
|    1.67    |             |
|   57.24    |             |
|   \(x\)    |             |
| length (cm) | length (m) |
|-------------|------------|
|     100     |     1      |
|     250     |            |
|    78.2     |            |
|    123.9    |            |
|    \(y\)    |            |
Complete each of the tables.
For each table, find the constant of proportionality.
What is the relationship between these constants of proportionality?
For each table, write an equation for the proportional relationship. Let
\(x\)
represent a length measured in meters and
\(y\)
represent the same length measured in centimeters.
Student Response
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Student Facing
Are you ready for more?
How many cubic centimeters are there in a cubic meter?
How do you convert cubic centimeters to cubic meters?
How do you convert the other way?
Student Response
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click here to register or sign in
for free access to Extension Student Response.
Activity Synthesis
Invite students to share their answers. These questions can guide the discussion:
"How can we find an equation for each table?"
"Where does the constant of proportionality occur in the table and equation?"
"What is the relationship between the two constants of proportionality? How can you use the equations to see why this should be true?"
The equations can help students see why the constants of proportionality are reciprocals:
\(\displaystyle y = 100x\)
\(\displaystyle \left(\frac{1}{100}\right)y = \frac{1}{100} \boldcdot (100x)\)
\(\displaystyle \left(\frac{1}{100}\right)y = x\)
\(\displaystyle x = \left(\frac{1}{100}\right)y\)
This line of reasoning illustrated above should be accessible to students, because it builds on grade 6 work with expressions and equations.
Ask students to interpret the meaning of the equations in the context: "What do the equations tell us about the conversion from meters to centimeters and back?"
Given the length in meters, to find the length in centimeters, multiply the number of centimeters by 100.
Given the length in centimeters, to find the the length in meters, multiply the number of meters by
\(\frac{1}{100}\)
.
Engagement: Develop Effort and Persistence.
Encourage and support opportunities for peer interactions. Prior to the whole-class discussion, invite students to share their work with a partner. Display sentence frames to support student conversation such as: “First, I _____ because….,” “I noticed _____ so I….,” “Why did you . . .?,” and “I agree/disagree because….”
Supports accessibility for: Language; Social-emotional skills
Speaking: MLR8 Discussion supports.
Provide students with sentence frames such as “I found the constant of proportionality by _____” to help explain their reasoning. Revoice student ideas to model mathematical language use by restating a response as a question in order to clarify, and apply appropriate language.
Design Principle(s): Maximize linguistic and cognitive awareness


correct_option_index: 0