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
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
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: 
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.”)

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

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_pos_0

1
standard_description: Write a function that describes a relationship between two quantities.
problem_activity: Activity
The purpose of this activity is for students to work with a function where either variable could be the independent variable. Knowing the total value for an unknown number of dimes and quarters, students are first asked to consider if the number of dimes could be a function of the number of quarters and then asked if the reverse is also true. Since this isn't always the case when students are working with functions, the discussion should touch on reasons for choosing one variable vs. the other, which can depend on the types of questions one wants to answer.
Identify students who efficiently rewrite the original equation in the third problem and the last problem to share during the discussion.
Launch
Arrange students in groups of 2. Give students 3–5 minutes of quiet work time followed by partner discussion for students to compare their answers and resolve any differences. Follow with a whole-class discussion.
Representation: Internalize Comprehension.
Provide appropriate reading accommodations and supports to ensure students access to written directions, word problems and other text-based content.
Supports accessibility for: Language; Conceptual processing
Reading: MLR6 Three Reads.
Use this routine to support reading comprehension and to set students up to interpret the representations of the situation provided in the task statement (an equation) and discussion (function diagrams). In the first read, students read the information with the goal of comprehending the situation (e.g., Jada has dimes and quarters). In the second read, ask students to identify important quantities. Listen for, and amplify, naming of the quantities that vary in relation to each other in this situation: number of dimes, total value of dimes, number of quarters, total value of quarters. After the third read, ask students to discuss possible strategies to answer the questions that follow, paying attention to the different coin values, and how each question is phrased. This will help students comprehend the problem and make sense of important quantities and variables when working with a function in which either variable could be the independent variable.
Design Principle(s): Support sense-making
Student Facing
Jada had some dimes and quarters that had a total value of
$
12.50. The relationship between the number of dimes,
\(d\)
, and the number of quarters,
\(q\)
, can be expressed by the equation
\(0.1d + 0.25q = 12.5\)
.
If Jada has 4 quarters, how many dimes does she have?
If Jada has 10 quarters, how many dimes does she have?
Is the number of dimes a function of the number of quarters? If yes, write a rule (that starts with
\(d = \)
...) that you can use to determine the output,
\(d\)
, from a given input,
\(q\)
. If no, explain why not.
If Jada has 25 dimes, how many quarters does she have?
If Jada has 30 dimes, how many quarters does she have?
Is the number of quarters a function of the number of dimes? If yes, write a rule (that starts with
\(q=\)
...) that you can use to determine the output,
\(q\)
, from a given input,
\(d\)
. If no, explain why not.
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 be unsure how to write rules for the number of dimes as a function of the number of quarters and vice versa. Prompt them to use the provided equation and what they know about keeping equations equal to create the new equations.
Activity Synthesis
Select previously identified students to share their rules for dimes as a function of the number of quarters and quarters as a function of the number of dimes, including the steps they used to rewrite the original equation.
Tell students that if we write an equation like
\(d = 125 - 2.5q\)
, this shows that
\(d\)
is a function of
\(q\)
because it is clear what the output (value for
\(d\)
) should be for a given input (value for
\(q\)
).
Display the diagrams for all to see:
[IMG]
When we have an equation like
\(0.1d + 0.25q = 12.5\)
, we can choose either
\(d\)
or
\(q\)
to be the independent variable. That means we are viewing one as depending on the other. If we know the number of quarters and want to answer a question about the number of dimes, it is helpful to write
\(d\)
as a function of
\(q\)
. If we know the number of dimes and want to answer a question about the number of quarters, it is helpful to write
\(q\)
as a function of
\(d\)
.
Ensure students understand that we can’t always do this type of rearranging with equations and have it make sense because sometimes only one variable is a function of the other, and sometimes neither is a function of the other. For example, students saw earlier that while squaring values is a function, the reverse—that is, identifying what value was squared—is not. We will continue to explore when these different things happen in future lessons.


aligns: no