In this lesson, students build fluency with adding signed numbers. First, they examine changes in elevation. They write addition expressions and draw number line diagrams to help find the final elevation after each change. Then they apply what they have learned to add signed numbers without a context.

Students generalize about the sum of two signed numbers based on the signs and relative magnitudes of the addends, including these observations:

• Adding two numbers with the same sign gives a sum that is farther away from zero than either addend.
• Adding two numbers with different signs gives a sum with the same sign as the addend with the greater magnitude.
• Adding a number and its opposite gives a sum of 0. (Opposites are numbers that are the same distance from zero but on opposite sides of the number line.)

As students use observations about the number line and the meaning of opposites to develop these generalizations, they are making use of repeated reasoning (MP8).

The last activity is optional because it provides an opportunity for additional practice adding signed numbers using physical manipulatives.

The term “opposites” appears bolded in this lesson, however, students were introduced to this term in a previous lesson of this unit.

If necessary during the Lesson Synthesis, explain that the term “magnitude” is another way to express a number’s absolute value.