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: Represent a system of linear equations as a single matrix equation in a vector variable.

Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x^(2 )+ y^(2) = 3.

Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).

Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
problem_activity: Problem 1
Which strategy would you use to solve each of the following problems? Justify your answer. (You do not need to solve them.)
$${\left\{\begin{matrix}2x-6y=24 \\ x+4y=16 \end{matrix}\right.}$$
$${\left\{\begin{matrix}4x-3y=15 \\ 2x+9y=32 \end{matrix}\right.}$$
Problem 2
Greg wants to buy a new car. He looks at two different models. Car A costs $40,000, and he estimates it will cost $2,000 per year for gas and maintenance. Car B costs $60,000, and he estimates it will cost about $1,000 per year for gas and maintenance. Under what circumstances would it make sense for Greg to buy Car A? Under what circumstances would it make sense for Greg to buy Car B? Justify your answer.


correct_option_index: 4