In this activity, students use the context of the scoring margins for a football team to calculate the average of a set of signed numbers. A positive number represents the number of points the team won by, and negative numbers represent the number of points the team lost by. Students reason abstractly and quantitatively about the teams' scores over the season in order to make comparisons about the teams in the situation (MP2). 

Monitor for groups who use these different strategies to find the sum of the numbers in the second problem. Here are some strategies students may use, from less efficient to more efficient:

• Add the numbers one at a time, in the order listed.
• Add all the positive numbers, then add all the negative numbers, and then add the two partial sums.
• Find combinations of positive and negative numbers that have opposite values, and understand that these will have a sum of 0. For example is the opposite of -6.

The purpose of this discussion is for students to share strategies they used when performing arithmetic operations with rational numbers. 

Invite previously selected groups to share their strategies for the second problem. Sequence the discussion of the strategies in the order listed in the Activity Narrative. If possible, record and display the students’ work for all to see.

Connect the different responses to the learning goals by asking questions such as:

• "What is the same and what is different about the strategies?"
• "Which strategy do you think is the most efficient for adding a large collection of positive and negative numbers?"
• "Do any of the strategies help improve the accuracy of the calculation?"
• "Are there certain situations where one strategy might be more efficient than another strategy?"
• "Did you use the same or a different strategy when finding the sum of the first set of scoring margins? Why?"

In this activity, students perform operations with rational numbers using the context of energy consumption. Students use what they have learned about signed numbers to interpret what positive and negative energy consumption means and determine the net consumption of electricity by a family that has installed solar panels (MP2). They determine the cost to purchase electricity per kWh and the cost to sell it back to the grid. They determine the effect an additional battery has on energy consumption and their net cost for electricity in a month.

The goal of this discussion is for students to share their responses and discuss the implications of electricity consumption in their community. Begin by inviting students to share their responses and reasoning to the last question. Consider discussing the following questions:

• “How did you determine the cost of the electricity used?” (I multiplied the number of kWh used by the cost for one kWh.)
• “How did you determine the cost of the electricity generated?” (I multiplied the number of kWh generated by the cost for one kWh.)
• “What does a negative cost for the electricity generated mean in this situation?” (A negative cost to the consumer means it is like a credit on their bill.)
• “Compare the electricity used and generated in the two months. What do you notice?” (The amount used went down by a lot, while the amount generated went up.)

If time allows, consider asking students to research average electricity consumption in the school’s city or state. Discuss the main sources of energy in the area and the potential benefits or consequences of alternative sources of energy.