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:
{
  "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.

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.

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.

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: Problem 1
A ball is thrown straight up from the top of a
$${48}$$
-foot tall building with an initial speed of
$${32}$$
feet per second. The height of the ball as a function of time can be modeled by the function
$$h(t)=-16t^2+{32}t+{48}$$
. Below is a graph and table of the function.
[IMG]
a. What are the solutions to this function? Interpret each solution in context of the situation.
b. What is the vertex of this function? Interpret the vertex in context of the situation.
Problem 2
The table below represents the value of Andrew’s stock portfolio, where
$$V$$
represents the value of the portfolio in hundreds of dollars and
$$t$$
is the time in months since he started investing. Answer the questions that follow based on the table of values.
{"table": [{"_attributes": {"align": "Center", "class": ["table", "table-bordered"], "style": "width:40%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$t$$"}], "_value": "(months)"}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$V(t)$$"}], "_value": "(hundreds of dollars)"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "2"}, {"_attributes": {"style": "text-align:center"}, "_value": "325"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "4"}, {"_attributes": {"style": "text-align:center"}, "_value": "385"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "6"}, {"_attributes": {"style": "text-align:center"}, "_value": "405"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "8"}, {"_attributes": {"style": "text-align:center"}, "_value": "385"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "10"}, {"_attributes": {"style": "text-align:center"}, "_value": "325"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "12"}, {"_attributes": {"style": "text-align:center"}, "_value": "225"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "14"}, {"_attributes": {"style": "text-align:center"}, "_value": "85"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "16"}, {"_attributes": {"style": "text-align:center"}, "_value": "-95"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "18"}, {"_attributes": {"style": "text-align:center"}, "_value": "-315"}]}]}]}]}
Assuming this data is quadratic, how much did Andrew invest in his stock initially? Explain how you arrived at this answer.
What is the maximum value of his stock and how long did it take to reach the maximum value?
After approximately how many months is Andrew’s stock portfolio valued at $0?
How fast is Andrew’s stock value decreasing between months 10 and 12? Find a two-month interval where the average rate of change is faster than it is between months 10 and 12 and explain why.
Problem 3
John is building a small rectangular pen for chickens. He wants the length to be 6 more feet than twice the width.
If the area of the pen is 36 square feet, what are the dimensions of the pen in feet?


correct_option_index: 2