For a comprehensive overview of Team Homework, refer to the Team Homework section of the Student Guide. A few important points are included below, followed by an example solution to a Team Homework problem.

Before you meet with your team, be sure to read over the problems and try to solve them on your own. This not only helps your team meetings run more efficiently, but it will also greatly help your personal understanding of the problems if you've already spent some time working on them alone.
When solving problems together, be sure that everyone is on the same page, and if you aren't sure about something, speak up! Your team should make decisions by consensus, not by majority vote. Even if the rest of your team seems sure of something, it's possible they're overlooking an error, so if you don't understand how the group got a certain answer, be sure to ask so that you can all double-check your solutions. (Plus, you're all responsible for understanding each problem. You don't want to gloss over something if it's giving you trouble!)
Do not have each team member work on separate problems! These problems are typically much more challenging than the problems discussed in class because they are meant to be carefully discussed in groups. Splitting up the work can make completing the individual problems more difficult and typically leads to overlooking various errors and overall poorer quality solutions. As the saying goes, "Two (or three or four) heads are better than one," and that's especially true with complex conceptual problems like Team Homework. Remember, also, that these problems are good preparation for the exams, so it's important that everyone understands how to solve all of the problems.
Remember that you can use the tools available to you, including Desmos, Math Lab, and your instructor's office hours.
Be sure to read over your past solutions after they've been graded! This not only helps you improve future solutions, but it is very likely that there will be at least one Team Homework lookalike problem on each exam, so you'll want to make sure you fully understand the correct approach.

The setup of a thorough solution:

Suppose we are answering the following question:

Ricardo wants to take a taxi ride 5 miles across town. He knows that there is a fee just to book the taxi and a fixed charge for each mile of the trip, but he can't remember the exact amounts. He does, however, remember that a 2-mile trip cost him $10, and an 8-mile trip cost him $28. Write a formula for C, the cost in dollars of a taxi ride to travel m miles. Use this formula to find the cost of Ricardo's 5-mile trip.

To answer this question, our solution should contain four main parts:

Restate the problem in your own words (i.e., do not copy the question verbatim). Explain the end goal and define any variables you use in the problem (and their units!).

Example:

Here, we are asked to find a formula for C, the cost in dollars of an m-mile taxi ride, which we will use to find the cost of Ricardo's 5-mile trip. We know that a 2-mile trip costs $10, an 8-mile trip costs $28, and the cost of a taxi ride is made up of a booking fee and an additional charge per mile.

As you write your solution to the problem, be sure to use complete sentences and include any computations within those sentences! You should be explaining each step of your process, including how your calculations connect to the context. Your solutions should be written like a cohesive essay, explaining how each step follows from the previous statement.

Note: A longer solution does not mean a better solution! You do not need to explain why 100-x=20 means that x=80.

Example:

Because the cost of the taxi will increase by the same amount for each additional mile of the trip, we know that the cost C will be a linear function of the miles m. To find the formula of a linear function, we first need to find the slope. In this case, we can use the average rate of change between a 2-mile trip and an 8-mile trip to find the slope because the slope is defined to be the constant rate of change between any two points on a line. Using the formula for the average rate of change, we found the slope to be $LaTeX: \frac{28-10}{8-2}=3$ dollars per mile, so each mile of the trip costs $3. After finding the slope, we chose to use the point-slope form of a line instead of the slope-intercept form because we have two points on the line, but we don't have the initial value. We can use the point LaTeX: (2,10) because a 2-mile trip costs $10, and combining this with our slope of 3, we get the formula LaTeX: C=3(m-2)+10 . Now that we have a formula for the cost of a taxi trip of m miles, we can use it to find the cost of Ricardo's 5 mile trip. Plugging the 5 miles in for m, we get that the trip would cost LaTeX: 3(5-2)+10=19 dollars.

Include any graphs, tables, or images that will help you explain your answer, even if the problem doesn't specifically ask for them.
- Note: In this problem, we did use any tables, but if we had used Desmos, for example, to help solve our problem, we would need to include a picture of the graph and an explanation of what the graph represents and why we're using it, to give a full explanation.

When you reach the end of your solution, you should tie it back to your statement of the problem in step 1 by explaining the units associated with the answer, explaining why the answer makes sense in the context of the problem, and summarizing what you've shown.

Example:

We have now found a formula for the cost C in dollars of an m-mile trip. To check our work, we see that our formula gives us a cost of LaTeX: 3(2-2)+10=10 dollars for a 2-mile trip and a cost of LaTeX: 3(8-2)+10=28 dollars for an 8-mile trip, which aligns with the values given in the statement of the problem. Finally, we also now know that Ricardo's 5-mile trip will cost $19. This makes sense in this context: 5 miles is between 2 and 8 miles, so we expect the cost to be between $10 and $28.

Note: Typically, there's a bit more explanation required to tie back to the original problem, but this problem was pretty straightforward since the problem statement was very short and all of our variables were given to us. If we had chosen our own variables, we would need to relate them back to the specific context of the problem statement.