Learn on PengiSaxon Math, Intermediate 4Chapter 2: Lessons 11–20, Investigation 2

Investigation 2: Units of Length and Perimeter, Activity Estimating the Perimeter

In this Grade 4 Saxon Math Investigation, students explore U.S. Customary units of length (inches, feet, yards, and miles) and metric units of length (millimeters, centimeters, meters, and kilometers), practicing conversions between units and comparing the two systems. Students also learn to calculate the perimeter of rectangles using the formula P = 2l + 2w and estimate real-world measurements by taking meter-long steps. The activity builds hands-on measurement skills using rulers, yardsticks, and metersticks as part of Chapter 2's Investigation 2.

Section 1

📘 Units of Length and Perimeter

New Concept

The distance around a shape is its perimeter. For a rectangle, we use the formula:

P=2l+2wP = 2l + 2w

Why it matters

Mastering perimeter teaches you to translate physical space into the language of mathematics, a core skill for engineering and design. This is your first step in using algebra to model and solve problems about the world around you.

What’s next

Next, you'll apply this concept by measuring objects and calculating the perimeter of various shapes like rectangles and squares.

Section 2

U.S. Customary Units of Length

Property

The standard system for measuring length in the United States. Key equivalents are 12 inches = 1 foot, 3 feet = 1 yard, and 5280 feet = 1 mile.

Examples

A bookshelf that is 4 feet tall is 4×12=484 \times 12 = 48 inches tall.
A room that is 5 yards long is 5×3=155 \times 3 = 15 feet long.

Explanation

Think of these units like building blocks for distance! Tiny inches stack up to make a foot, a few feet make a yardstick for bigger things, and a whole lot of feet stretch out to become a mile for long journeys. We use this system every day in the U.S.!

Section 3

Metric Units of Length

Property

A measurement system used worldwide, based on powers of ten. Key facts: 10 millimeters = 1 centimeter, 100 centimeters = 1 meter, and 1000 meters = 1 kilometer.

Examples

A table that is 2 meters long is 2×100=2002 \times 100 = 200 centimeters long.
A 5 kilometer race is 5×1000=50005 \times 1000 = 5000 meters long.

Explanation

This system is logical, like money! Ten millimeters form a centimeter, 100 centimeters make a meter (think cents in a dollar), and 1000 meters create a kilometer. This base-ten structure makes converting between units a breeze and is used globally, especially in science.

Section 4

Perimeter

Property

The perimeter is the total distance around the outside of a shape. It is found by adding the lengths of all its sides.

Examples

The perimeter of a triangle with sides 6 cm, 8 cm, and 10 cm is 6+8+10=246 + 8 + 10 = 24 cm.
The perimeter of a square with sides 10 inches long is 10+10+10+10=4010 + 10 + 10 + 10 = 40 inches.

Explanation

Think of perimeter as the length of a fence around a yard or a frame around a picture. If you were to walk along the very edge of a shape, the total distance you travel to get back to where you started is the perimeter. Just add up all the sides!

Book overview

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Chapter 2: Lessons 11–20, Investigation 2

  1. Lesson 1

    Lesson 11: Addition Word Problems with Missing Addends

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  2. Lesson 2

    Lesson 12: Missing Numbers in Subtraction

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  3. Lesson 3

    Lesson 13: Adding Three-Digit Numbers, Activity Adding Money

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  4. Lesson 4

    Lesson 14: Subtracting Two-Digit and Three-Digit Numbers, Missing Two-Digit Addends

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  5. Lesson 5

    Lesson 15: Subtracting Two-Digit Numbers with Regrouping, Activity Subtracting Money

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  6. Lesson 6

    Lesson 16: Expanded Form, More on Missing Numbers in Subtraction

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  7. Lesson 7

    Lesson 17: Adding Columns of Numbers with Regrouping

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  8. Lesson 8

    Lesson 18: Temperature, Activity Measuring Temperature

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  9. Lesson 9

    Lesson 19: Elapsed Time Problems, Activity Finding Elapsed Time

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  10. Lesson 10

    Lesson 20: Rounding

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  11. Lesson 11Current

    Investigation 2: Units of Length and Perimeter, Activity Estimating the Perimeter

