few_shots: Example:
Problem/activity:
Problem 1
Solve using the standard algorithm. If you get stuck, use an area model and/or the partial products algorithm to help. Then assess the reasonableness of your answer.
a.
$$5,803\times46$$
b.
$$63\times2,116$$
Problem 2
Dunkin' introduced a croissant doughnut in 2014. In the first three months of its debut, they sold 7,870 dozen of them per day. How many croissant doughnuts were sold in the first three months?


Mathematical concept/skill options: 
A. Use place value understanding and properties of operations to perform multi-digit arithmetic. (A range of algorithms may be used.)
B. Understand place value.
C. Understand the place value system.
D. Extend the counting sequence.
E. Work with numbers 11–19 to gain foundations for place value.
F. Use place value understanding and properties of operations to perform multi-digit arithmetic.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
G. Perform operations with multi-digit whole numbers and with decimals to hundredths.
H. Generalize place value understanding for multi-digit whole numbers.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
I. Use place value understanding and properties of operations to add and subtract.


Your response:
{
  "explanation": "This set of problems asks students to perform multiplication, which is an operation, on multi-digit whole numbers.",
  "answer": "G"
}

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_000674

5
options: Understand the concept of a function and use function notation.

Prove and apply trigonometric identities.

Build new functions from existing functions.

Build a function that models a relationship between two quantities.

Analyze functions using different representations.

Model periodic phenomena with trigonometric functions.

Interpret functions that arise in applications in terms of the context.

Use functions to model relationships between quantities.

Define, evaluate, and compare functions.

Extend the domain of trigonometric functions using the unit circle.

Interpret expressions for functions in terms of the situation they model.

Construct and compare linear and exponential models and solve problems.
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
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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.


correct_option_index: 0