few_shots: Example:
Problem/activity:
Task
Cruz and Erica were both getting ready for soccer.
Cruz ran 1 lap around the school.
Erica ran 3 laps around the playground.
Erica said,
I ran more laps, so I ran farther.
Cruz said,
4 laps around the school is 1 mile, but it takes 12 laps around the playground to go 1 mile. My laps are much longer, so I ran farther.
Who is right? Draw a picture to help you explain your answer.


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. Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
E. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
F. 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.


Your response:
{
  "explanation": "In this problem, students learn to recognize equivalent fractions. That is, three laps around the playground is 3/12 mile, which is equivalent to 1/4, which is one lap around the school.",
  "answer": "B"
}

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_000212

4
options: Understand the relationship between zeros and factors of polynomials.

Solve systems of equations.

Reason about and solve one-variable equations and inequalities.

Work with equal groups of objects to gain foundations for multiplication.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Understand and apply properties of operations and the relationship between addition and subtraction.

Analyze patterns and relationships.

Use the four operations with whole numbers to solve problems.

Use polynomial identities to solve problems.

Represent and solve problems involving addition and subtraction.

Understand the connections between proportional relationships, lines, and linear equations.

Understand solving equations as a process of reasoning and explain the reasoning.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Rewrite rational expressions.

Perform arithmetic operations on polynomials.

Represent and solve problems involving multiplication and division.

Work with radicals and integer exponents.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Represent and solve equations and inequalities graphically.

Understand properties of multiplication and the relationship between multiplication and division.

Add and subtract within 20.

Generate and analyze patterns.

Create equations that describe numbers or relationships

Write and interpret numerical expressions.

Interpret the structure of expressions.

Gain familiarity with factors and multiples.

Represent and analyze quantitative relationships between dependent and independent variables.

Write expressions in equivalent forms to solve problems.

Multiply and divide within 100.

Use properties of operations to generate equivalent expressions.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Solve equations and inequalities in one variable.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Work with addition and subtraction equations.
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: 22

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