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: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
problem_activity: Optional activity
In this activity, students explore percentages that describe parts of a whole. They find both
\(B\)
and
\(C\)
, where
\(A\%\)
of
\(B\)
is
\(C\)
, in the context of available and consumed water on a hike.
Students who use a double number line may notice that the value of
\(B\)
is the same in both questions, so the same double number line can be used to solve both parts of the problem. To solve the second question, however, the diagram needs to be partitioned with more tick marks.
As in the previous task, students may solve using other strategies, including by simply multiplying or dividing, i.e.,
\((1.5) \boldcdot 2 = 3.0\)
and
\(\frac{80}{100} \boldcdot (3.0) = 2.4\)
. Encourage them to also explain their reasoning with a double number line, table, or tape diagram. Monitor for at least one student using each of these representations.
Launch
Give students quiet think time to complete the activity and then time to share their explanation with a partner. Follow with a whole-class discussion.
Student Facing
During the first part of a hike, Andre drank 1.5 liters of the water he brought.
If this is 50% of the water he brought, how much water did he bring?
If he drank 80% of his water on his entire hike, how much did he drink?
Student Response
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Student Facing
Are you ready for more?
Decide if each scenario is possible.
Andre plans to bring his dog on his next hike, along with 150% as much water as he brought on this hike.
Andre plans to drink 150% of the water he brought on his hike.
Student Response
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for free access to Extension Student Response.
Anticipated Misconceptions
After students create a double number line diagram with tick marks at 50% and 100%, some may struggle to know how to fit 80% in between. Encourage them to draw and label tick marks at 10% increments or work with a table instead. Some students may think that the second question is asking for the amount of water Andre drank on the second part of the hike. Clarify that it is asking for his total water consumption on the entire hike.
Activity Synthesis
Select 1–2 students who used a double number line, a table of equivalent ratios, and a tape diagram to share their strategies. As students explain, illustrate and display those representations for all to see.
Ask students how they knew what 100% means in the context. At this point it is not necessary for students to formally conceptualize the two ways percentages are used (to describe parts of whole, and to describe comparative relationships). Drawing their attention to concrete and contextualized examples of both, however, serves to build this understanding intuitively.
Reading, Writing, Speaking: MLR3 Clarify, Critique, Correct.
Before students share their answers for the second question, present an incorrect answer and explanation. For example, “If Andre drank 80% of his water on his entire hike, then he drank 1.2 liters of water because 0.8 times 1.5 liters is 1.2 liters.” Ask students to identify the error, critique the reasoning, and write a correct explanation. As students discuss in partners, listen for students who identify and clarify the assumption in the statement. For example, the author assumed that Andre brought 1.5 liters for his entire hike; however, the problem states that Andre drank 1.5 liters of the water he brought. This will remind students to carefully identify the quantity they are finding a percentage of.
Design Principle(s): Optimize output (for explanation); Maximize meta-awareness


aligns: yes