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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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)


Standard options: 
A. Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.
B. Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.
C. 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.”)


Your response, in json format:
{
  "explanation": "This activity asks students to compose three-dimensional shapes, using geoblocks, to create composite shapes.",
  "answer": "C"
}

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: im_lesson_009431

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options: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.  For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
problem_activity: Warm-up
The goal of this warm-up is to review the meaning of a function presented graphically. While students do not need to use function notation here, interpreting the graph in terms of the context will prepare them for their work with functions in the rest of the unit.
Launch
Tell students to close their books or devices. Display the graph for all to see. Ask students to observe the graph and be prepared to share one thing they notice and one thing they wonder. Select students to briefly share one thing they noticed or wondered to help ensure all students understand the information conveyed in the graph. Ask students to open their books or devices and answer the questions about the graph. Follow with a whole-class discussion.
Student Facing
Here is a graph of the accumulated rainfall in Las Vegas, Nevada, in the first 60 days of 2017.
[IMG]
Use the graph to support your answers to the following questions.
Is the accumulated amount of rainfall a function of time?
Is time a function of accumulated rainfall?
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
If students struggle to see from the graph how the accumulated rainfall is a function of time but time is not a function of accumulated rainfall, consider displaying the data in a table. Shown here is the data for the first 20 days of 2017. Help students see that for every value of
\(t\)
, the time in days, there is one value of
\(r\)
, the accumulated rainfall in inches, but this is not true the other way around.
{"table": [{"_attributes": {"border": "1", "class": ["c-table-compressed"]}, "tbody": [{"tr": [{"th": [{"_attributes": {"scope": "row"}, "span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "166"}, "_value": "\\(t\\)"}], "_value": "(days)"}], "td": [{"_value": "1"}, {"_value": "2"}, {"_value": "3"}, {"_value": "4"}, {"_value": "5"}, {"_value": "6"}, {"_value": "7"}, {"_value": "8"}, {"_value": "9"}, {"_value": "10"}, {"_value": "11"}, {"_value": "12"}, {"_value": "13"}, {"_value": "14"}, {"_value": "15"}, {"_value": "16"}, {"_value": "17"}, {"_value": "18"}, {"_value": "19"}, {"_value": "20"}]}, {"th": [{"_attributes": {"scope": "row"}, "span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "832"}, "_value": "\\(r\\)"}], "_value": "(inches)"}], "td": [{"_value": "0"}, {"_value": "0"}, {"_value": "0"}, {"_value": "0"}, {"_value": "0"}, {"_value": "0"}, {"_value": "0"}, {"_value": "0"}, {"_value": "0"}, {"_value": "0"}, {"_value": "0"}, {"_value": "0.03"}, {"_value": "0.1"}, {"_value": "0.1"}, {"_value": "0.1"}, {"_value": "0.1"}, {"_value": "0.1"}, {"_value": "0.1"}, {"_value": "0.11"}, {"_value": "0.38"}]}]}]}]}
Activity Synthesis
Make sure students understand why the accumulated rain is a function of time but not the other way around.
Then, recall the notation for writing, using function notation, accumulated rain fall as a function of time. If
\(r\)
represents the amount of rainfall in inches and
\(t\)
is time in days, then
\(r(t)\)
is the amount of rain that has fallen in the first
\(t\)
days of 2017. For example,
\(r(2) = 0\)
tells us that the accumulated rainfall after in the first two days of the year was 0 inches.
\(r(48)=1\)
means that there was 1 inch of accumulated rain in the first 48 days of the year. Ask students to write and explain the meaning of a few other statements using function notation.


correct_option_index: 0

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