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: 
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: 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.
problem_activity: In Class Launch
Use after Unit 4, Lesson 16
Ask students to give examples of situations where there is exponential change (population growth, compounding interest, radioactive decay). Write down students’ ideas for all to see.
Then ask students for an example of an exponential function (
\(y=2e^{\text-t}\)
). Write it for all to see. Here are some possible questions for discussion:
“What situation could this function model?” (Since the exponent is negative, this models decay. The coefficient of the exponential part is 2, so the initial value is 2. The amount is divided by
\(e\)
every time
\(t\)
increases by 1. So it’s a small amount of something and it’s decreasing. How fast it decreases depends on what
\(t\)
represents.)
“What questions about a situation could this function help you answer?” (I could find out what
\(t\)
is when the value of the function is a specific number, like 0.01. If
\(t\)
represents time, I could find out how often the value of the function doubles.)
Tell students that in this task they will ask and answer their own questions about a situation that can be modeled with an exponential function.
Teacher Instructions
After students have finished the task, they should see what questions were asked about each situation. One way to do this would be to have groups that looked at the same situation get together to compare their questions and the assumptions they made about the situation. Groups that made up their own situations can get together and share what they did. Then one or two representatives from each large group can summarize the discussion for the whole class.
Student-Facing Statement
Choose one of these situations to think about, or write a similar one of your own:
There are currently 61 million cars in a certain country, increasing by 6% annually.
A vampire enters a town. He looks around for about an hour, and then chooses someone to bite. The person he bit is now also a vampire. Both of them take an hour to choose new victims, and then they each bite someone. All the vampires continue choosing victims in the same way.
The population in millions,
\(W\)
, of the country of West Mathlandia is modeled by
\(W(x) = 17.9e^{0.0015x}\)
, where
\(x\)
is the number of years since September 1998. The population in millions,
\(E\)
, of East Mathlandia is modeled by
\(E(x) = 13.5e^{0.0128x}\)
.
There are 10,000 bacteria in a petri dish. The population of bacteria declines to 4,000 in 4 hours.
An artifact is discovered. It has 57% of the carbon-14 it originally contained. Carbon-14 decays at the rate of 0.0125% per year.
The number of books,
\(B\)
, in a small library increases according to the function
\(B = 5,\!300e^{0.02t}\)
, where
\(t\)
is measured in years.
The growth in the population,
\(P\)
, of a certain species of rodent at a landfill is modeled by the exponential function
\(P(t)= 648e^{0.016t}\)
, where
\(t\)
is the number of years since 1987.
The initial mass of a certain compound is 448 g, and every 27 hours it decreases by half.
Write down questions you could ask about the situation you chose. Write as many questions as you can think of. As a group, you will choose some interesting questions to answer. If you would need to do calculations, make a sketch, or draw a graph in order to answer a question, then it’s probably an interesting question.
You should answer 2 questions for every person in your group. Multiple people can work on a question together—each person in the group does not have to answer 2 questions by themselves.
Write a report to explain your questions and answers. The report should include:
A context for your situation. Write a story that includes all the relevant information. If the description of the situation is missing some details, fill them in however you want.
An equation to describe the situation, with an explanation of what each part of the equation represents.
A labeled graph of the situation.
The questions you chose and your answers. Include your process for finding the answers. Say what the answers mean in the context of this situation.
Teacher Instructions
After students have finished the task, they should see what questions were asked about each situation. One way to do this would be to have groups that looked at the same situation get together to compare their questions and the assumptions they made about the situation. Groups that made up their own situations can get together and share what they did. Then one or two representatives from each large group can summarize the discussion for the whole class.
Student-Facing Statement
Choose one of these situations to think about, or write a similar one of your own:
A vampire enters a town. He looks around for about an hour, and then chooses someone to bite. The person he bit is now also a vampire. Both of them take an hour to choose new victims, and then they each bite someone. All the vampires continue choosing victims in the same way.
The population in millions,
\(W\)
, of the country of West Mathlandia is modeled by
\(W(x) = 17.9e^{0.0015x}\)
, where
\(x\)
is the number of years since September 1998. The population in millions,
\(E\)
, of East Mathlandia is modeled by
\(E(x) = 13.5e^{0.0128x}\)
.
There are 10,000 bacteria in a petri dish. The population of bacteria declines to 4,000 in 4 hours.
The number of books,
\(B\)
, in a small library increases according to the function
\(B = 5,\!300e^{0.02t}\)
, where
\(t\)
is measured in years.
The growth in the population,
\(P\)
, of a certain species of rodent at a landfill is modeled by the exponential function
\(P(t)= 648e^{0.016t}\)
, where
\(t\)
is the number of years since 1987.
Write down questions you could ask about the situation you chose. Write as many questions as you can think of. As a group, you will choose some interesting questions to answer. If you would need to do calculations, make a sketch, or draw a graph in order to answer a question, then it's probably an interesting question. To get you started, here are some example questions you could ask about each situation:
If there are 200 people in the town, how long will it be before all of them are vampires?
Will the populations of East and West Mathlandia ever be the same, and if so, when?
How much does the population of bacteria decline each hour?
How long will it be before the library has 1 million books?
How many rodents were born between 1987 and now?
You should answer 2 questions for every person in your group. Multiple people can work on a question together—each person in the group does not have to answer 2 questions by themselves.
Write a report to explain your questions and answers. The report should include:
A context for your situation. Write a story that includes all the relevant information. If the description of the situation is missing some details, fill them in however you want.
An equation to describe the situation, with an explanation of what each part of the equation represents.
A labeled graph of the situation.
The questions you chose and your answers. Include your process for finding the answers. Say what the answers mean in the context of this situation.


aligns: yes