few_shots: 
Example:
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.”)

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)


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

Now, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: im_lesson_009431_pos_0

1
standard_description: Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).
problem_activity: Activity
This activity is designed to give students opportunities to use their understandings from this unit to perform mathematical modeling.
The trail mix context is familiar from the previous activity, but students are challenged to choose quantities, determine how to represent them, interpret and reason about them, and use the model they create to make choices. It also enables students to reflect on their model and revise it as needed (MP4).
Students are likely to want to use graphing technology, as the nutritional information involves decimals and the inequalities written would be inconvenient to graph by hand. This is an opportunity for students to choose tools strategically (MP5).
No time estimate is given here because the time would depend on decisions about the research students do and on the expectations for collaboration and presentation.
Launch
Arrange students in groups of 2–4. Provide access to Desmos or other graphing technology.
Explain the expectations for researching nutritional values, for collaboration with group members, and for presentation of student work. (If each group is presenting one response, provide each group with tools for creating a visual display. If each student is presenting a response, give each student tools for creating a visual display.)
Engagement: Develop Effort and Persistence.
Provide prompts, reminders, guides, rubrics, or checklists that focus on increasing the length of on-task orientation in the face of distractions. For each question, allot a specific amount of work time and display expectations. Display a countdown timer, along with a bulleted list of what teams or individuals are to produce to complete a given step. For instance, during question 1, display a 5 minute countdown timer and the list: “You’re finished if you. . . (1) Have your two ingredients (2) Have the nutrition information ready.”
Supports accessibility for: Attention; Social-emotional skills
Student Facing
It's time to design your own trail mix!
Choose two ingredients that you like to eat. (You can choose from the ingredients in the previous activity, or you can look up nutrition information for other ingredients.)
Think about the constraints for your trail mix. What do you want to be true about its calories, protein, sugar, fat, or fiber?
Write inequalities to represent your constraints. Then, graph the inequalities.
[IMG]
Is it possible to make trail mix that meets all your constraints using your ingredients? If not, make changes to your constraints or your ingredients and record them here.
Write a possible combination of ingredients for your trail mix.
Pause here so your teacher can review your work and give further instructions for displaying your work.
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
Select groups to share their visual displays. Encourage students to ask questions about the mathematical thinking or design approach that went into creating the display. Here are questions for discussion, if not already mentioned by students:
What constraints did every group use?
How do the graphs of the various mixes compare?
Did anyone have to revise or change their model in order to come up with a solution they could use?
How did you use the graph to choose a recipe for your mix?
Representing, Conversing: MLR7 Compare and Connect.
Use this routine to prepare students for the whole-class discussion. At the appropriate time, invite groups to create a visual display of their work. Students should consider what types of details (annotations, notes, diagrams, arrows, etc.) to include on their displays that will help communicate their reasoning. Begin the whole-class discussion by selecting and arranging 2–4 displays for all to see. Give students 2–3 minutes of quiet think time to interpret the displays before inviting the authors to present their work.
Design Principle(s): Optimize output; Cultivate conversation


aligns: no