1. How would you explain this relationship using a mathematical model?
Standard: 7.n.s.1 a. Describe situations in which opposite quantities combine to make zero
A hydrogen atom has an electron and a proton. A proton has a positive or + charge and an electron has a negative or – charge.
How would you explain this relationship using a mathematical model?
What type of mathematical model would you use to represent the relationship and why?
Please discuss this in your group and be prepared to discuss it as a class.

2. Why did you choose to represent it the way you did?
Standard: 7.n.s.1.b: understand p + q as the number located a distance a from, p in the positive or negative direction depending on whether q is negative or positive. Show that a number and its opposite have a sum of zero (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
Mr. Hunter lives 35 and ½ miles from Sage Charter School. Using a mathematical model show the distance that Mr. Hunter travels.
When Mr. Hunter returns home how many miles does he have to drive home? Please show this on your mathematical model. Be prepared to share and discuss with the class.
Why did you choose to represent it the way you did?
If we subtract the distance traveled to school from the distance returning home what is the answer? How would this be expressed both on a mathematical model and using an addition algorithm?
What does this tell us about the properties of distance, and the relationship of the starting point to the ending point?
How would you express this algebraically?

3. Standard: understand subtraction of rational numbers as adding the additive inverse, p-q = P + (-q). Show that the distance between the two rational numbers on the number line is the absolute value of their difference, and apply to real world context.
Jackie walked a distance west on the beach of ¾ of a mile. Then she turned around and walked east for 1 and a 1/2 miles. How far past her original walking point did she go when she walked east?
Things to consider
Can you represent this with a mathematical model?
Can you represent this with addition using a negative number?
Can you have a negative distance? How does this relate to this problem?

4. Extension
Jackie walked a distance west on the beach of ¾ of a mile. Then she turned around and walked east for 1 and a 1/2 miles. How many different ways can you express the distance or absolute value of the total distance she walked?
Things to consider
Can you represent this with a mathematical model?
Can you represent this with addition using a negative number?