A girl rides a big colorful Ferris wheel at a fair

The Amazing Turn

Nadia rides the Ferris wheel at the fair. It turns part of the way around, then stops. How can we measure how far it turned?

4th Grade Math

Step 1: A Circle Cut Into Tiny Turns

Nadia Imagine slicing the wheel's circle into tiny, equal turns. Each tiny turn is called a degree. An angle that turns through 1/360 of a circle is a one-degree angle.

How many one-degree angles fit in one full turn of a circle?

A full circle holds 360 one-degree angles. Each one is 1/360 of the whole turn. So a full turn measures 360 degrees.

Step 2: A Half Turn

The wheel turns through the shaded part: 1/2 of the circle. That is a fraction of the 360 degrees. How many degrees is a half turn?

1/2 of the circle means split 360 into 2 equal parts. 360 ÷ 2 = 180. A half turn is 180 degrees.

Step 3: A Quarter Turn

Now the wheel stops after just the shaded part: 1/4 of the circle. The denominator 4 tells how many equal parts to make. How many degrees is a quarter turn?

1/4 of the circle means split 360 into 4 equal parts. 360 ÷ 4 = 90. A quarter turn is 90 degrees.

Let's Remember

Angles Are Fractions of a Circle

          Step 1: Find the fraction of the circle the angle turns through.

          Step 2: Divide 360 by the denominator.

          Step 3: A full turn = 360 degrees, so 1/360 = 1 degree.

This rule helps you determine any angle's size. Turning is like sharing a pie: more equal parts means a smaller angle.

Picture the Turn

0

90

180

270

360

This number line shows a turn unrolled like a ribbon. A quarter turn lands on 90. A half turn lands on 180. Three quarters lands on 270, and a full turn reaches 360.

Solve It!

An angle turns through 1/6 of a circle. How many degrees does it measure?

1/6 of a circle means 360 ÷ 6 = 60. The angle measures 60 degrees.

Word Problem

A round pizza is cut into 8 equal slices. Every slice makes an angle at the center of the pizza. What is the angle of one slice?

One slice is 1/8 of the circle. 360 ÷ 8 = 45. Each slice makes a 45-degree angle.

What Goes in the Blank?

An angle measures 90 degrees. What number finishes the equation?

90° = 360° ÷ ?

360 ÷ 4 = 90. A 90-degree angle turns through 1/4 of a circle.

Work Backward!

An angle measures 180 degrees. What fraction of a circle does it turn through? Use the fraction rule in reverse.

180 out of 360 degrees is 180/360, which equals 1/2. The angle turns through half the circle.

Watch Out!

A Common Mistake

          Some students think 1/4 of a circle is 4 degrees. That is wrong!

          The 4 tells how many equal parts to make.

          You must divide: 360 ÷ 4 = 90 degrees.

The denominator is a part counter, not the answer. Always divide 360 to find the degrees.

Challenge Round!

Nadia's Ferris wheel turns 1/4 of a circle, then stops. Next it turns 1/6 of a circle more. How many degrees did it turn in all?

First turn: 360 ÷ 4 = 90 degrees. Second turn: 360 ÷ 6 = 60 degrees. Add them: 90 + 60 = 150 degrees.

Clock hands, doorknobs, and skateboard tricks all turn through parts of circles. Where else could you measure a turn in degrees?

Great Work!

0/8

correct

angle degree fraction denominator determine