4.MD.5.Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees. 4.MD.6. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. 4.MD.7. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Anchor Standard/Mathematical Practice(s)

MP.2. Reason abstractly and quantitatively. MP.5. Use appropriate tools strategically. MP.6. Attend to precision. MP.7. Look for and make use of structure.

Information Technology Standard

Use technology tools and skills to reinforce classroom concepts and activities.

Revised Bloom's Level of thinking

Remembering Understanding Applying Analyzing

Learning Target/Task Analysis

4.MD.5 This standard calls for students to explore the connection between angles (measure of rotation) and circular measurement (360 degrees). The diagram below will help students understand that an angle measurement is not related to an area since the area between the 2 rays is different for both circles yet the angle measure is the same. Students explore an angle as a series of ―one-degree turns.‖ A water sprinkler rotates onedegree at each interval. If the sprinkler rotates a total of 100 degrees, how many one-degree turns has the sprinkler made? 4.MD.6 Before students begin measuring angles with protractors, they need to have some experiences with benchmark angles. They transfer their understanding that a 360º rotation about a point makes a complete circle to recognize and sketch angles that measure approximately 90º and 180º. They extend this understanding and recognize and sketch angles that measure approximately 45º and 30º. They use appropriate terminology (acute, right, and obtuse) to describe angles and rays (perpendicular). Students should estimate angles, measure angles and sketch angles. They need to experience measuring angles using an angle ruler as well as a protractor. (The angle ruler allows them to “see” the turns or rotations). 4.MD.7 This standard addresses the idea of decomposing (breaking apart) an angle into smaller parts. Example: A lawn water sprinkler rotates 65 degrees and then pauses. It then rotates an additional 25 degrees. What is the total degree of the water sprinkler rotation? To cover a full 360 degrees how many times will the water sprinkler need to be moved? If the water sprinkler rotates a total of 25 degrees then pauses. How many 25 degree cycles will it go through for the rotation to reach at least 90 degrees?

I can...

I can recognize an angle as a geometric shape. I can define circular arc. I can recognize the relationship between an angle and a circle. I can measure an angle correctly. I can draw an angle of a specific degree.

I can explain how one angle can be broken down into several smaller angles.

I can explain how several smaller angles can be put together to form one large angle.

I can solve addition and subtraction problems to find unknown angles.

Essential Vocabulary

rays, circular arc, center point, angle, vertex, end point, one degree angle, circle, measure angles, protractor, decompose

Sample Assessments

Scavenger Hunt to find and identify types of angles within the school. Students record their findings and share witht the class. Post on bulleting board. Use protracters to measure angles and draw angles of specified degrees. This is modeled by the teacher before students attempt it. Students use protracter to draw a circle. Discuss terminology associated with turn to create a measuremement. Use marshmallows and tootpicks to create different shapes and identify the angles within the shapes. Use a Thinking Map to record angles of shapes.

Differentiation

Intervention:

Angles are geometric shapes composed of two rays that are infinite in length. Students can understand this concept by using two rulers held together near the ends. The rulers can represent the rays of an angle. As one ruler is rotated, the size of the angle is seen to get larger. Ask questions about the types of angles created. Responses may be in terms of the relationship to right angles. Introduce angles as acute (less than the measure of a right angle) and obtuse (greater than the measure of a right angle). Have students draw representations of each type of angle. They also need to be able to identify angles in two-dimensional figures. Students can also create an angle explorer (two strips of cardboard attached with a brass fastener) to learn about angles.

Students can compare angles to determine whether an angle is acute or obtuse. This will allow them to have a benchmark reference for what an angle measure should be when using a tool such as a protractor or an angle ruler. Provide students with four pieces of straw, two pieces of the same length to make one angle and another two pieces of the same length to make an angle with longer rays. Another way to compare angles is to place one angle over the other angle. Provide students with a transparency to compare two angles to help them conceptualize the spread of the rays of an angle. Students can make this comparison by tracing one angle and placing it over another angle. The side lengths of the angles to be compared need to be different. Students are ready to use a tool to measure angles once they understand the difference between an acute angle and an obtuse angle. Angles are measured in degrees. There is a relationship between the number of degrees in an angle and circle which has a measure of 360 degrees. Students are to use a protractor to measure angles in whole-number degrees. They can determine if the measure of the angle is reasonable based on the relationship of the angle to a right angle. They also make sketches of angles of specified measure.

Enrichment:

Use Anglegs to show measurements of acute, right, and obtuse angles.

Angles Project http://www.learnnc.org/lp/media/lessons/MathScienceEducationNetwork1062002602/WSp1.jpg Sir Cumference and the Great Knight of Angleland: In this story, young Radius, son of Sir Cumference and Lady Di of Ameter, undertakes a quest, the successful completion of which will earn him his knighthood. With the help of a family heirloom that functions much like a protractor, he is able to locate the elusive King Lell and restore him to the throne of Angleland. In gratitude, King Lell bestows knighthood on Sir Radius. Nctm.org Figure This: What’s My Angle? math Challenge # 10 - Students can estimate the measures of the angles between their fingers when they spread out their hand.Figure This: What's My Angle?

## Common Core Standards

4.MD.5.Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.

b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

4.MD.6. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

4.MD.7. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

## Anchor Standard/Mathematical Practice(s)

MP.2. Reason abstractly and quantitatively.MP.5. Use appropriate tools strategically.

