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: 
Recognize area as an attribute of plane figures and understand concepts of area measurement.

Answer: 
No. This activity does not teach students area as an attribute of plane figures. Instead, the activity focuses on solid, three-dimensional figures.

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_neg_0

1
standard_description: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
problem_activity: Activity
This task contains two distinct parts. Depending on what students need and time constraints, you could decide to do either or both.
In the associated Algebra 1 lesson, students will need to evaluate the functions
\(6x^2\)
and
\(3^x\)
for different input values. The purpose of the first part is to prepare them to avoid some common mistakes. Analyzing and correcting incorrect work is an opportunity to critique the reasoning of others (MP3).
The purpose of the second part is to revisit ways to tell whether a function is linear, quadratic, or exponential, and to practice the skills of generating a table and sketching a graph for a given function.
Student Facing
Different students are evaluating two expressions,
\(3\boldcdot 6^x\)
and
\(5^x\)
. Analyze their work, describe any errors made, and then evaluate each expression correctly.
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "row"}}, {"_attributes": {"scope": "col"}, "_value": "Noah\u2019s work"}, {"_attributes": {"scope": "col"}, "_value": "Mai\u2019s work"}, {"_attributes": {"scope": "col"}, "_value": "corrected work"}]}]}], "tbody": [{"tr": [{"th": [{"_attributes": {"scope": "row"}, "span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "11191"}, "_value": "\\(5^x\\)"}, {"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "50"}, "_value": "\\(x\\)"}], "_values": ["Evaluate", "when", "is 6."]}], "td": [{"p": [{"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "11191"}, "_value": "\\(5^x\\)"}]}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "29657"}, "_value": "\\(5^6\\)"}]}, {"_value": "30"}]}, {"p": [{"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "11191"}, "_value": "\\(5^x\\)"}]}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "29657"}, "_value": "\\(5^6\\)"}]}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "failed-conversion"}, "_value": "\\(6 \\boldcdot 6 \\boldcdot\u00a06 \\boldcdot\u00a06 \\boldcdot6\\)"}]}, {"_value": "7,776"}]}, {}]}, {"th": [{"_attributes": {"scope": "row"}, "span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "9091"}, "_value": "\\(3 \\boldcdot 6^x\\)"}, {"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "50"}, "_value": "\\(x\\)"}], "_values": ["Evaluate", "when", "is 2."]}], "td": [{"p": [{"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "failed-conversion"}, "_value": "\\(3 \\boldcdot\u00a06^x\\)"}]}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "29795"}, "_value": "\\(3\\boldcdot 6^2\\)"}]}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "29846"}, "_value": "\\(3 \\boldcdot 12\\)"}]}, {"_value": "36"}]}, {"p": [{"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "9091"}, "_value": "\\(3 \\boldcdot 6^x\\)"}]}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "29893"}, "_value": "\\(3 \\boldcdot 6^2\\)"}]}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "24976"}, "_value": "\\(18^2\\)"}]}, {"_value": "324"}]}, {}]}]}]}]}
Here are three functions. For each function:
Complete the table of values.
Sketch a graph.
Decide whether each function is linear, quadratic, or exponential, and be prepared to explain how you know.
\(f(x)=3 \boldcdot 2^x\)
{"table": [{"_attributes": {"border": "1"}, "tbody": [{"tr": [{"th": [{"_attributes": {"scope": "row"}, "span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "50"}, "_value": "\\(x\\)"}]}], "td": [{"_value": "-1"}, {"_value": "0"}, {"_value": "1"}, {"_value": "2"}, {"_value": "3"}, {"_value": "5"}]}, {"th": [{"_attributes": {"scope": "row"}, "span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "287"}, "_value": "\\(f(x)\\)"}]}], "td": [{}, {}, {}, {}, {}, {}]}]}]}]}
[IMG]
\(g(x)=3 \boldcdot x^2\)
{"table": [{"_attributes": {"border": "1"}, "tbody": [{"tr": [{"th": [{"_attributes": {"scope": "row"}, "span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "50"}, "_value": "\\(x\\)"}]}], "td": [{"_value": "-1"}, {"_value": "0"}, {"_value": "1"}, {"_value": "2"}, {"_value": "3"}, {"_value": "5"}]}, {"th": [{"_attributes": {"scope": "row"}, "span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "970"}, "_value": "\\(g(x)\\)"}]}], "td": [{}, {}, {}, {}, {}, {}]}]}]}]}
[IMG]
\(h(x)=3 \boldcdot 2x\)
{"table": [{"_attributes": {"border": "1"}, "tbody": [{"tr": [{"th": [{"_attributes": {"scope": "row"}, "span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "50"}, "_value": "\\(x\\)"}]}], "td": [{"_value": "-1"}, {"_value": "0"}, {"_value": "1"}, {"_value": "2"}, {"_value": "3"}, {"_value": "5"}]}, {"th": [{"_attributes": {"scope": "row"}, "span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "1834"}, "_value": "\\(h(x)\\)"}]}], "td": [{}, {}, {}, {}, {}, {}]}]}]}]}
[IMG]
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
For the first part, invite students to describe the errors they see, and share how to correctly evaluate each expression.
For the second part, display the tables and graphs for all to see. Ask students to share some ways they can tell a function is linear, exponential, or quadratic using the different representations. For example:
The graph of the linear function is a straight line.
The table shows the exponential function has a growth factor of 2. Each time
\(x\)
increases by 1, the
\(f(x)\)
values increase by a factor of 2.
The table shows the quadratic function does not have a constant rate of change or a constant growth factor.


aligns: no