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} $

Standard options: 
A. Understand a fraction as a number on the number line; represent fractions on a number line diagram.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
B. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
C. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.


Your response, in json format:
{
  "explanation": "By arranging the fractions in this problem, students learn to compare fractions by reasoning about their size.",
  "answer": "B"
}

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: im_task_000157

3
options: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.
problem_activity: Activity
In this activity, students work to solve linear equations and recognize the solution in graphs. This skill will help students when they examine quadratic equations and their solutions in the associated Algebra 1 lesson.
Student Facing
A person is hiking from the top of a mountain into a valley. The function
\(2,\!000 - 32t\)
represents their elevation in feet above sea level,
\(t\)
minutes after they started their hike.
What does a solution to the equation
\(2000-32t=0\)
mean?
Use technology to create a graph of
\(y=2,\!000-32t\)
. Where do you see the solution to that equation on the graph?
A new electronic device originally costs
$
1,000 but loses
$
175 worth of value every year.
Write a function that represents the worth of the device after
\(s\)
years.
How many years until the device is worth
$
0?
Use technology to graph the function. Where can you see the solution to your equation on the graph?
Student Response
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Activity Synthesis
The purpose of the discussion is to notice the connection between solutions of equations and the graph of both sides of the equation. Select students to share their solutions. Ask students:
“Why are both solutions to these questions related to the horizontal intercept?” (Since both questions asked about when the value is 0, it makes sense to look at the points where
\(y = 0\)
which is along the horizontal axis.)
“How could you find the worth of the electronic device after 4.5 years?” (Substitute 4.5 for
\(s\)
in the equation and solve for the value.)
“How could you find the number of minutes it takes to reach an elevation of 100 feet above sea level?” (Substitute 100 in the equation for
\(y\)
and solve for
\(t\)
.)


correct_option_index: 2