MP.6. Attend to precision.

MP.7. Look for and make use of structure.

## Information Technology Standard

Use technology tools and skills to reinforce classroom concepts and activities.## Revised Bloom's Level of thinking

RememberingUnderstanding

Applying

Analyzing

## Learning Target/Task Analysis

4.MD.5This standard calls for students to explore the connection between angles (measure of rotation) and circular measurement (360 degrees).

The diagram below will help students understand that an angle measurement is not related to an area since the area between the 2 rays is different for both circles yet the angle measure is the same.

Students explore an angle as a series of ―one-degree turns.‖ A water sprinkler rotates onedegree at each interval. If the sprinkler rotates a total of 100 degrees, how many one-degree turns has the sprinkler made?

4.MD.6

Before students begin measuring angles with protractors, they need to have some experiences with benchmark angles. They transfer their understanding that a 360º rotation about a point makes a complete circle to recognize and sketch angles that measure approximately 90º and 180º. They extend this understanding and recognize and sketch angles that measure approximately 45º and 30º. They use appropriate terminology (acute, right, and obtuse) to describe angles and rays (perpendicular).

Students should estimate angles, measure angles and sketch angles. They need to experience measuring angles using an angle ruler as well as a protractor. (The angle ruler allows them to “see” the turns or rotations).

4.MD.7

This standard addresses the idea of decomposing (breaking apart) an angle into smaller parts.

Example:

A lawn water sprinkler rotates 65 degrees and then pauses. It then rotates an additional 25 degrees. What is the total degree of the water sprinkler rotation? To cover a full 360 degrees how many times will the water sprinkler need to be moved?

If the water sprinkler rotates a total of 25 degrees then pauses. How many 25 degree cycles will it go through for the rotation to reach at least 90 degrees?

## I can...

I can recognize an angle as a geometric shape.I can define circular arc.

I can recognize the relationship between an angle and a circle.

I can measure an angle correctly.

I can draw an angle of a specific degree.

## I can explain how one angle can be broken down into several smaller angles.

## I can explain how several smaller angles can be put together to form one large angle.

## I can solve addition and subtraction problems to find unknown angles.

## Essential Vocabulary

## rays, circular arc, center point, angle, vertex, end point, one degree angle, circle, measure angles, protractor, decompose

## Sample Assessments

Scavenger Hunt to find and identify types of angles within the school. Students record their findings and share witht the class. Post on bulleting board.Use protracters to measure angles and draw angles of specified degrees. This is modeled by the teacher before students attempt it.

Students use protracter to draw a circle. Discuss terminology associated with turn to create a measuremement.

Use marshmallows and tootpicks to create different shapes and identify the angles within the shapes. Use a Thinking Map to record angles of shapes.

## Differentiation

## Intervention:

Angles are geometric shapes composed of two rays that are infinite in length. Students can understand this concept by using two rulers held together near the ends. The rulers can represent the rays of an angle. As one ruler is rotated, the size of the angle is seen to get larger. Ask questions about the types of angles created. Responses may be in terms of the relationship to right angles. Introduce angles as acute (less than the measure of a right angle) and obtuse (greater than the measure of a right angle). Have students draw representations of each type of angle. They also need to be able to identify angles in two-dimensional figures.Students can also create an angle explorer (two strips of cardboard attached with a brass fastener) to learn about angles.

Students can compare angles to determine whether an angle is acute or obtuse. This will allow them to have a benchmark reference for what an angle measure should be when using a tool such as a protractor or an angle ruler. Provide students with four pieces of straw, two pieces of the same length to make one angle and

another two pieces of the same length to make an angle with longer rays. Another way to compare angles is to place one angle over the other angle. Provide students with a transparency to compare two angles to help them conceptualize the spread of the rays of an angle. Students can make this comparison by tracing one angle and placing it over another angle. The side lengths of the angles to be compared need to be different. Students are ready to use a tool to measure angles once they understand the difference between an acute angle and an obtuse angle. Angles are measured in degrees. There is a relationship

between the number of degrees in an angle and circle which has a measure of 360 degrees. Students are to use a protractor to measure angles in whole-number degrees. They can determine if the measure of the angle is reasonable based on the relationship of the angle to a right angle. They also make sketches of angles of specified measure.

## Enrichment:

Use Anglegs to show measurements of acute, right, and obtuse angles.## Illuminations Angle Game

## Instructional Resources

Angles Projecthttp://www.learnnc.org/lp/media/lessons/MathScienceEducationNetwork1062002602/WSp1.jpg

Sir Cumference and the Great Knight of Angleland: In this story, young Radius, son of Sir Cumference and Lady Di of Ameter, undertakes a quest, the successful completion of which will earn him his knighthood. With the help of a family heirloom that functions much like a protractor, he is able to locate the elusive King Lell and restore him to the throne of Angleland. In gratitude, King Lell bestows knighthood on Sir Radius.

Nctm.org Figure This: What’s My Angle? math Challenge # 10 - Students can estimate the measures of the angles between their fingers when they spread out their hand.Figure This: What's My Angle?

## Lesson Plan-Angles,Degrees,Protractors...Oh My!

## Notes and Additional Information