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Lesson overview

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Section 1

📘 Units of Length and Perimeter

New Concept

The distance around a shape is its perimeter. For a rectangle, we use the formula:

P=2l+2wP = 2l + 2w

Why it matters

Mastering perimeter teaches you to translate physical space into the language of mathematics, a core skill for engineering and design. This is your first step in using algebra to model and solve problems about the world around you.

What’s next

Next, you'll apply this concept by measuring objects and calculating the perimeter of various shapes like rectangles and squares.

Section 2

U.S. Customary Units of Length

Property

The standard system for measuring length in the United States. Key equivalents are 12 inches = 1 foot, 3 feet = 1 yard, and 5280 feet = 1 mile.

Examples

A bookshelf that is 4 feet tall is 4×12=484 \times 12 = 48 inches tall.
A room that is 5 yards long is 5×3=155 \times 3 = 15 feet long.

Explanation

Think of these units like building blocks for distance! Tiny inches stack up to make a foot, a few feet make a yardstick for bigger things, and a whole lot of feet stretch out to become a mile for long journeys. We use this system every day in the U.S.!

Section 3

Metric Units of Length

Property

A measurement system used worldwide, based on powers of ten. Key facts: 10 millimeters = 1 centimeter, 100 centimeters = 1 meter, and 1000 meters = 1 kilometer.

Examples

A table that is 2 meters long is 2×100=2002 \times 100 = 200 centimeters long.
A 5 kilometer race is 5×1000=50005 \times 1000 = 5000 meters long.

Explanation

This system is logical, like money! Ten millimeters form a centimeter, 100 centimeters make a meter (think cents in a dollar), and 1000 meters create a kilometer. This base-ten structure makes converting between units a breeze and is used globally, especially in science.

Section 4

Perimeter

Property

The perimeter is the total distance around the outside of a shape. It is found by adding the lengths of all its sides.

Examples

The perimeter of a triangle with sides 6 cm, 8 cm, and 10 cm is 6+8+10=246 + 8 + 10 = 24 cm.
The perimeter of a square with sides 10 inches long is 10+10+10+10=4010 + 10 + 10 + 10 = 40 inches.

Explanation

Think of perimeter as the length of a fence around a yard or a frame around a picture. If you were to walk along the very edge of a shape, the total distance you travel to get back to where you started is the perimeter. Just add up all the sides!

Book overview

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

Continue this chapter

Chapter 2: Lessons 11–20, Investigation 2

  1. Lesson 1

    Lesson 11: Addition Word Problems with Missing Addends

    LearnPractice
  2. Lesson 2

    Lesson 12: Missing Numbers in Subtraction

    LearnPractice
  3. Lesson 3

    Lesson 13: Adding Three-Digit Numbers, Activity Adding Money

    LearnPractice
  4. Lesson 4

    Lesson 14: Subtracting Two-Digit and Three-Digit Numbers, Missing Two-Digit Addends

    LearnPractice
  5. Lesson 5

    Lesson 15: Subtracting Two-Digit Numbers with Regrouping, Activity Subtracting Money

    LearnPractice
  6. Lesson 6

    Lesson 16: Expanded Form, More on Missing Numbers in Subtraction

    LearnPractice
  7. Lesson 7

    Lesson 17: Adding Columns of Numbers with Regrouping

    LearnPractice
  8. Lesson 8

    Lesson 18: Temperature, Activity Measuring Temperature

    LearnPractice
  9. Lesson 9

    Lesson 19: Elapsed Time Problems, Activity Finding Elapsed Time

    LearnPractice
  10. Lesson 10

    Lesson 20: Rounding

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  11. Lesson 11Current

    Investigation 2: Units of Length and Perimeter, Activity Estimating the Perimeter

    LearnPractice