Unit 6 — Measurement and Geometry

Welcome back!

Mathematics helps us describe the world around us.

We measure distances, build homes, design playgrounds, draw maps, and create works of art using measurement and geometry.

Today you will strengthen these important mathematical skills.

Measuring Length

Length tells us how long something is.

Common units include:

• inches
• feet
• yards
• centimeters
• meters

Choose the unit that best matches the object you are measuring.

For example:

• a pencil is measured in inches or centimeters
• a classroom is measured in feet or meters
• a road is measured in miles or kilometers

Measuring Weight and Mass

Weight and mass help describe how heavy an object is.

Common units include:

• ounces
• pounds
• grams
• kilograms

Different units are useful for different sizes of objects.

Measuring Capacity

Capacity tells us how much a container can hold.

Examples include:

• cups
• pints
• quarts
• gallons
• milliliters
• liters

Recipes often use these measurements.

Perimeter

The perimeter is the distance around the outside of a shape.

To find the perimeter:

Add the lengths of all the sides.

Example:

A rectangle has sides:

5 feet

3 feet

5 feet

3 feet

Perimeter:

5 + 3 + 5 + 3 = 16 feet

Area

Area measures the amount of space inside a flat shape.

One way to find area is by counting equal-sized squares.

For rectangles:

Length × Width

Example:

A rectangle is:

6 feet long

4 feet wide

Area:

6 × 4 = 24 square feet

Lines and Angles

Geometry also studies lines and angles.

Some examples are:

• straight lines
• curved lines
• parallel lines
• intersecting lines

An angle is formed when two lines meet.

Examples include:

• right angle
• acute angle
• obtuse angle

We see angles in buildings, roads, and many everyday objects.

Two-Dimensional and Three-Dimensional Shapes

Flat shapes are called two-dimensional (2D) shapes.

Examples include:

• square
• rectangle
• triangle
• circle
• pentagon
• hexagon

Solid objects are called three-dimensional (3D) shapes.

Examples include:

• cube
• sphere
• cylinder
• cone
• rectangular prism
• pyramid

Geometry helps us describe both flat and solid objects.

Activity

Walk through your home or classroom.

Find:

• three rectangles
• three circles
• one cube
• one cylinder

Measure one object and calculate:

• its perimeter
• its area (if possible)

Practice

Answer these questions.

What does perimeter measure?

What does area measure?

Name four units of length.

What is the difference between a 2D shape and a 3D shape?

Name three solid shapes.

Review

Today you learned:

• how to measure length, weight, and capacity
• perimeter measures distance around a shape
• area measures space inside a shape
• geometry studies lines, angles, and shapes
• shapes can be two-dimensional or three-dimensional

Measurement and geometry help us understand and describe the physical world with accuracy.

Looking Ahead

Next we will learn how graphs, charts, and careful reasoning help us solve mathematical problems and understand information more clearly.