Week+1+Assignments

​Welcome to week 1 of Introduction to Geometry. During this week in the computer lab, you will be expected to complete the following tasks, discussions, blog posts, and performance assessments.

1** ||= 8:00-9:00 1st Homeroom ||= 9:00-10:00 2nd Homeroom ||= 10:00-11:00 3rd Homeroom ||= 11:00-12:00 4th Homeroom ||= 1:00-2:00 5th Homeroom || (Part 2 and part 3) Part 3 can be completed in class or at home. ||= **Task 1** (Part 2 and Part 3) Part 3 can be completed in class or at home. ||= **Task 1** (Part 2 and Part 3) Part 3 can be completed in class or at home. ||= **Task 1** (Part 2 and Part 3) Part 3 can be completed in class or at home. ||= **Task 1** (Part 2 and Part 3) Part 3 can be completed in class or at home. || Part 1 ||= **Task 2** Part 1 ||= **Task 2** Part 1 ||= **Task 2** Part 1 ||= **Task 2** Part 1 || Part 2 ||= **Task 2** Part 2 ||= **Task 2** Part 2 ||= **Task 2** Part 2 ||= **Task 2** Part 2 || Part 1 and 2 ||= **Task 3** Part 1 and 2 ||= **Task 3** Part 1 and 2 ||= **Task 3** Part 1 and 2 ||= **Task 3** Part 1 and 2 ||
 * = **Week
 * = **Monday** ||= **Task 1** (Part 1) ||= **Task 1** (Part 1) ||= **Task 1** Part 1 ||= **Task 1** Part 1 ||= **Task 1** Part 1 ||
 * = **Tuesday** ||= **Task 1**
 * = **Wednesday** ||= **Task 2**
 * = **Thursday** ||= **Task 2**
 * = **Friday** ||= **Task 3**
 * =  ||= Mrs. Evans ||= Mrs. Gober ||= Mr. Cole ||= Mrs. Howe ||= Mrs. Duncan ||

**__ Assignment Overview: __**

Task 1 part 1 "King Arthur's Round Table" Complete the following:


 * 1. __Read:__** //Sir Cumference and the First Round Table// by Cindy Neuschwander before participating in the lesson.

Pay attention to how the area of a circle relates to the area of a parallelogram.
 * 2. __Explore__** the following Websites:

This site shows the animation for deriving the circle formula.
 * http://curvebank.calstatela.edu/circle/circle.htm

This site has a non-animated version for finding the area of a circle.
 * http://www.worsleyschool.net/science/files/circle/area.html


 * 3. __Take Accelerate Reader test__** on the book to test comprehension of the reading material.


 * __Ta​s​k 1: Discussion topic__**


 * King Arthur’s meeting room measures 20 m x 20 m. He needs your help to find the perfect table for his meeting room. Which shape is the best one to use to make a table for the room? How big should the table be in order to seat all the knights and have plenty of room to walk around the table​? **

1. Consider…How much space does each table require? How can you find this out? Create a formula to find the area for each shape.

· What if the table’s shape is a rectangle?

· What if the table’s shape is a square?

· What if the table’s shape is a parallelogram?

· What if the table’s shape is a triangle?

2. For each table (rectangle, square, parallelogram, triangle), create a chart. Include the table’s measurements (base and height) and area. Don’t forget to include decimals and fractions in some of the measurements.

3. What if the table is a circle? How big should it be?


 * Use your paper as the table and follow Sir Cumference’s and Lady Di’s steps to modify their “table” or paper. As students work on formulas, they want to use square tiles or grid paper to help determine a formula for area of a square and rectangle (A= b x h). It is important to use base and height instead of length times width (l x w) and side x side (s2) so that students will be able to make the connection to the formulas for parallelograms and triangles. **


 * Box 1**

base= 4 units hight= 3 units Area = 12 units squared

A=b x h

A=b x h base= 4 units hight= 4 units Area = 16 units squared
 * Box 2**

If you know the formula for finding the area of squares and rectangles, you can use this knowledge to find the formula for parallelograms and triangles.


