few_shots: Example:
Problem/activity:
Task
 Arrange the fractions in order from least to greatest. Explain your answer with a picture.
 $\frac{1}{5}, \frac{1}{7}, \frac{1}{3} $
 $\frac{2}{5}, \frac{2}{7}, \frac{2}{3} $
 $\frac{5}{6}, \frac{3}{6}, \frac{1}{6} $
 $\frac{5}{12}, \frac{8}{12}, \frac{4}{12} $

Mathematical concept/skill options: 
A. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
B. Extend understanding of fraction equivalence and ordering.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
C. Use equivalent fractions as a strategy to add and subtract fractions.
D. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
E. Understand decimal notation for fractions, and compare decimal fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
F. Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.


Your response, in json format:
{
  "explanation": "This problem involves understanding fractions as numbers by comparing their quantities.",
  "answer": "F"
}

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_000157

3
options: Extend the domain of trigonometric functions using the unit circle.

Use functions to model relationships between quantities.

Build a function that models a relationship between two quantities.

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

Construct and compare linear and exponential models and solve problems.

Prove and apply trigonometric identities.

Understand the concept of a function and use function notation.

Analyze functions using different representations.

Build new functions from existing functions.

Model periodic phenomena with trigonometric functions.

Define, evaluate, and compare functions.

Interpret functions that arise in applications in terms of the context.
problem_activity: Activity
If students also use technology to create the tables, they are using appropriate tools strategically (MP5).
Launch
Provide access to graphing technology. Students may need some assistance adjusting their graphing window to see the relevant features of each graph. Either help them set the window before they start to a domain of
\(\text-2 \le x \le 8\)
and range of
\(\text-60 \le y \le 600\)
, or wait until they have attempted to graph at least one function and remind them of what they have learned about changing the graphing window.
Student Facing
Each function represents the amount in a bank account after
\(t\)
weeks.
\(A(t) = 500\)
\(B(t) = 500 + 40t\)
\(C(t) = 500 - 40t\)
\(D(t) = 500 \boldcdot (1.5)^t\)
\(E(t) = 500 \boldcdot (0.75)^t\)
Make a table for each bank account showing the money in the account at 0, 1, 2, and 3 weeks.
Describe in words how the money in the account is changing week by week.
Use technology to create a graph of each function. How can you see your description in each graph?
Student Response
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Activity Synthesis
Focus the discussion on the connection between the equations, descriptions and graphs. Discuss questions such as:
“What do all functions have in common?” (The vertical intercept is 500, each bank account starts with $500)
“How does the money change each week? How do we see this change in the graph?"
“How are
\(B\)
and
\(C\)
the same and different?” (They are the same because they are each linear, and each start with
$
500 and change by
$
40 per week. They are different because B increases and C decreases (or the rate of change is positive versus negative.)
“How are
\(D\)
and
\(E\)
the same and different?” (They are the same because they are each exponential, and each start with
$
500. They are different because
\(D\)
increases and
\(E\)
decreases (or the growth factor is greater than 1 versus less than 1.))


correct_option_index: 3

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