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: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
problem_activity: Optional activity
In this partner activity, students take turns matching a sequence to a definition. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).
One sequence and one definition do not have matches. Students are tasked with writing the corresponding match.
Monitor for students using clear reasoning as they create a recursive definition for the sequence 18, 20, 22, 24 to share during the discussion.
Making a spreadsheet available gives students an opportunity to choose appropriate tools strategically (MP5).
Launch
Arrange students in groups of 2. Tell students that for each sequence, one partner finds its matching recursive definition and explains why they think it matches. The partner's job is to listen and make sure they agree. If they don't agree, the partners discuss until they come to an agreement. For the next sequence, the students swap roles. If necessary, demonstrate this protocol before students start working.
Ensure that students notice that one sequence and one definition do not have matches, and they are tasked with writing the corresponding match for each.
Conversing: MLR8 Discussion Supports.
Use this routine to support small-group discussion as students should take turns finding a match. Display the following sentence frames for all to see: "Sequence _____ and definition _____ match because . . .” and “I noticed _____, so I matched . . .” Encourage students to challenge each other when they disagree, and to press for precise mathematical language. This will help students clarify their reasoning about each match.
Design Principle(s): Support sense-making; Maximize meta-awareness
Engagement: Provide Access by Recruiting Interest.
Leverage choice around perceived challenge. Invite groups of students to find matches for at least 4 of the sequences. Chunking this task into more manageable parts may also support students who benefit from additional processing time.
Supports accessibility for: Organization; Attention; Social-emotional skills
Student Facing
Take turns with your partner to match a sequence with a recursive definition. It may help to first figure out if the sequence is arithmetic or geometric.
For each match that you find, explain to your partner how you know it’s a match.
For each match that your partner finds, listen carefully to their explanation. If you disagree, discuss your thinking and work to reach an agreement.
There is one sequence and one definition that do not have matches. Create their corresponding match.
Sequences:
3, 6, 12, 24
18, 36, 72, 144
3, 8, 13, 18
18, 13, 8, 3
18, 9, 4.5, 2.25
18, 20, 22, 24
Definitions:
\(G(1)=18, G(n)=\frac12 \boldcdot G(n-1), n\ge2\)
\(H(1)=3, H(n)=5 \boldcdot H(n-1), n\ge2\)
\(J(1)=3, J(n)=J(n-1)+5, n\ge2\)
\(K(1)=18, K(n)=K(n-1)-5, n\ge2\)
\(L(1)=18, L(n)=2 \boldcdot L(n-1), n\ge2\)
\(M(1)=3, M(n)=2 \boldcdot M(n-1), n\ge2\)
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
Some students may not be sure how to begin matching terms in a sequence to a definition. Encourage them to start by picking a definition and calculating the first few terms of the sequence it represents.
Activity Synthesis
Once all groups have completed the matching, ask “How did you decide which definitions to match to sequence 3, 6, 12, 24 and sequence 18, 36, 72, 144 when they both involve doubling?” (They are both geometric with a growth factor of 2, but since they have different first terms you can use those to match the sequences to
\(M\)
and
\(L\)
.)
Next, invite previously identified students to share the recursive definition they created for sequence 18, 20, 22, 24 and their strategy for writing it.
If time allows and students need extra practice graphing functions, assign students one function each from the task statement to sketch a graph for. After work time, select students to share their sketches, displaying them for all to see and compare.


aligns: yes