Adding and Subtracting to Solve Problems

Student Summary

Sometimes we use positive and negative numbers to represent quantities in context. Here are some contexts we have studied that can be represented with positive and negative numbers:

  • Temperature
  • Elevation
  • Money
  • Inventory

Using positive and negative numbers (and operations on positive and negative numbers) helps us understand and analyze the situations in context. To solve problems in these situations, we just have to understand what it means when a quantity is positive, what it means when a quantity is negative, and what it means to add and subtract quantities.

When two points in the coordinate plane lie on a horizontal line, we can find the distance between them by subtracting their xx-coordinates.

When two points in the coordinate plane lie on a vertical line, we can find the distance between them by subtracting their yy-coordinates.

Five line segments on a coordinate plane.
Five line segments on a coordinate plane with the origin labeled “O”. The numbers negative 5 through 5, are indicated on the horizontal axis and the numbers negative 4 through 5 are indicated on the vertical axis. Each line segment is either vertical or horizontal. The first line segment is vertical that begins at the point negative 5 comma 3 and ends at the point negative 5 comma negative 4; the line segment is labeled with the expression 3 minus negative 4. The second line segment is horizontal and begins at the point negative 5 comma negative 4 and ends at the point negative 2 comma negative 4; the line segment is labeled with the expression negative 2 minus negative 5. The third line segment is vertical and begins at the point negative 2 comma negative 4 and ends at the point negative 2 comma 2; the line segment is labeled with the expression 2 minus negative 4. The fourth line segment is horizontal and begins at the point negative 2 comma 2 and ends at the point three comma 2; the line segment is labeled with the expression 3 minus negative 2. The fifth line segment is vertical and begins at the point 3 comma 2 and ends at the point 3 comma five; the line segment is labeled with the expression 5 minus 2.

Remember: The distance between two numbers is independent of the order, whereas the difference depends on the order.

Visual / Anchor Chart

Standards

Building On
7.NS.1

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers. Represent addition and subtraction on a horizontal or vertical number line.

Addressing
7.NS.3

Solve real-world and mathematical problems involving the four operations with rational numbers.

7.NS.1

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers. Represent addition and subtraction on a horizontal or vertical number line.

7.NS.1.c

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers. Represent addition and subtraction on a horizontal or vertical number line.

Building Toward
7.EE.4

Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.