Common Core Standards
CCSS.MATH.CONTENT.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Addresses all 8 Standards for Mathematical Practice


Day #1 Elements of a Circle Lesson
Objective
Students will understand the defining elements of a circle and be able to find the radius and diameter of a circle.

Big Idea
The students will be able to identify and draw the parts of a circle. 
The students will be able to identify and/or calculate the measure of the diameter and radius of a circle.
The students will be able to identify the total number of degrees in a circle.

Vocabulary

    Circle- The set of all points in a plane that are the same distance from a point called the center. 
    Diameter- The distance across a circle through the center.
    Radius- The distance from the center of a circle to any point on the circle. 
    Chord- A line segment that has both endpoints on the circle. 
    Arc- A curved line that is part of the circumference of a circle. 
    Central Angle- An angle whose vertex is the center of the circle.
    Center Point- The point inside a circle that is the same distance from all points on the circle.
    Circumference- The distance around the circle.


Explore
Ask students to draw a large circle on a sheet of paper. From this position,  ask students how they formed the circle and what a circle is. As students share out, have a class scribe (write down) their ideas on their notes. To deepen the understanding of what a circle is, I will visually model what a circle is. Continue the class discussion on what a circle is until I have had 1-3 students to contribute their ideas.

Students may need a bit of support. The main ideas we are trying to get are as follows:
A circle is a series of points all equal distance away from a defined point (the center).
A circle is a continuous curve.
The circle is technically the space confined within the points.

Review students’ notes.

Create a foldable on the parts of a circle. 

Each student needs to obtain two small square sheets of paper in two different colors. Have the students trace the same small circular item (bottom of mug, jar lid, etc.) on each sheet of paper. Cut out both circles. You should now have two congruent circles. Fold both circles horizontally and vertically. Cut a slit to the center on each. Overlap the two circles. (see attachment for example)

Each student will proceed to label the parts of the circle to better understand the parts/concept of the parts of a circle. 

Summarize
Exit Ticket students will participate in an online interactive activity testing their understanding/concept of what was reviewed today.  


Day #2 Relationship Between Circumference and Diameter - What is pi?

Objective
Students will understand the relationship between circumference and diameter.

Big Idea
Did you say pie? or pi? Bring in a circular item for class, and it if happens to be food - AWESOME!

Students will understand the relationship between circumference and diameter.

Explore
Pi Lab:  As an introduction to the unit, students will along with me to explore the ratio between the circumference of a circle and its diameter.  I ask students in advance to bring in one circular item.  While the students are completing the discovery activity, I will monitor progress and providing assistance when necessary.  It is important that this be a student discovery, MP 1, however, so my help will be limited to procedures of wrapping string around the item, and finding the diameter - attention to precision MP 6 will be important as this will help with developing the formula later on.  As students begin to finish the activity, we will come back together as a class and discuss their findings.  Hopefully, students will correctly identify the formula and pi. Analyzing their findings and looking at developing formulas brings in mathematical practices 7 and 8 - looking for repeated reasoning.  This lesson will not work for all students, so I have included some Scaffolding Ideas. 

Summarize

Exit Ticket: After all classwork, problems have been worked out on the board, I will wrap up the lesson by asking two questions: “How is the circumference of a circle related to its diameter?” and “How do we calculate the circumference of a circle given the diameter or the radius?”  I will have students write their answers on the back of their opener and turn in as an exit ticket.



Day #3 Circumference and Area of Circles

Objective
Students will be able to apply the formulas for area and circumference of circles to solve real-world and mathematical problems. 
Big Idea
Ever play a song back in your head over and over? You will be singing about the area and circumference all day after this lesson!

Launch
Students will watch the following 

https://www.flocabulary.com/circles/  This song is a catchy way for students to remember the area and circumference of circles.  I will play the song while I get the notes passed out.

Area and Circumference Notes:  After the fun song, I will move into some formal notes on area, and then a few whole class practice problems.  I will work a few problems out with the kids and then set the off to complete the remaining problems on their own. I am curious to see how kids do with the bicycle question - I have found in the past that many students struggle to realize this is a circumference question.

Instructional Strategy - How do table challenges work?: Students will respond to 7 area and circumference problems.  This is a good way for me to assess who gets it and who doesn't :)  Additionally, their are word problems included so students will have to determine whether they are solving for area or circumference.

  Summarize + Homework
Class Discussion:   I will wrap up the lesson by asking “Who can give us a real world example of when we would apply the area of a circle problem?” (MP 4) taking volunteers for responses.  The purpose of this activity will be to make sure that students understand when it would be appropriate to calculate area, versus circumference.  Normally, lots of hands go up for this question – which is always a good sign!

Homework:  After discussion of the question, Students will have homework, and allow students the last few minutes of class to look it over and ask any questions needed for clarification. Philosophy on Homework


Day #4 Virtual review time

Students will be given an online activity with performance task to test for mastery. 

Outcome 1: Students will utilize operations with rational numbers and use the order of operations to evaluate numerical and algebraic expressions. 
1.1 Add, subtract, multiply, and divide positive rational numbers (integers, fractions, decimals). 
1.2 Add, subtract, multiply, and divide positive and negative rational numbers. 
1.3 Evaluate numerical and algebraic expressions using the order of operations. 
1.4 Evaluate exponential and radical expressions. 

Outcome 2: Students will solve simple one-variable equations. 
2.1 Solve one-step, one-variable equations. 

Outcome 3: Students will calculate perimeter, circumference, area, surface area, and volume of two and three-dimensional shapes. 
3.1 Define basic concepts associated with geometry. 
3.2 Calculate the perimeter/circumference of a two-dimensional shape. 

Outcome 4: Students will use various problem-solving strategies to solve real-life applications. 
4.1 Translate a verbal model into an algebraic expression or equation. 
4.2 Solve problems involving percents, ratios, and proportions. 
4.3 Convert units of measurement within a system (U.S. Customary or Metric). 


Outcome 5: Students will analyze and interpret a given set of data. 
5.2 Graph data and interpret graphs of data. 
5.3 Find the overall mean given the means of two or more sets of data. 

Outcome 6: Students will use the basic properties of the number system. 
6.1 Restate the equivalent form of numbers using exponents, radicals, scientific notation, absolute values, fractions, decimals, and percents. 
6.2 Use the number line to order numbers, add and subtract signed numbers, and graph one-variable inequalities. 
6.3 Use place value to order and round numbers. 
6.4 Factor whole numbers and find the least common multiple and greatest common factors of two or more numbers. 
6.5 Classify a number as prime or composite using division rules.