Cool Crafts
UNIT NAME: REAL NUMBERS AND THE COORDINATE PLANE
Directions: Follow the directions to complete a posting for the CoolCrafts website
explaining how to create a string of pennant flags. Your completed posting will be
submitted as your portfolio assessment.
Try It
The best way to explain a process is to first follow the process yourself! Follow
these instructions to design your own string of pennant flags.
1. Choose a room you would like to decorate. Measure its length or width. This
measurement will be the length of your pennant string.
2. Choose a size of paper square to use. (Hint: Whole number side lengths will
make the calculations easier.)
3. Cut the square in half along the diagonal to form two paper triangles
(pennant flags).
4. Measure the length of the diagonal. Then use the Pythagorean Theorem to
find its exact length.
5. You will attach each triangle to the string along its diagonal side, with no
space between triangles. Divide the length of the string by the length of the
diagonal to determine how many triangles you will need.
© 2015 Connections Education LLC. All rights reserved. 2
Analyze It
Use your pennant string design to analyze the process.
Why is your measurement of the diagonal's length different than the length
you found using the Pythagorean Theorem?
Which special version of the Pythagorean Theorem can you use to find the
length of any square's diagonal, d, using only the length of its side, s?
Why do you have to use estimation to find the number of triangles you need
for the string?
Explain It
Use your design and analysis to write a website posting describing the process
readers can use to make a string of pennant flags using any length string and any
size square. Your posting should include the following:
step-by-step instructions
a formula that can be used to find the diagonal length of any paper square
and a formula that can be used to find the total number of triangles needed
diagrams that make the instructions and formulas easier to understand
an explanation of why this craft project must involve estimation and your
recommended level of precision that readers should use
You may also wish to include a photograph of your string of pennant flags in your
posting. Alternatively, you can include a drawing of your completed project.
Title: DIY Pennant Flag String: A Fun and Easy Craft Project
Introduction:
Welcome to CoolCrafts! In this tutorial, we will guide you through the process of creating your own string of pennant flags. This project is perfect for adding a touch of creativity and color to any room. Let's get started!
Materials Needed:
- String or ribbon of desired length
- Paper squares of chosen size
- Scissors
- Ruler or measuring tape
Step-by-Step Instructions:
1. Choose a room for decoration: Select the room you wish to decorate and measure either its length or width. This measurement will determine the length of your pennant string.
2. Select a paper square size: To make calculations easier, choose a paper square with whole number side lengths. For example, a square with side length 10cm or 6 inches.
3. Cut the square in half: Take your selected square and cut it along the diagonal, creating two identical paper triangles or pennant flags.
4. Measure the diagonal length: Take one of the paper triangles and measure the length of its diagonal using a ruler or measuring tape. Write down this measurement.
5. Use the Pythagorean Theorem: To find the exact length of the diagonal, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the diagonal is the hypotenuse, and the sides are the two equal legs of the triangle, which are the same as the side length of the square.
The special version of the Pythagorean Theorem for finding the length of a square's diagonal is:
d^2 = s^2 + s^2
Where:
- d is the length of the diagonal
- s is the length of the side of the square
6. Determine the number of triangles needed: Attach each paper triangle to the string along its diagonal side, with no space between triangles. To find out how many triangles you need, divide the length of the string by the length of the diagonal. Round up to the nearest whole number for accuracy.
Formula for the number of triangles needed:
Number of triangles = (Length of the string) ÷ (Length of the diagonal)
Involvement of Estimation:
You may have noticed that your measurement of the diagonal's length differs slightly from the length calculated using the Pythagorean Theorem. This discrepancy arises due to the limitations of measuring tools, human error, or rounding during calculations. In craft projects like this, some level of estimation is involved. It is recommended to use a reasonable level of precision, such as rounding measurements to the nearest centimeter or inch.
Tips for Precision:
- Take accurate measurements using a ruler or measuring tape.
- Ensure the string is taut when attaching the pennant flags to maintain consistency.
- Consider using a larger sample size of triangles to minimize estimation errors.
Visual Aids:
Include diagrams or photographs for better understanding of the instructions and formulas. These visual aids will enhance the clarity of your post and make it easier for readers to follow along.
Conclusion:
Now that you have all the information and steps to create your own string of pennant flags, it's time to unleash your creativity! This project allows you to customize the size and length of your string, making it suitable for any room. Get ready to add a personal touch to your space and enjoy the colorful ambiance of your handcrafted pennant flag string. Happy crafting!
(Optional: Include a photograph or drawing of your completed project as inspiration for others.)