Understanding Angles and Unit Angles Lesson 16-3 CCSS 4.MD.5, 4.MD.5a, 4.G.1 Literature Link: Sir Cumference and the Great Knight of Angleland by Cindy Neuschwander 5-6 pages per day

MATH Essential Questions How can lines, angles, and shapes be described, analyzed, and classified? MATH Essential Questions

MATH Essential Questions How are angles measured, added, and subtracted? MATH Essential Questions

Warm Up There are 7 cars, 4 tricycles, and 5 bicycles parked in the driveway. How many wheels are there?

Think and Write Right angles are angles that make a perfect L . Look around your classroom. Where do you see right angles?

Today’s Lesson In this lesson, you will learn how to use equivalent fractions to find the measure of an angle. Let’s look at the Envision Video for this lesson and take the quiz.

Unit Angles We need a standard way to describe the size of an angle. Mathematicians describe the measure of an angle by using the unit angle of 1/360 of a circle. Remember a circle is 360 degrees. Angles can be measured in units called degreesº. 1/360 is known as 1 degree or a unit angle. There are 360 unit angles in a circle because each unit angle is 1/360 of a circle.

Understanding Angles and Unit Angles Jill drew a right angle and wants to find its measurement. Right angles divide a circle into 4 equal parts. Divide 360º (degrees in a circle) by the number of equal parts (4) to find the single measure of a right angle. 360º / 4 = 90º The angle measure of a right angle is 90º.

Straight Angle A circle (360 degrees) is divided into 2 equal parts. What is the measure of each angle? Think: 360 ÷ 2. This is called a straight angle. A straight angle divides a circle into 2 equal parts. 360º / 2 = 180º.

Practice Find the measure of an angle that cuts off 1/6 of a circle. 1/6 means 1 of 6 equal parts. Divide by 6 to find the angle measure. 360º / 6 = 60º. The angle measure is 60º. A circle is divided into 9 equal parts. What is the angle measure of one of those parts? The angle cuts off 1/8 of the circle. What is the measure of the angle? The angle cuts off 1/5 of the circle. What is the measure of the angle? The angle cuts off 3/8 of the circle. What is the measure of the angle?

Think About Clocks… The hands of a clock make an angle. If one hand points to 12 and the other hand points to 9, how could you describe the angle by the two hands, measuring clockwise from the small hand pointing to the 9 to the big hand pointing to the 12? Work with a partner. Set your clock to the time shown here. Discuss the question above with your partner. Discuss your solutions with the class.

More Practice with Clocks What is the angle measure on these clocks? – Set your clocks and work with your partner to discover the answer.

Problem 1 Hannah cut a circular cake into 6 slices with equal angles. What is the angle measure of each piece? Remind students that a full circle is 360 degrees so to find the measure of each angle, divide 360 by 6.

Problem 2 Mrs. Soto made a pie shaped like a perfect circle. She cut the pie into 12 equal pieces with equal angles. What is the angle measure of each piece?

Problem 3 Sal slices his round pizza into 10 perfect slices with equal angles. What is the measure of each angle?

Problem 4 Greg is making a circular garden. He divides his garden into 8 equal sections with equal angle measures to grow different vegetables. He measures the angle of the tomato section. What is its angle measure?

Lesson Wrap Up In this lesson, you learned how to use unit angles and fractions to find angle measures. Homework (16-3 Practice) for one “Paw Signature” and (16-3 Reteaching & Practice) if you want two “Paw Signatures.” Website for Practice: https://www.ixl.com/math/grade-4/acute-right-obtuse-and-straight-angles