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: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
problem_activity: Activity
This activity is a continuation of the previous one. Students match each situation from the previous activity with an equation, solve the equation by any method that makes sense to them, and interpret the meaning of the solution. Students are still using any method that makes sense to them to reason about a solution. In later lessons, a hanger diagram representation will be used to justify more efficient methods for solving. For example, when they are using tape diagrams, they could just say “I subtracted the 9 extra markers and then divided the remaining 21 markers by 7.” Later, when working with hanger diagrams, we can press them to say “I can subtract 9 from each side and then divide each side by 7.”
For each equation, monitor for a student using their diagram to reason about the solution and a student using the structure of the equation to reason about the solution.
Launch
Keep students in the same groups. 5 minutes to work individually or with a partner, followed by a whole-class discussion.
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 “To find the solution, first I ____ because...”, “I made this match because I noticed...”, “Why did you...?”, or “I agree/disagree because…”
Supports accessibility for: Language; Social-emotional skills
Student Facing
Each situation in the previous activity is represented by one of the equations.
\(7x+9=30\)
\(30=9x+7\)
\(30x+7=9\)
Match each situation to an equation.
Find the solution to each equation. Use your diagrams to help you reason.
What does each solution tell you about its situation?
Student Response
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for free access to Student Response.
Student Facing
Are you ready for more?
While in New York City, is it a better deal for a group of friends to take a taxi or the subway to get from the Empire State Building to the Metropolitan Museum of Art? Explain your reasoning.
Student Response
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for free access to Extension Student Response.
Activity Synthesis
For each equation, ask one student who reasoned with the diagram and one who reasoned only about the equation to explain their solutions. Display the diagram and the equation side by side, drawing connections between the two representations. If no students bring up one or both of these approaches, demonstrate maneuvers on a diagram side by side with maneuvers on the corresponding equation. For example, “I subtracted the 9 extra markers and then divided the remaining 21 markers by 7,” can be shown on a tape diagram and on a corresponding equation. It is not necessary to invoke the more abstract language of “doing the same thing to each side” of an equation yet.
Speaking, Representing: MLR3 Clarify, Critique, Correct.
Present an incorrect match of an equation with a situation and/or diagram (e.g.,
\(30 = 9x + 7\)
with Situation 1). Invite students to clarify and then critique the error (e.g., there are 7 packs of an unknown amount of markers in Situation 1; not 9 as illustrated in the equation). Press for details, if needed. For example, students can reference “markers” in Situation 1, not “x”, as the unknown value represent by the variable
\(x\)
. This will help students reflect on the quantity of the unknown values that would be a reasonable solution and improve on their reasoning when matching an equation to a situation.
Design Principle(s): Optimize output (for justification)


aligns: yes