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.


Concept/skill: 
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Answer: 
Yes. This task asks students to compare two fractions that are equal. The students need to explain why the two fractions are equal by drawing a picture, which involves using visual fraction models.

Now, does the following problem or activity enable students to learn the full intent of the following concept or skill?

shot_info: im_task_000212_pos_0

4
standard_description: 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
This activity gives students another opportunity to write and rearrange equations in two variables and to do so in context.
Unlike in previous activities, students no longer start by computing one quantity given numerical values of the other quantity and then generalizing the process. Instead, they are prompted to write one equation, solve for each variable, and interpret the solution. Students also articulate why one model might be more helpful than the other under a certain circumstance. Along the way, students reason quantitatively and abstractly (MP2) and engage in aspects of modeling (MP4).
Making spreadsheet technology available gives students an opportunity to choose appropriate tools strategically (MP5).
Launch
Familiarize students with the idea of organizational budgets, if needed. Explain that every governmental agency has a budget (not unlike a budget for a pizza party) and needs to decide how to allocate a limited amount of funds. Ask students to think of examples of expenses that a city's Department of Streets might have (road repairs, new street construction, additional workers, new equipment, and so on). Given a set budget, spending more on one thing means having less to spend on something else, so the agency would need to weigh their options and prioritize their needs.
Reading, Listening, Conversing: MLR6 Three Reads.
Ask students to keep their books or devices closed and display only the image and the task statement without revealing the questions that follow. Use the first read to orient students to the situation. Ask students to describe what the situation is about without using numbers (a city department has money to resurface roads this year). Use the second read to identify quantities and relationships. Ask students “What can be counted or measured?” Listen for, and amplify, the important quantities that vary in relation to each other in this situation: the total amount of money available, the cost to resurface 1 mile of a 2-lane road, the average worker’s salary, and the number of miles of road to resurface. After the third read, reveal the first question and ask students to brainstorm possible strategies to write an equation. This routine helps students interpret the language within a given situation needed to create an equation.
Design Principle(s): Support sense-making
Representation: Internalize Comprehension.
Provide appropriate reading accommodations and supports to ensure student access to written directions, word problems, and other text-based content.
Supports accessibility for: Language; Conceptual processing
Student Facing
The Department of Streets of a city has a budget of \$1,962,800 for resurfacing roads and hiring additional workers this year.
The cost of resurfacing a mile of 2-lane road is estimated at \$84,000. The average starting salary of a worker in the department is \$36,000 a year.
[IMG]
Write an equation that represents the relationship between the miles of 2-lane roads the department could resurface,
\(m\)
, and the number of new workers it could hire,
\(p\)
, if it spends the entire budget.
Take the equation you wrote in the first question and:
Solve for
\(p\)
. Explain what the solution represents in this situation.
Solve for
\(m\)
. Explain what the solution represents in this situation.
The city is planning to hire 6 new workers and to use its entire budget.
Which equation should be used to find out how many miles of 2-lane roads it could resurface? Explain your reasoning.
Find the number of miles of 2-lane roads the city could resurface if it hires 6 new workers.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Anticipated Misconceptions
Some students may have trouble sorting out the given information because of unfamiliarity with the context or with certain terms. Ask them to explain the setup of the problem as best they understand it, and then point out any information that might be missing.
Activity Synthesis
Verify that the equations students wrote correctly isolate each variable. If students wrote expressions in different forms for a variable (for instance,
\(\dfrac {4,\!907 - 210m}{90}\)
and
\(\dfrac {1,\!962,\!800 -84,\!000m}{36,\!000}\)
for
\(p\)
), discuss how the expressions are equivalent.
If time permits, consider asking students to use their equations to answer these questions:
"How many people could be hired if the department is resurfacing 16 miles of roads?" (17 people) "3 miles?" (47 people)
"How many miles of roads could be resurfaced if the department is hiring 2 new workers?" (22.5 miles) "If no new workers are hired?" (About 23.37 miles)
Make sure students understand that solving for
\(p\)
makes it possible to quickly find the number of people that the department could hire given some miles of road to be resurfaced (and while sticking to the budget). Similarly, solving for
\(m\)
makes it possible to quickly find the miles that could be resurfaced given any number of new hires.


aligns: yes