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Curriculum Unit Design

## Topic Angles, Degrees, and Circles

Estimated Time: Maximum ofTwo weeks – one hour each day

## EL Level: whole class/beginning to advanced

Tools/Materials/Resources:

Overheads for Teacher – projector or a Smart Board and laptop

Worksheets for each student – 1 ea. Day or Internet reflection oral report

Internet math games and constructive manipulatives

5 classroom computers

#### Content and Concepts: Relationships of circles, angles, and degrees and calculate circumference and area of a circle

Knowledge/Vocabulary: Define circle, circumference, turns, angle, degree, obtuse, acute, right angle, radius, Pi, and diameter

Alignment with Standards Understand the relationship between degrees in a circle and ½, ¼, ¾ and full turns. Calculate circumference and area of a circle.

Use a variety of methods such as words, symbols, charts, graphs, tables, diagrams, and models to comprehend and define angles, degrees, turns, and circles

#### Objectives and Foundations of learning

• Students define obtuse, right and acute angles, radius, and diameter and discussion of what students already know,
• Students will relate degrees of angles to ¼, ½, ¾, and full turns and calculate the circumference and area of a circle.
• All students will be engaged and attentive to lesson presented on overhead.
• Students will participate in a group activity and each group will turn in a completed worksheet.
• Students will play Internet math games, keep scores, and will practice fairness in taking turns so that all get to participate fully and equally.

### Procedure

Name of Instructional Model – Direct teach andGroup activities as well as Internet learning – incorporates elements of efficiency and constructivist models for learning.

#### Classroom Management Details – Request eye contact and listening at start of lesson/ or hand signals/ Instruct students to raise hand to answer or ask questions. Monitor by walking around and observing small groups. (Countdown for noise reduction if needed) Remember to facilitate in a manner that lets the students construct the answers and then guide them in the right direction when needed.

Learning Environment: Four or five groups of tables with three or more students at each table. Each table will have a computer with Internet access.

# Student Groupings: Small groups of 4 or 5 students each

Specific Details throughout Lessons

When necessary, regain the students’ attention by hand signal or verbally, depending on number of students and noise level and ask questions on the material covered. Monitor behavior closely by walking around to visit groups and observing/assisting. Watch carefully for full participation from all students

Introduction/Focus: Review/ask questions about what students already know about angles and degrees. Use knowledge from what students already know to guide pace of unit. Give examples from real life that students can relate to and explain that we are going to learn how degrees of angles are measured. Use an example about a race in the Olympics, a dance step or about a marching band in a parade. Then lead into what we will be learning for the next two weeks. Let the students know that they will be working in groups and then at the end of each lesson, one person from each group can share with the class what they learned each day. When covering diameter, area and circumference – use examples such as creating a circular shaped garden or building a structure such a sports arena or floor of a tower.

Development of Content/Activities/Tools: Use an overhead that illustrates how angles are measured. Spend some time with whole class using an overhead to explain degrees and how to calculate different numbers of angles and degrees. Start with showing how there are four 90-degree angles in a circle. (Use manipulatives as necessary.) Ask students what happens if I were to cut each of the 90-degree angles into two pieces. How many of these would make a complete circle? How is a 90-degree angle related to a ¼ turn? Do the same for ½ turn and ¾ turn. Define obtuse and acute angles and then ask students to identify these from pictures in the room or use body language to illustrate by used raised arms at different angles. Use student volunteers and then give groups time to practice concept during group participation. Ask if everyone understands the concept and if most students understand, then move on. If not, explain again. Ask how many angles of 40 degrees each make up a circle. How do we figure it out? Explain how we can use what we already know to figure out the answer. (360/40 = 9) Then go over the re-teach sheet and practice sheet for about 10 minutes. Request that the two students of the week pass out the group worksheets – quietly and quickly. Arrange students into groups of two or three each. Use a timer – give them 15 to 20 minutes to practice and let students know when they have 2 minutes to go. Then, refocus students’ attention and ask two or three volunteers to come up front and share their answers with the rest of the class. After volunteers have shared, start to wrap up by asking the students what they learned today. Use the same type process for each part of the unit. Have the students of the week collect the worksheets each day and then assess and strategize for the next day’s lesson. Review from previous day and then cover as much as reasonable each day - then wrap and review at end of unit. Every other day, instead of worksheets– allow students to play Math games on the Internet for about ½ hour as group participation. Remember to monitor for fairness and equity.

Closure: Hand out the in-class worksheet and request that students complete as much of the in-class work as possible. Let students know that they will work on any unfinished class work the next day. As indicated above – every other day will be an oral report/reflection on Internet experience. (Alternating leaders for each group works well)

Modifications: students who have trouble seeing the overhead can sit close to the front of room. Group students together with varying ability levels. (Based on knowledge of students). Pull small group for instructional assistant re-teach, if necessary. For students who were absent – request instructional assistance as needed.

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Systems of Assessment: Grade worksheets that were completed during group work. All students will participate. 90 % accuracy rate on worksheets and exams overall. Keep students informed of their progress throughout progression of unit. Give a final, accumulative assessment at end of unit. Based on results, either re-teach as necessary or move on to next unit.

Scores for participation and objective scoring on written exams

Sample worksheets follow

# Degrees and Turns Unit used to measure an angle ________________________

How many right angles are in a circle? ________

How many total degrees in a circle? _______

How many 45-degree angles does it take to make a circle? ___________

How many degrees are equal to ¼ turn? _______

How many degrees are equal to ½ turn? _______

# Degrees and Turns Unit used to measure an angle ________________________

How many right angles are in a circle? ________

How many total degrees in a circle? _______

How many 45 degree angles can be divided into a circle? ___________

# Circumference and Area Define Radius:

Define Diameter:

What is the formula for Circumference? (Pi = 3.14)

What is the formula for Area?

Circle: The set of points in a plane that are a fixed distance from a given point, called the center