Lesson 7Adding and Subtracting to Solve Problems

Learning Goal

Let’s apply what we know about signed numbers to different situations.

Learning Targets

  • I can solve problems that involve adding and subtracting rational numbers.

Lesson Terms

  • deposit
  • withdrawal

Warm Up: Positive or Negative?

Problem 1

Without computing:

  1. Is the solution to positive or negative?

  2. Which of the following are solutions to ?

Activity 1: Phone Inventory

Problem 1

A store tracks the number of cell phones it has in stock and how many phones it sells. The table shows the inventory for one phone model at the beginning of each day last week. The inventory changes when they sell phones or get shipments of phones into the store.

inventory

change

Monday

Tuesday

Wednesday

Thursday

Friday

  1. What do you think it means when the change is positive? Negative?

  2. What do you think it means when the inventory is positive? Negative?

  3. Based on the information in the table, what do you think the inventory will be at on Saturday morning? Explain your reasoning.

  4. What is the difference between the greatest inventory and the least inventory?

Activity 2: Solar Power

Problem 1

Han’s family got a solar panel. Each month they get a credit to their account for the electricity that is generated by the solar panel. The credit they receive varies based on how sunny it is.

A photo of a house with solar panels on the roof.

In January they used $83.56 worth of electricity and generated $6.75 worth of electricity. Here is their electricity bill from January.

Current charges: $83.56

Solar Credit: -$6.75

Amount due: $76.81

  1. In July they were traveling away from home and only used $19.24 worth of electricity. Their solar panel generated $22.75 worth of electricity. What was their amount due in July?

  2. The table shows the value of the electricity they used and the value of the electricity they generated each week for a month. What amount is due for this month?

    used ($)

    generated ($)

    week 1

    week 2

    week 3

    week 4

  3. What is the difference between the value of the electricity generated in week 1 and week 2? Between week 2 and week 3?

Are you ready for more?

Problem 1

While most rooms in any building are all at the same level of air pressure, hospitals make use of “positive pressure rooms” and “negative pressure rooms.” What do you think it means to have negative pressure in this setting? What could be some uses of these rooms?

Activity 3: Differences and Distances

Problem 1

  1. Plot these points on the coordinate grid:

    open applet in presentation mode

  2. What shape is made if you connect the dots in order?

  3. What are the side lengths of figure ?

  4. What is the difference between the -coordinates of and ?

  5. What is the difference between the -coordinates of and ?

  6. How do the differences of the coordinates relate to the distances between the points?

Print Version

  1. Plot these points on the coordinate grid:

    A blank coordinate grid with the origin labled “O”. The x axis has the numbers negative 10 through 10 indicated and the y-axis has the numbers negative 10 through 10 indicated.

  2. What shape is made if you connect the dots in order?

  3. What are the side lengths of figure ?

  4. What is the difference between the -coordinates of and ?

  5. What is the difference between the -coordinates of and ?

  6. How do the differences of the coordinates relate to the distances between the points?

Lesson 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

  • inventory

  • an account balance

  • electricity flowing in and flowing out

In these situations, using positive and negative numbers, and operations on positive and negative numbers, helps us understand and analyze them. To solve problems in these situations, we just have to understand what it means when the quantity is positive, when it is negative, and what it means to add and subtract them.

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

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

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, but the difference depends on the order.