 * __Questions to consider and promote discussion:__**

1. How are parallelograms and rectangles alike?

2. Is there anything I can do to make a parallelogram look like a rectangle WITHOUT changing the area?

3. Or, is there anything I can do to make a rectangle look like a parallelogram WITHOUT changing the area?


 * Case 1- A rectangle can be turned into a parallelogram by cutting off a triangle and sliding it to the opposite side as shown below. Since parallelograms can be created from a rectangle WITHOUT changing the area, the formula for the area of a parallelogram is the same as the formula for the area of a rectangle… A = b x h. **


 * Case 2- A parallelogram can be turned into a rectangle by cutting off a triangle and sliding it to the opposite side as shown below. Since a parallelogram can be arrange​d into a rectangle WITHOUT changing the area, the formula for the area of a parallelogram is the same as the formula for the area of a rectangle … A = b x h. **


 * More questions to consider:**

1. How are triangles and rectangles alike?

2. How is the area of a triangle related to the area of a rectangle?

3. If you draw a diagonal in the rectangle, you get two triangles. So, a triangle is ½ a rectangle. Therefore, the formula for finding the area of a tri​angle would be ½ the formula for the area of a rectangle… A = ½ b x h or A= b x h/2


 * __Explore the following websites:__**
 * Since we know the formula for the area of a parallelogram, we can derive the area for a circle.**

[] This site shows the animation for deriving the circle formula.

[]This site has a non-animated version for finding the area of a circle.

The circumference is the distance around the circle (C = 3.14 x d ). However, when the sections of the circle are arranged into a rectangle, the circumfere​nce becomes the TWO bases of the rectangle. Each base is ½ the circumference or r.


 * __Task 1 Part 2:__**
 * Answer the following questions though a group discussion of your content knowledge:**

1. How much space does each table require? How can you find this out?

2. Create a formula to find the area for each shape.

· What if the table’s shape is a rectangle?

· What if the table’s shape is a square?

· What if the table’s shape is a parallelogram?

· What if the table’s shape is a triangle?

3. For each table (rectangle, square, parallelogram, triangle), create a chart. Include the table’s measurements (base and height) and area. Don’t forget to include decimals and fractions in some of the measurements.

4. What if the table is a circle? How big should it be?

__ **Task 1 Part 3:** __ <span style="font-family: 'Arial','sans-serif'; font-size: 9pt;"> **Answering the following on Week 1's Blog page:**


 * King Arthur’s meeting room measures 20 m x 20 m. He needs your help to find the perfect table for his meeting room. Which shape is the best one to use to make a table for the room? How big should the table be in order to seat all the knights and have plenty of room to walk around the table? Summarize your group’s answers to the questions during your Skype discussion. **

<span style="font-family: 'Arial','sans-serif'; font-size: 120%;">**__Task 2: “It’s As Easy As Pi”__ Discover how pi relates to the circumference of a circle by using an Elluminate Live session. ** **<span style="color: #0000ff; font-family: 'Arial','sans-serif'; font-size: 9pt; mso-bidi-font-weight: bold; msobidifontweight: bold;">Video presentation will allow all users to see the teacher’s demonstration of the discovery process. **

For this activity you will need different size circular objects (soda cans, CD’s wastebaskets, paper plates), string, scissors, tape. This is a hands-on way to divide a circle’s circumference by its diameter. You will s hare your findings through a class discussion.

1. Carefully wrap string around the circumference of your circular object. (Ask a partner to help.)

2. Cut the string when it is exactly the same length as the circumference.

3. Now take your “string circumference” and stretch it across the diameter of your circular object.

4. Cut as many “string diameters” as you can.

5. How many diameters could you cut?

6. Try this with at least 3 different size circles. What do you notice?

Discussion suggestions: Compare your data with others.

1. What do you notice? 2. How do you think the diameter and circumference of a circle are related? <span style="font-family: 'Calibri','sans-serif'; font-size: 11pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-weight: bold; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;">.

