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: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
problem_activity: Optional activity
This activity is optional. It gives students an opportunity to reason about and to graph the rules of piecewise functions without a context.
Students are given the equations that define two piecewise functions, along with strips of paper, each containing a part of a graph and a portion of the horizontal axis (no scale is shown). Their job is to arrange the strips, apply a scale on each axis, and add open and closed circles to the graph to accurately represent the function values at each interval of input.
Unlike the piecewise functions students saw earlier in the lesson, each function here contains intervals defined by non-constant linear expressions. Support students as needed in reasoning about those intervals. If desired, this activity could be done over two class periods. (Students could piece together the graph of the first function in one class period and do the same for the second function at another time.)
To create an accurate graph, students need to make sense of the values, expressions, and inequality symbols in each equation and persevere in discerning their connections to the graph (MP1).
Here are images of the graphs on the blackline master for reference and planning. Cut each graph along the dashed lines and the vertical axis before giving it to students.
Function
\(f\)
[IMG]
Function
\(g\)
[IMG]
Launch
Arrange students in groups of 2–3. Give each group the strips for function
\(f\)
(pre-cut from the blackline master), glue or glue stick, and a sheet of paper on which to adhere the pieces.
Tell students that they are to arrange the pieces according to the rules that define
\(f\)
, as shown in the activity statement, and to add a label and a scale to each axis after the pieces are arranged. Explain that each piece contains a part of the horizontal axis, and the gridlines are 1 unit apart. Encourage students to double check their graph before gluing the pieces on another sheet of paper.
Consider discussing students' graphs of function
\(f\)
before giving students the pieces for function
\(g\)
and asking them to do another round.
Student Facing
Your teacher will give your group strips of paper with parts of a graph of a function. Gridlines are 1 unit apart.
Arrange the strips of paper to create a graph for each of the following functions.
\(\displaystyle f(x)=\begin{cases} \begin{align} \text-5,&\qquad \text-10< x< \text-5 \\ x,&\qquad \text-5\leq x< 0 \\ 1, &\qquad 0\leq x< 3\\ x-2, &\qquad 3\leq x< 8\\6, &\qquad 8\leq x < 1 0\ \end{align} \end{cases}\)
\(\displaystyle g(x)=\begin{cases} \begin{align} 5.5,&\qquad \text-10< x\leq \text-8 \\ 4,&\qquad \text-8< x\leq \text-3 \\ \text-x, &\qquad \text-3< x\leq 2\\ \text-3.5, &\qquad 2< x\leq 5 \\ x-5, &\qquad 5< x\leq 10 \end{align} \end{cases}\)
To accurately represent each function, be sure to include a scale on each axis and add open and closed circles on the graph where appropriate.
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
Invite students to display their completed graphs and their reasoning. In particular, discuss how students determined the appearance of the intervals defined by non-constant linear expressions such as
\(x\)
,
\(x-4\)
, or
\(\text-x\)
.
If different groups created different graphs for the same function, ask them to analyze one another's work and try to reach an agreement.
If time permits, ask students to identify the domain and range of each function.
Speaking, Representing: MLR8 Discussion Supports.
Make sure students can explain their visual display and how they reasoned about the rules for different intervals. If needed, give them additional time to prepare their explanation. Invite groups to rehearse what they will say when they share with the whole class. Rehearsing provides students with additional opportunities to speak and clarify their thinking, and will improve the quality of explanations shared during the whole-class discussion.
Design Principle(s): Support sense-making; Cultivate conversation


correct_option_index: 2