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

Lesson overview

Expand to review the lesson summary and core properties.

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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