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.

Extend the domain of trigonometric functions using the unit circle.

Build new functions from existing functions.

Model periodic phenomena with trigonometric functions.

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

Analyze functions using different representations.

Define, evaluate, and compare functions.

Construct and compare linear and exponential models and solve problems.

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

Use functions to model relationships between quantities.

Build a function that models a relationship between two quantities.

Prove and apply trigonometric identities.
problem_activity: Activity
In this warm-up, students make sense of a linear function with a negative rate of change, set in a familiar context. Students have seen similar relationships between the amount of water in a tank and time in an earlier unit (on solving and graphing equations). Here, they think about the quantities in terms of input and output, interpret statements in function notation, and sketch a graph of the function.
The work here prepares students to find and interpret the inverse of functions written in function notation, and to use inverse functions to solve problems.
Launch
Arrange students in groups of 2. Provide access to scientific or four-function calculators, if requested.
Student Facing
A tank contained some water. The function
\(w\)
represents the relationship between
\(t\)
, time in minutes, and the amount of water in the tank in liters. The equation
\(w(t) = 80 - 2.5t\)
defines this function.
Discuss with a partner:
How is the water in the tank changing? Be as specific as possible.
What does
\(w(t)\)
represent? Is
\(w(t)\)
the input or the output of this function?
Sketch a graph of the function. Be sure to label the axes.
[IMG]
Student Response
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Activity Synthesis
Select students to share their responses, including their graph.
Make sure students recall that in an equation such as
\(w(t)=80-2.5t\)
,
\(w(t)\)
is the output when the input is
\(t\)
, that they can interpret the equation in terms of the situation, and see why the graph is a downward-slanting line.


correct_option_index: 0

4