Learn on PengiSaxon Math, Intermediate 4Chapter 3: Lessons 21–30, Investigation 3

Lesson 21: Triangles, Rectangles, Squares, and Circles, Activity Drawing a Circle

In this Grade 4 Saxon Math lesson, students learn to identify and draw triangles, rectangles, squares, and circles, including the concept that a square is a special kind of rectangle and that an equilateral triangle has three equal sides. Students also explore circle geometry, learning how to use a compass to draw circles and understanding key terms such as radius, diameter, and circumference. The lesson includes hands-on practice measuring and drawing shapes using a ruler and compass.

Section 1

📘 Triangles, Rectangles, Squares, and Circles

New Concept

A circle is a closed, curved shape in which all points on the shape are the same distance from the center.

What’s next

Next, you’ll practice drawing these basic shapes and explore their key properties, such as radius and diameter.

Section 2

A Square is a Special Kind of Rectangle

Property

A square is a special kind of rectangle.

Examples

  • A shape with sides of 44 inches, 44 inches, 44 inches, and 44 inches is a square and also a rectangle.
  • A shape with sides of 55 cm and 33 cm is a rectangle, but it is not a square because the sides are not all equal.

Explanation

Think of 'rectangle' as a club with two rules: you must have four sides and four square corners. A square follows both rules perfectly, but it has one extra, VIP rule: all its sides must be the same length. So, every square gets into the rectangle club, but not every rectangle is special enough to be a square!

Section 3

Radius and Diameter

Property

The radius of a circle is the distance from the center to the edge. The diameter is the distance across the circle through the center. The diameter of a circle equals two radii.

Examples

  • If a pizza has a radius of 77 inches, its diameter is 2×7=142 \times 7 = 14 inches.
  • If the diameter of a bike wheel is 2626 inches, its radius is 26÷2=1326 \div 2 = 13 inches.

Explanation

Imagine a pizza! The radius is the length from the exact center to the yummy crust. The diameter is a straight cut all the way across the pizza that passes through the center point. Since that cut is made of one radius going from the center to the left and another to the right, the diameter is always twice as long!

Section 4

Circumference

Property

The circumference of a circle is the distance around—or the perimeter of—a circle.

Examples

  • The total length of a hula hoop is its circumference.
  • If you wrap a measuring tape around a basketball, the measurement you get is the ball's circumference.
  • The distance a car tire travels in one full rotation is equal to its circumference.

Explanation

Circumference is just the fancy, official name for a circle's perimeter. Imagine you could unpeel the edge of a cookie and lay it out in a straight line. The length of that line is the circumference! It’s the total distance an ant would have to walk to complete one full lap around the edge of the cookie.

Book overview

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

Continue this chapter

Chapter 3: Lessons 21–30, Investigation 3

  1. Lesson 1Current

    Lesson 21: Triangles, Rectangles, Squares, and Circles, Activity Drawing a Circle

  2. Lesson 2

    Lesson 22: Naming Fractions, Adding Dollars and Cents, Activity Counting Money

  3. Lesson 3

    Lesson 23: Lines, Segments, Rays, and Angles, Activity Real-World Segments and Angles

  4. Lesson 4

    Lesson 24: Inverse Operations

  5. Lesson 5

    Lesson 25: Subtraction Word Problems

  6. Lesson 6

    Lesson 26: Drawing Pictures of Fractions

  7. Lesson 7

    Lesson 27: Multiplication as Repeated Addition, More Elapsed Time Problems, Activity Finding Time

  8. Lesson 8

    Lesson 28: Multiplication Table

  9. Lesson 9

    Lesson 29: Multiplication Facts: 0s, 1s, 2s, 5s

  10. Lesson 10

    Lesson 30: Subtracting Three-Digit Numbers with Regrouping, Activity Subtracting Money

  11. Lesson 11

    Investigation 3: Multiplication Patterns, Area, Squares and Square Roots, Activity 1 Finding Perimeter and Area, Activity 2 Estimating Perimeter and Area

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

📘 Triangles, Rectangles, Squares, and Circles

New Concept

A circle is a closed, curved shape in which all points on the shape are the same distance from the center.

What’s next

Next, you’ll practice drawing these basic shapes and explore their key properties, such as radius and diameter.

Section 2

A Square is a Special Kind of Rectangle

Property

A square is a special kind of rectangle.

Examples

  • A shape with sides of 44 inches, 44 inches, 44 inches, and 44 inches is a square and also a rectangle.
  • A shape with sides of 55 cm and 33 cm is a rectangle, but it is not a square because the sides are not all equal.

Explanation

Think of 'rectangle' as a club with two rules: you must have four sides and four square corners. A square follows both rules perfectly, but it has one extra, VIP rule: all its sides must be the same length. So, every square gets into the rectangle club, but not every rectangle is special enough to be a square!

Section 3

Radius and Diameter

Property

The radius of a circle is the distance from the center to the edge. The diameter is the distance across the circle through the center. The diameter of a circle equals two radii.

Examples

  • If a pizza has a radius of 77 inches, its diameter is 2×7=142 \times 7 = 14 inches.
  • If the diameter of a bike wheel is 2626 inches, its radius is 26÷2=1326 \div 2 = 13 inches.

Explanation

Imagine a pizza! The radius is the length from the exact center to the yummy crust. The diameter is a straight cut all the way across the pizza that passes through the center point. Since that cut is made of one radius going from the center to the left and another to the right, the diameter is always twice as long!

Section 4

Circumference

Property

The circumference of a circle is the distance around—or the perimeter of—a circle.

Examples

  • The total length of a hula hoop is its circumference.
  • If you wrap a measuring tape around a basketball, the measurement you get is the ball's circumference.
  • The distance a car tire travels in one full rotation is equal to its circumference.

Explanation

Circumference is just the fancy, official name for a circle's perimeter. Imagine you could unpeel the edge of a cookie and lay it out in a straight line. The length of that line is the circumference! It’s the total distance an ant would have to walk to complete one full lap around the edge of the cookie.

Book overview

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

Continue this chapter

Chapter 3: Lessons 21–30, Investigation 3

  1. Lesson 1Current

    Lesson 21: Triangles, Rectangles, Squares, and Circles, Activity Drawing a Circle

  2. Lesson 2

    Lesson 22: Naming Fractions, Adding Dollars and Cents, Activity Counting Money

  3. Lesson 3

    Lesson 23: Lines, Segments, Rays, and Angles, Activity Real-World Segments and Angles

  4. Lesson 4

    Lesson 24: Inverse Operations

  5. Lesson 5

    Lesson 25: Subtraction Word Problems

  6. Lesson 6

    Lesson 26: Drawing Pictures of Fractions

  7. Lesson 7

    Lesson 27: Multiplication as Repeated Addition, More Elapsed Time Problems, Activity Finding Time

  8. Lesson 8

    Lesson 28: Multiplication Table

  9. Lesson 9

    Lesson 29: Multiplication Facts: 0s, 1s, 2s, 5s

  10. Lesson 10

    Lesson 30: Subtracting Three-Digit Numbers with Regrouping, Activity Subtracting Money

  11. Lesson 11

    Investigation 3: Multiplication Patterns, Area, Squares and Square Roots, Activity 1 Finding Perimeter and Area, Activity 2 Estimating Perimeter and Area