Pascal’s Triangle, named after Blaise Pascal, a famous French Mathematician and Philosopher, is more than a triangular shape of numbers.  The patterns found within the triangle are FASCINATING! Investigate some of the treasures found within the triangle in this math mini spark.

1

1     1

1     2     1

1     3     3     1

1     4     6     4     1

1     5     10     10     5     1

Spark your math thinking!

1. Set up your math mini spark recording page: #6: The Mathematical Secrets of Pascal’s Triangle

2. Watch this video about Pascal’s Triangle. On your recording page answer these questions: Describe a pattern you notice within the triangle. What numbers would be in the next row?

3. At 1:20 in the video, the Triangular Numbers are highlighted.  The picture below shows the first 5 triangular numbers.  Draw the next 2 triangular numbers on your recording page.

4. At 1:58 in the video, the Pentagonal Numbers are highlighted.  The picture below shows the first 5 pentagonal numbers.  Draw the next 2 pentagonal numbers on your recording page.

5. Do some more research on Pascal’s Triangle at Math is Fun. Don’t feel like you have to explain everything about the triangle, just pick a couple patterns to highlight on your recording page.

6. This TED Ed Video takes the explanation of Pascal’s Triangle to a higher level, but it’s worth a watch to discover even more patterns within the triangle. Record 5 details from the video on your recording sheet.

7. Share your math mini spark recording page with your teacher/EY coordinator.

A sieve is a kitchen utensil that is used to strain solids from liquids or for separating coarser from finer particles.  The Sieve of Eratosthenes is similar because it’s used to separate out all the prime numbers from a given set of numbers.

Spark your math thinking!

1. Set up your math mini spark recording page: #5: Sieve of Eratosthenes

2. Listen to the pronunciation  of Eratosthenes several times. Practice saying “Eratosthenes”

3. Learn about Prime Numbers at Math is Fun and then answer these question on your recording page.  What is a prime number anyway?  What is the smallest prime number?  Is 1 prime?  Why or Why not?  Are all odd numbers prime?  How many prime numbers are there between 1 and 100?

4. Watch this video about the Sieve of Eratosthenes.

5. Do this online prime number activity and Add a picture of the finished chart to your recording page. If you would rather use paper, print out this 100 chart and find the prime numbers.

6. Read this article and find out about Eratosthenes.  Consider the following questions as you read and record your responses on your recording sheet.

What were 2 of Eratosthenes’ nicknames and what did they mean?

What is Eratosthenes known for besides the Sieve named after him?

What kind of man was Eratosthenes?

7. Share your math mini spark recording page with your teacher/EY coordinator.

This math mini spark explores Weird But True! Size Edition.

Spark your math thinking!

1. Set up your math mini spark recording page:#4: Weird But True! Size
2. Explore math facts at National Geographic Kids Weird but True! Size Edition.
3. To move from fact to fact click the arrows.
4. There are 8 facts in total. Record your favorite four facts on your recording sheet.
5. Do research about each of the four topics so that you can add 3-5 more details for each one.
6. Share your math mini spark recording page with your teacher/EY coordinator.

The Eiffel Tower is named after a man named Gustave Eiffel, but he didn’t actually create it. Instead, two of his top engineers, Maurice Koechlin and Emile Nouguier, designed the tower. The names of 72 different artists, engineers, and mathematicians who helped with the design are carved into the tower so that everyone can remember them!

Spark your math thinking!

1. Set up your math mini spark recording page: #3: Eiffel Tower Math

2. Read this article about the Eiffel Tower. Record 3 math details about this structure on your recording page.

3. Watch the Geometry of the Eiffel Tower.  Record 3 details from the video on your recording sheet.

4. Answer one of these these questions on your recording page.  Reminder for your teacher that answer key can be found in the math mini spark folder.

• Describe the significance of the Eiffel Tower’s height and how it compares to football fields.
•  Who was Gustave Eiffel, and what was his profession before designing the Eiffel Tower?
• Explain what a truss is and how it functions in supporting structures like bridges.
•  What are the two types of forces mentioned that act on the truss, and how do they differ?
• What is meant by “static equilibrium,” and why is it important for the stability of a well-designed bridge?

5. Global Math Stories combine math, history, and cultural stories. Check out the information about the Eiffel Tower. Answer 2 of these questions on your math recording page.  Reminder for your teacher that answer key can be found in the math mini spark folder.

1. The tower has 1,665 steps in total. If you were allowed to climb all the way from the bottom to the top, how long do you think it would take you? Explain your reasoning.
2. Every repainting of the tower requires 50-60 tons of paint. Find the mean and median of the amount of paint that has been used during these applications: 52, 60, 58, 54, 59, 52, 60, 51, and 55 tons.
3. Imagine the Statue of Liberty and the Eiffel Tower are standing side by side with the sun shining on them. The Statue of Liberty is 93 meters tall, and its shadow is 10.7 meters long. If the Eiffel Tower is 330 meters tall, how long will its shadow be?

6. Share your math mini spark recording page with your teacher/EY coordinator.

You can use step 5 as the first story for the Global Math Stories Badge that can be found on the EY badge page.