Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.
Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
A mountaineer is climbing on a cliff. She is 400 feet above the ground. If she climbs up, this will be a positive change. If she climbs down, this will be a negative change.
Complete the table.
starting
elevation
(feet)
change
(feet)
final
elevation
(feet)
A
+400
300 up
B
+400
150 down
C
+400
400 down
D
+400
+50
Write an addition equation and draw a number line diagram for B. Include the starting elevation, change, and final elevation in your diagram.
A spelunker is down in a cave next to the cliff. If she climbs down deeper into the cave, this will be a negative change. If she climbs up, whether inside the cave or out of the cave and up the cliff, this will be a positive change.
Complete the table.
starting elevation
(feet)
change
(feet)
final elevation
(feet)
A
-200
150 down
B
-200
100 up
C
-200
200 up
D
-200
250 up
E
-200
-500
Write an addition equation and draw a number line diagram for C and D. Include the starting elevation, change, and final elevation in your diagram.
What does the expression tell us about the spelunker? What does the value of the expression tell us?
7.3
Activity
Adding Rational Numbers
Standards Alignment
Building On
Addressing
7.NS.1.b
Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
What do you notice about finding the sum of two numbers with the same sign compared to finding the sum of two numbers with different signs?
7.4
Activity
School Supply Number Line
Standards Alignment
Building On
Addressing
7.NS.1.b
Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
Follow these instructions to create a number line.
Fold the paper in half along its length and along its width.
Unfold the paper, and draw a line along each crease.
Label the line in the middle of the paper 0. Label the right end of the paper and the left end of the paper .
Select two objects of different lengths, for example, a pen and a glue stick. The length of the longer object is , and the length of the shorter object is .
Use the objects to measure and label each of the following points on your number line.
Complete each statement using <, >, or =. Use your number line to explain your reasoning.
_____
_____
_____
_____
_____
Student Lesson Summary
The opposite of a number is the same distance from 0 but on the other side of 0.
A number line with the numbers negative 10 through 10 indicated. An arrow starts at 0, points to the left, and ends at negative 9. There is a solid dot indicated at negative 9. A second arrow starts at 0, points to the right, and ends at 9. There is a solid dot indicated at 9.
The opposite of -9 is 9. When we add opposites, we always get 0. The following diagram shows that .
A number line with the numbers negative 10 through 10 indicated. An arrow starts at 0, points to the right, and ends at 9. A second arrow starts at 9, points to the left, and ends at 0. there is a solid dot indicated at 0.
When we add two numbers with the same sign, the arrows that represent them point in the same direction. When we put the arrows tip to tail, we see the sum has the same sign as the original numbers.
A number line, an arrow starts at 0, points to the right, and ends at 4. A second arrow starts at 4, points to the right, and ends at 7. There is a solid dot indicated at 7.
A number line, an arrow starts at 0, points to the left, and ends at negative 5. A second arrow starts at negative 5, points to the left, and ends at negative 9. There is a solid dot indicated at negative 9.
To find the sum, we add the magnitudes and give it the correct sign. For example, .
On the other hand, when we add two numbers with different signs, we subtract their magnitudes (because the arrows point in the opposite direction) and give it the sign of the number with the larger magnitude. For example, .
A number line with the numbers negative 10 through 10 indicated. An arrow starts at 0, points to the left, and ends at negative five. A second arrow starts at negative five, points to the right, and ends at 7. There is a solid dot indicated at 7.
Glossary
opposite
Two numbers are opposites if they are the same distance from 0 on the number line, but on different sides. One is negative, and the other is positive.
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Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.
Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
