We included **HMH Into Math Grade 4 Answer Key PDF** **Module 13 Lesson 3 Relate Angles to Fractional Parts of a Circle **to make students experts in learning maths.

## HMH Into Math Grade 4 Module 13 Lesson 3 Answer Key Relate Angles to Fractional Parts of a Circle

I Can measure an angle as it relates to the fractional part of the circle.

**Spark Your Learning**

For part of his art career, Russian painter and art thinker Wassily Kandinsky focused on painting circles, half-circles, angles, lines, and curves. In his paintings, he overlapped circles and used thick lines to cut circles into pieces forming angles. How can you describe the measure of the orange angle in the circle?

Answer:

270 degrees of orange.

Explanation:

There are 4 parts in the circle of size white angle = 90 degrees

360/90 = 4

its 4 parts

3 x 90 = 270 degrees of orange.

**Turn and Talk** If you join the white angle and the orange angle, how many angles fill the circle?

Answer:

4 angles

Explanation:

The circle is of 360 degrees, each angle is of 90 degrees.

**Build Understanding**

Question 1.

Many painters and sculptors use circles in their works. Often, it is helpful to know the measure of a circle when assembling different pieces. How can you describe the measure of this circle?

A. How can you use a \(\frac{1}{4}\) fraction piece to make an angle on the circle?

Answer:

Explanation:

from center \(\frac{1}{4}\) part is measured

from center to pointing on the outer circle at P and Q

angle formation from center C as POQ 90 degrees is \(\frac{1}{4}\) part of the circle.

B. How can you make another angle on the circle?

Answer:

Explanation:

Draw a line from the center to pointing on the outer circle at P and Q,

angle formation from center C as POQ 90 degrees is \(\frac{1}{4}\) part of the circle,

and another angle by ex tending the line from O to R as straight line.

So, the angle between RQ is 180 degrees.

C. You have traced 2 fraction pieces. How can you label the total number of fractions?

Answer:

\(\frac{2}{4}\)

Explanation:

2 fraction pieces are traced, as the circle is divided into 4 equal parts.

D. How many times will you need to turn the fraction piece to form the circle?

Answer:

4 times

Explanation:

4\(\frac{1}{4}\) fraction piece to form the circle.

As the circle is divided into 4 equal parts of each \(\frac{1}{4}\)

E. How many angles come together in the center to form the circle?

The measure of the circle is _________ angles.

Answer:

4 angles of 90 degrees

Explanation:

As the circle is divided into 4 equal parts of each \(\frac{1}{4}\)

The measure of the circle is 4 angles.

**Turn and Talk** How does the number of angles that it takes to form a circle relate to the measure of a circle?

Answer:

Angles that are formed inside of a circle by two chords create four arcs on a circle.

Explanation:

360 degrees/ number of parts of the circle.

Angle is 360 degrees from the center point of the circle.

Number of angles depends on the size of the angle.

Question 2.

In planning an abstract painting, Penn draws a circle and uses fraction pieces to make angles in the circle. What is the fractional measure of the shaded angle?

A. How can you find the number of angles that come together in the center of the circle?

Answer:

45 degrees

Explanation:

Circle is divided into 8 equal parts.

360 degrees/ number of parts of the circle

\(\frac{360}{8}\)

= 45 degrees

B. What fraction of the circle is shaded green?

Answer:

\(\frac{3}{8}\)

Explanation:

circle is divided into 8 equal parts, 3 parts of fraction is shaded.

\(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) = \(\frac{3}{8}\)

**Turn and Talk** If Penn chose to use \(\frac{1}{12}\) fraction pieces to make the angles in the circle, how would it change the measure of the circle?

Answer:

30 degrees

Explanation:

circle is divided into 12 equal parts, sum of angle sin circle is 360 degrees.

360 x \(\frac{1}{12}\) = 30 degrees

**Check Understanding**

**What is the fractional measure of the shaded angle?**

Question 1.

Answer:

\(\frac{3}{5}\)

Explanation:

whole is divided into 5 equal parts,

the sum of the whole is 360 degrees.

\(\frac{3}{5}\) of fraction is shaded.

Question 2.

Answer:

whole circle is shaded.

Explanation:

The sum of the whole is 360 degrees.

In the given figure complete circle is shaded.

Question 3.

Joyce cut a strawberry pie into 10 equal slices. She shares 7 slices of the pie with her family. What is the fractional measure of the angle of the pie that is left?

Answer:

\(\frac{7}{10}\) = 36 degrees

Explanation:

Joyce cut a strawberry pie into 10 equal slices.

She shares 7 slices of the pie with her family.

The fractional measure of the angle of the pie left

\(\frac{360}{10}\)= 36 degrees

**On Your Own**

Question 4.

Mateo cut a pizza into 8 equal pieces. He and Layla ate 3 pieces of the pizza. How can you find the fractional measure of the angle of the pizza that they ate?

Answer:

360 x \(\frac{3}{8}\) = 45 x 3 = 135

Explanation:

Mateo cut a pizza into 8 equal pieces.

He and Layla ate 3 pieces of the pizza.

The fractional measure of the angle of the pizza that they ate

360 x \(\frac{3}{8}\) = 45 x 3 = 135 degrees

**What is the fractional measure of the shaded angle?**

Question 5.

Answer:

\(\frac{5}{12}\)

Explanation:

whole is divided into 12 equal parts,

the sum of the whole is 360 degrees.

\(\frac{5}{12}\) of fraction is shaded.

360 x \(\frac{5}{12}\) = 5 x 30 = 150 degrees

Question 6.

Answer:

\(\frac{4}{8}\)

Explanation:

whole is divided into 8 equal parts,

the sum of the whole is 360 degrees.

\(\frac{4}{8}\) is shaded.

360 x \(\frac{4}{8}\)

= 360 x \(\frac{1}{2}\)

= 180 degrees

Question 7.

**Reason** Maya divided a circle into 8 equal parts. She shades 3 angles of the circle. Then she shades 2 more angles. What is the fractional measure of the shaded angles of the circle? _________ What is the fractional measure of the unshaded angles of the circle? ________

Answer:

\(\frac{3}{8}\)

\(\frac{3}{8}\) + \(\frac{2}{8}\) = \(\frac{5}{8}\)

360 x \(\frac{5}{8}\)

= 360 x \(\frac{1}{2}\)

= 225 degrees

the fractional measure of the unshaded angles of the circle

360 – 225 = 135 degrees

Question 8.

**Open Ended** How do the shaded angles of the circles for Problems 5 and 6 compare?

Answer:

Comparison between 5 and 6 problems

more number of fractional part of a circle lesser the angle between the parts.

Explanation:

In Problem 5 the circle is divided in to 12 parts, 5 parts is shaded

In Problem 6 the circle is divided in to 8 parts, 4 parts is shaded.

In both the problems the circle is of with complete angle 360 degrees.

Angle of each part in the problem 5 is of 30 degrees.

Angle of each part in the problem 6 is of 45 degrees.

**I’m in a Learning Mindset!**

How can I keep myself on task when I am not sure how to find the fractional measure of the angle of a circle?

Answer:

First one should know that fraction is a part of the circle.

Measure of an angle is an arc drawn from the center of the circle and degree is the unit of measure of angle.

Explanation:

Degrees are related to fractional parts of a circle because \(\frac{1}{360}\) of a circle is equal to one degree.

There are 360 degrees in a circle.

For fraction of a circle with 360as the denominator and the number will be the degrees of angle.