This task is an introduction to pi. No matter what circle you use, you will be able to cut 3 complete diameters and have a small bit of string left over. Estimate what fraction of the diameter this small piece could be (about 1/7). The Circle’s Measure task fully develops the relationship between the circumference and the diameter of a circle. You have “cut pi, “about 3 and 1/7 pieces of string, by determining how many diameters can be cut from the circumference. Tape the 3 + pieces of string onto paper and explain their significance. The important aspect of this task is for you to see that it takes a little more than 3 diameters to make the circumference. If you do not get the 1/7 that is fine. __**Task 2 Part 2 :**__

Explore how large pi actually is:

Digits of pi []

1. Post what pi is and how they discovered it on their blog site. <span style="font-family: 'Comic Sans MS',cursive; font-size: 130%; mso-bidi-font-weight: bold; msobidifontweight: bold;">

Extension:

The first 10,000 digits of pi [] Digits of pi [] Where is your Birthday in pi [] Teach pi.org [] Pi day activities []

<span style="font-family: 'Arial','sans-serif'; font-size: 9pt;">**Task 3: “The Circle’s Measure”** Read: Sir Cumference and the Dragon Pi by Cindy Neuschwander.

Take an Accelerated Reader test on the story.

<span style="font-family: 'Arial','sans-serif'; font-size: 9pt;">**Task 3 Part 2:** <span style="font-family: 'Arial','sans-serif'; font-size: 9pt;">Skype discussion (synchronous discussion), wiki exploration, and classroom blog post (asynchronous discussion)

<span style="font-family: 'Arial','sans-serif'; font-size: 9pt; mso-bidi-font-weight: bold;">Make a valuable connection between the circumference and diameter of circles in their learning groups.

<span style="font-family: 'Arial','sans-serif'; font-size: 9pt; mso-bidi-font-weight: bold; mso-fareast-font-family: Arial; msobidifontweight: bold; msofareastfontfamily: Arial; msolist: Ignore;">1. <span style="font-family: 'Arial','sans-serif'; font-size: 9pt; mso-bidi-font-weight: bold;">Display the Circle’s Measure on the wiki. Explain that it is their job, as a group, to find the solution to the riddle and save Sir Cumference before the knights get to him.

<span style="font-family: 'Arial','sans-serif'; font-size: 9pt; mso-bidi-font-weight: bold; mso-fareast-font-family: Arial; msobidifontweight: bold; msofareastfontfamily: Arial; msolist: Ignore;">2. <span style="font-family: 'Arial','sans-serif'; font-size: 9pt; mso-bidi-font-weight: bold;">Reveal the flasks on the wiki. Have students download the Sir Cumference worksheet, so they can participate in the activity.

<span style="font-family: 'Arial','sans-serif'; font-size: 9pt; mso-bidi-font-weight: bold; mso-fareast-font-family: Arial; msobidifontweight: bold; msofareastfontfamily: Arial; msolist: Ignore;">3. <span style="font-family: 'Arial','sans-serif'; font-size: 9pt; mso-bidi-font-weight: bold;">Have students complete part A individually. Encourage students to share their ideas and thoughts with their group. Share their ideas in classroom discussion page.

<span style="font-family: 'Arial','sans-serif'; font-size: 9pt; mso-bidi-font-weight: bold; mso-fareast-font-family: Arial; msobidifontweight: bold; msofareastfontfamily: Arial; msolist: Ignore;">4. <span style="font-family: 'Arial','sans-serif'; font-size: 9pt; mso-bidi-font-weight: bold;">If at this time students don’t bring up circumference and diameter, help them make this connections.

<span style="font-family: 'Arial','sans-serif'; font-size: 9pt; mso-fareast-font-family: Arial; msofareastfontfamily: Arial; msolist: Ignore;">5. <span style="font-family: 'Arial','sans-serif'; font-size: 9pt; mso-bidi-font-weight: bold;">By now, students may understand that there is a connection between diameter and circumference and that the answer is very close to 3. If this is not the case, hold a brief discussion.

