Unit 10 — Measurement and Geometry

Welcome back!

Measurement and geometry help us understand the size, shape, and position of objects around us.

Builders, architects, engineers, artists, scientists, and mapmakers all use these mathematical ideas every day.

Today you will strengthen your skills in measuring, estimating, and working with geometric figures.

Measuring Length

Length tells how long something is.

Common metric units include:

• millimeters (mm)
• centimeters (cm)
• meters (m)
• kilometers (km)

Common U.S. customary units include:

• inches (in.)
• feet (ft.)
• yards (yd.)
• miles (mi.)

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

Measuring Mass and Weight

Mass measures the amount of matter in an object.

Weight measures the pull of gravity on an object.

Common units include:

Metric:

• grams (g)
• kilograms (kg)

Customary:

• ounces (oz.)
• pounds (lb.)

Different situations require different units.

Measuring Capacity

Capacity tells how much a container can hold.

Examples include:

Metric:

• milliliters (mL)
• liters (L)

Customary:

• cups
• pints
• quarts
• gallons

Understanding capacity helps with cooking, science, and many everyday tasks.

Perimeter

Perimeter is the distance around a figure.

To find the perimeter:

Add the lengths of all sides.

Example:

A rectangle measures:

Length = 8 cm

Width = 5 cm

Perimeter:

8 + 5 + 8 + 5 = 26 cm

Area

Area measures the amount of surface inside a shape.

For rectangles:

Area = length × width

Example:

8 cm × 5 cm = 40 square centimeters

Remember that area is measured in square units.

Angles

An angle forms where two lines meet.

Angles are measured in degrees (°).

Types of angles include:

• acute (less than 90°)
• right (exactly 90°)
• obtuse (greater than 90° but less than 180°)
• straight (180°)

A protractor is used to measure angles.

Polygons

A polygon is a closed figure made of straight sides.

Examples include:

• triangle
• quadrilateral
• pentagon
• hexagon
• octagon

Polygons are classified by the number of their sides.

Symmetry

A figure has symmetry if it can be divided into matching halves.

Some shapes have:

• one line of symmetry
• several lines of symmetry
• rotational symmetry

Symmetry is common in nature, art, architecture, and engineering.

Activity

Measure five objects in your home or classroom.

Record:

• length
• estimated length
• actual length
• appropriate unit of measurement

Then calculate the perimeter and area of a rectangular object.

Finally, identify three polygons and describe their properties.

Practice

Answer these questions.

What is perimeter?

How is area different from perimeter?

What units measure length?

What units measure capacity?

Name the four basic types of angles.

What is symmetry?

Review

Today you learned:

• measurement uses appropriate units
• perimeter measures distance around a figure
• area measures the space inside a figure
• angles are measured in degrees
• polygons are classified by their sides
• symmetry helps describe many shapes

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

Looking Ahead

Next we will begin Grade 4 Science by learning how scientists study matter, energy, and the physical properties of the world around us.