Learn on PengiPengi Math (Grade 7)Chapter 1: The Integer System and Operations

Lesson 6: Solving Real-World Integer Problems

In this Grade 7 Pengi Math lesson from Chapter 1: The Integer System and Operations, students apply integers to real-world contexts such as temperature changes, elevation, and financial transactions. They calculate net change, final values, and mean rate of change using all four integer operations. Multi-step word problems challenge students to connect integer arithmetic to everyday situations.

Section 1

Calculating a Final Value After a Change

Property

We denote gains by positive numbers and losses by negative numbers.
We can find the net change in a quantity by adding those gains and losses.

Examples

  • A football team gains 12 yards and then loses 5 yards. The net change in position is found by the sum (+12)+(5)=+7(+12) + (-5) = +7 yards.
  • The temperature drops 8 degrees overnight and then rises 15 degrees during the day. The net change in temperature is (8)+(+15)=+7(-8) + (+15) = +7 degrees.

Section 2

Solving word problems with integer subtraction

Property

To solve word problems involving integer subtraction:

  1. Identify the numbers and what operation is needed
  2. Write the subtraction expression
  3. Convert subtraction to addition: ab=a+(b)a - b = a + (-b)
  4. Simplify using integer addition rules
  5. State the answer with appropriate units

Examples

Book overview

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Continue this chapter

Chapter 1: The Integer System and Operations

  1. Lesson 1

    Lesson 1: Integers, Opposites, and Absolute Value

  2. Lesson 2

    Lesson 2: Adding Integers

  3. Lesson 3

    Lesson 3: Subtracting Integers

  4. Lesson 4

    Lesson 4: Multiplying Integers

  5. Lesson 5

    Lesson 5: Dividing Integers

  6. Lesson 6Current

    Lesson 6: Solving Real-World Integer Problems

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Calculating a Final Value After a Change

Property

We denote gains by positive numbers and losses by negative numbers.
We can find the net change in a quantity by adding those gains and losses.

Examples

  • A football team gains 12 yards and then loses 5 yards. The net change in position is found by the sum (+12)+(5)=+7(+12) + (-5) = +7 yards.
  • The temperature drops 8 degrees overnight and then rises 15 degrees during the day. The net change in temperature is (8)+(+15)=+7(-8) + (+15) = +7 degrees.

Section 2

Solving word problems with integer subtraction

Property

To solve word problems involving integer subtraction:

  1. Identify the numbers and what operation is needed
  2. Write the subtraction expression
  3. Convert subtraction to addition: ab=a+(b)a - b = a + (-b)
  4. Simplify using integer addition rules
  5. State the answer with appropriate units

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 1: The Integer System and Operations

  1. Lesson 1

    Lesson 1: Integers, Opposites, and Absolute Value

  2. Lesson 2

    Lesson 2: Adding Integers

  3. Lesson 3

    Lesson 3: Subtracting Integers

  4. Lesson 4

    Lesson 4: Multiplying Integers

  5. Lesson 5

    Lesson 5: Dividing Integers

  6. Lesson 6Current

    Lesson 6: Solving Real-World Integer Problems