<span style="font-family: 'Arial','sans-serif'; font-size: 9pt; mso-bidi-font-weight: bold; mso-fareast-font-family: Arial; msobidifontweight: bold; msofareastfontfamily: Arial; msolist: Ignore;">6. <span style="font-family: 'Arial','sans-serif'; font-size: 9pt; mso-bidi-font-weight: bold;">Experiment with various objects to find the true answer to the problem. Direct the students’ attention to Part B of the work sheet. Review how to measure the circumference and diameter of an object in centimeters and record the data in the table.

<span style="font-family: 'Arial','sans-serif'; font-size: 9pt; mso-bidi-font-weight: bold; mso-fareast-font-family: Arial; msobidifontweight: bold; msofareastfontfamily: Arial; msolist: Ignore;">7. <span style="font-family: 'Arial','sans-serif'; font-size: 9pt; mso-bidi-font-weight: bold;">Post on the wiki page: Have students measure their objects and record their data on the centimeter grid.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 130%;">**Task 3: The Circle’s Measure:**


 * Radius and Lady Di of Ameter need your help!**
 * Sir Cumference has turned into a dragon!**
 * They must find a cure before he is slain by the King’s knights.**
 * You must solve the riddle to discover the cure!**
 * Hurry, there isn’t much time!**

In this lesson, students make a valuable connection between the circumference and diameter of circles. For any given diameter, the circumference of the object is diameter x π. This relationship is often expressed in the formula:

Circumference = pi x diameter or c = π x d

Thus, if an object has a diameter of 2 cm, the circumference of that objects is approximately 6.28cm.


 * 2cm circumference =** 2 x π x r
 * = 6.28cm**

Discussion:

For each group:

<span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-bidi-font-weight: bold; mso-fareast-font-family: Symbol; msobidifontfamily: Symbol; msobidifontweight: bold; msofareastfontfamily: Symbol; msolist: Ignore;">· Several circular objects <span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-bidi-font-weight: bold; mso-fareast-font-family: Symbol; msobidifontfamily: Symbol; msobidifontweight: bold; msofareastfontfamily: Symbol; msolist: Ignore;">· 1 recipe Dragon’s Breath: 1 Erlenmeyer flask (or sealed jar or bottle) filled with 100 ml of water and 2 drops of green food coloring, sealed with a rubber stopper. Attach a copy of “The Circle’s Measure” to each flask. <span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-bidi-font-weight: bold; mso-fareast-font-family: Symbol; msobidifontfamily: Symbol; msobidifontweight: bold; msofareastfontfamily: Symbol; msolist: Ignore;">· Eyedropper <span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-bidi-font-weight: bold; mso-fareast-font-family: Symbol; msobidifontfamily: Symbol; msobidifontweight: bold; msofareastfontfamily: Symbol; msolist: Ignore;">· Saving Sir Cumference worksheet <span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-bidi-font-weight: bold; mso-fareast-font-family: Symbol; msobidifontfamily: Symbol; msobidifontweight: bold; msofareastfontfamily: Symbol; msolist: Ignore;">· Measuring tape (metric) <span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-bidi-font-weight: bold; mso-fareast-font-family: Symbol; msobidifontfamily: Symbol; msobidifontweight: bold; msofareastfontfamily: Symbol; msolist: Ignore;">· Pencil <span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-bidi-font-weight: bold; mso-fareast-font-family: Symbol; msobidifontfamily: Symbol; msobidifontweight: bold; msofareastfontfamily: Symbol; msolist: Ignore;">· Yarn or string <span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-bidi-font-weight: bold; mso-fareast-font-family: Symbol; msobidifontfamily: Symbol; msobidifontweight: bold; msofareastfontfamily: Symbol; msolist: Ignore;">· Centimeter grid paper

Explain Background information about pi:

