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: Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
problem_activity: Activity
The purpose of this activity is to review how to create a scatter plot using technology and come up with a function to model the data. This work is similar to the work in the associated Algebra 1 lesson, but includes more explicit instructions and steps toward analyzing data and choosing an appropriate model (MP4).
Launch
Display the table of data for all to see, and ask students whether they think a linear or exponential model would be a better fit for this data. After a minute of quiet think time, ask a few students to share their reasoning.
If needed, demonstrate using graphing technology to input the given data and create a scatter plot.
If the graphing technology platform you are using allows it, consider showing students how to create sliders. In Desmos, simply type
\(y=mx+c\)
in the expressions list, and then click “all” to add sliders for both
\(m\)
and
\(c\)
. You may need to adjust the maximum value of one or both sliders to be able to use them to create a good model for this data.
Student Facing
In the spring, an agave plant sends up a flower spike. Here are some data collected from an agave plant in a garden in Tucson, AZ, starting on April 2:
[IMG]
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}, "_value": "day"}, {"_attributes": {"scope": "col"}, "_value": "height in inches"}]}]}], "tbody": [{"tr": [{"td": [{"_value": "0"}, {"_value": "17"}]}, {"td": [{"_value": "1"}, {"_value": "23"}]}, {"td": [{"_value": "2"}, {"_value": "29"}]}, {"td": [{"_value": "3"}, {"_value": "37"}]}, {"td": [{"_value": "4"}, {"_value": "45"}]}, {"td": [{"_value": "5"}, {"_value": "52"}]}, {"td": [{"_value": "6"}, {"_value": "62"}]}, {"td": [{"_value": "7"}, {"_value": "70"}]}, {"td": [{"_value": "8"}, {"_value": "80"}]}]}]}]}
Use graphing technology to create a scatter plot, using days as the first coordinate and height as the second coordinate.
Would a linear or exponential model be a better fit for this data?
Create a function that is a good model for the data. If you chose an exponential model, start with the equation
\(y=a \boldcdot b^x\)
and select values for
\(a\)
and
\(b\)
. If you chose a linear model, start with the equation
\(y=mx+c\)
, and select values for
\(m\)
and
\(c\)
.
Graph your equation on that same coordinate plane as your scatter plot. Adjust the numbers you used in the equation to improve your model.
Explain what each number in your equation means in this situation.
Use your model to predict the height of the flower spike on day 10.
Describe any limitations on the domain of the function modeling the data.
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 the scatter plot using technology. Explore some of the different equations students used as a model. Discuss which model is the better fit, and what makes a model a good fit. Invite students to share their responses to the last three questions.


aligns: no