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)


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:
C

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

1
options: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
problem_activity: Activity
The purpose of this activity is to show how a context can impose restrictions on the domain and range of a function. Given a description of a context, students determine the restrictions on the domain and range imposed by the context. Considering how a context restricts the domain or range of a function modeling it is an important part of mathematical modeling (MP4). This prepares students to interpret exponential functions and make sense of whether the graph should be discrete or continuous in the associated Algebra 1 lesson.
Launch
Remind students that domain refers to possible values of the independent variable, and range refers to possible values of the dependent variable. Use a few examples from the previous activity to illustrate. For example, for the cab ride, the domain is all numbers that are greater than 0, and the range is all numbers that are greater than 3.5. This presumes that a ride must have some distance (it can’t be 0 miles long), and can be any number of miles long. A modeler might decide not to consider any cab rides that are longer than, say, 100 miles, in which case the domain would be all numbers between 0 and 100. Sometimes restrictions on the domain are a decision made by the modeler. In contrast, for the function modeling the admission price to the park based on number of people, the domain only contains whole, positive numbers, since the number of people must be a whole, positive number.
Arrange students in groups of 2. After a few minutes of quiet work time, ask students to compare their responses to their partner’s and decide if they are both correct, even if they look different. Follow with a whole-class discussion.
Student Facing
To make sense in a given context, many functions need restrictions on the domain and range. For each description of a function
describe the domain and range
describe what its graph would look like (separate dots, or connected?)
weight of a puppy as a function of time
number of winter coats sold in a store as a function of temperature outside
number of books in a library as a function of number of people who live in the community the library serves
height of water in a tank as a function of volume of water in the tank
amount of oxygen in the atmosphere as a function of elevation above or below sea level
thickness of a folded piece of paper as a function of number of folds
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
Much discussion takes place between partners. Invite students to share how they determined the domain and range of the function representing the context. Ask if other groups have different responses. Choose as many different groups as time allows. Attend to the language that students use to describe their pairing, giving them opportunities to describe their relationships more precisely.


correct_option_index: 0