Pi was probably discovered sometime after people started using the wheel. The people of Mesopotamia (now Iran and Iraq) certainly knew about the ration of diameter to circumference. The Egyptians knew it, as well. They gave it a value of 3.16. Later, the Babylonians figured it to 3.125. But it was the Greek mathematician Archimedes who really got serious about the ratio. He was the one who figured that the ration was less than 22/7, but greater than 221/77. But pi wasn’t called “pi” until William Jones, and English mathematician, started referring to the ration with the Greek letter pi or “p” in 1706. Even so, pi really didn’t catch on until the more famous Swiss mathematician, Leonhard Euler, picked up on it in 1737. Thus, pi evolved through the contribution of several individuals and cultures.

Read Sir Cumference and the Dragon Pi by Cindy Neuschwander. Arrange students in groups of three or four.

<span style="mso-bidi-font-weight: bold; mso-fareast-font-family: 'Times New Roman'; msobidifontweight: bold; msofareastfontfamily: 'Times New Roman'; msolist: Ignore;">1. Have students read pages 1-12 or have it displayed on the computer.

<span style="mso-bidi-font-weight: bold; mso-fareast-font-family: 'Times New Roman'; msobidifontweight: bold; msofareastfontfamily: 'Times New Roman'; msolist: Ignore;">2. Display the Circle’s Measure on the computer. Explain that it is their job, as a group, to find the solution to the riddle and save Sir Cumference before the knights get to him.

<span style="mso-bidi-font-weight: bold; mso-fareast-font-family: 'Times New Roman'; msobidifontweight: bold; msofareastfontfamily: 'Times New Roman'; msolist: Ignore;">3. Reveal the flasks. Have students download the Sir Cumference worksheet, so they can participate in the activity. Have students complete part A individually (think). Encourage students to share their ideas and thoughts with their group (pair). Allow 2-3 students to discuss their ideas with the class (share).

<span style="mso-bidi-font-weight: bold; mso-fareast-font-family: 'Times New Roman'; msobidifontweight: bold; msofareastfontfamily: 'Times New Roman'; msolist: Ignore;">4. If at this time students don’t bring up circumference and diameter, help them make this connections.

<span style="mso-bidi-font-weight: bold; mso-fareast-font-family: 'Times New Roman'; msobidifontweight: bold; msofareastfontfamily: 'Times New Roman'; msolist: Ignore;">5. After the students understand circumference, and diameter are the two measurements open what the boy, Radius as done (14-18 only).

<span style="mso-bidi-font-weight: bold; mso-fareast-font-family: 'Times New Roman'; msobidifontweight: bold; msofareastfontfamily: 'Times New Roman'; msolist: Ignore;">6. By now, students may understand that there is a connection between diameter and circumference and that the answer is very close to 3. If this is not generally hold a brief discussion.

<span style="mso-bidi-font-weight: bold; mso-fareast-font-family: 'Times New Roman'; msobidifontweight: bold; msofareastfontfamily: 'Times New Roman'; msolist: Ignore;">7. Experiment with various objects to find the true answer to the problem. Direct the students’ attention to Part B of the work sheet. Review how to measure the circumference and diameter of an object in centimeters and record the data in the table. (String or yarn may be used to wrap around circular object, and then told not to go, or my 4H club). Have students measure their objects and record their data on the centimeter grid.

<span style="font-family: Calibri; mso-bidi-font-family: Calibri; mso-bidi-font-weight: bold; mso-bidi-theme-font: minor-latin; msobidifontfamily: Calibri; msobidifontweight: bold; msobidithemefont: minor-latin; msolist: Ignore;">8. By looking at the data, can you see any relationships? Encourage the students to find a more exact number. After the students have identified the number (3.1 or 3.2) you may introduce the symbol to represent (the ratio of the circumference diameter of a circle).

When mos​t students have completed part C, regain that attention findings the class and discuss their findings. Guide the discussion by asking certain type of question. By looking at the data, can you see any relationships The graphs should be admitted with a slight