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)


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: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
problem_activity: Optional activity
Earlier in this lesson, students found the area of regions around circles and the area of fractions of circles in separate problems. In this activity, students combine these two strategies to find the area of a complex real-world object. Students engage in MP2 as they decide how to decompose the running track into measurable pieces and how to use the given information about the dimensions of the track to calculate areas.
Launch
Arrange students in groups of 2. Give students 3–4 minutes of partner work time followed by small-group and whole-class discussions.
Action and Expression: Internalize Executive Functions.
Provide students with a graphic organizer to organize the information provided in the problem and to structure their problem-solving strategy. The graphic organizer should include the prompts: “What do I need to find out?”, “What do I need to do?”, “How I solved the problem.”, and “How I know my answer is correct.”
Supports accessibility for: Language; Organization
Student Facing
The field inside a running track is made up of a rectangle 84.39 m long and 73 m wide, together with a half-circle at each end. The running lanes are 9.76 m wide all the way around.
[IMG]
What is the area of the running track that goes around the field? Explain or show 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.
Anticipated Misconceptions
Some students may think they can calculate the area of the running track by multiplying half of the perimeter times the radius, as if the shape were just a circle. Prompt them to see that they need to break the overall shape into rectangular and circular pieces.
Activity Synthesis
Pair the groups of 2 to create groups of 4. Have students compare answers and explain their reasoning until they reach an agreement.
As a whole group, discuss how finding the area of the track in this activity was similar or different to solving the two area problems in the previous activity. Make sure to highlight these points:
Like the first problem in the previous activity, finding the area of the track can be done by finding the area of the larger shape (the track and the field inside) and then taking away the area of the field inside.
Like the second problem in the previous activity, there are semicircles whose area can be found by composing them to make a full circle or by taking half the area of the corresponding full circle.
Representing, Speaking, Listening: MLR7 Compare and Connect.
Ask students to prepare a visual display that shows how they calculated the area of the running track that goes around the field, and look for students with different strategies for calculating the area of the curved parts of the track. As students investigate each other’s work, ask students to share what worked well in a particular approach. During this discussion, listen for and amplify any comments that clarify that the curved parts of the running track are half circles with a smaller circle missing from the inside. Then encourage students to make connections between the quantities representing areas and the shapes in the diagram. Ask questions such as, “What does the quantity 6,719.561 represent in the diagram?” and “What does the quantity 4,183.265 represent in the diagram?” During this discussion, listen for and amplify language students use to reason that these quantities represent the areas of larger and smaller circles, respectively. This will foster students’ meta-awareness and support constructive conversations as they compare strategies for finding the area of a complex real-world object.
Design Principle(s): Cultivate conversation; Maximize meta-awareness


aligns: no