Download 7.NS.A.1.b Distances on a Number Line 2 Task

Illustrative Mathematics
7.NS Distances on the Number Line 2
Alignments to Content Standards
Alignment: 7.NS.A.1
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On the number line above, the numbers a and b are the same distance from 0. What is a + b ?
Explain how you know.
Commentary
The purpose of this task is meant to reinforce students' understanding of rational numbers as
points on the number line and to provide them with a visual way of understanding that the sum
of a number and its additive inverse (usually called its "opposite") is zero. Students should have
lots of opportunities to represent adding specific rational numbers before they work on
answering this one.
Solutions
Solution: Solution
We are given that a and b are the same distance from zero. However, from the above
number line we can see that a and b are on different sides of zero. We can visualize this by
representing a and b as directed distances on the number line:
If we start at zero and move a units to the right, and then move the same number of units to
the left, we will be back at 0.
We can also represent this symbolically. Since a and b are the same distance from zero but
are on opposite sides of zero, we know that they are opposites, so b = −a. The sum of a
number and its opposite is always zero.
a + b = a + (−a)
= a−a
=0
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