### 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.

Ones are on the outside of the triangle and it also goes like 10 10 5 5 4 4

Yes Dominic, ones are on the outside, but where did you get the 10, 10, 5, 5, and 4, 4?

I can now do the Pascal’s triangle easy

What did you learn about Pascal’s Triangle? Can you tell me the numbers in Row 10?

The tenth row is 1,10,45,120,210,252,210,120,45,10,1

I see now you do ones on the outside and then 12345678910 on the first inside. Then just add in triangles until you get on the tenth row 1 10 45 120 210 252 210 120 45 10 1

The triangle is so sophisticated. What would it be used for?

DON’T READ THIS IF YOU DO NOT WANT TO KNOW WHAT THE TENTH ROW IS!!!!!!!!!!!!!!!!

Row 10 is: 1, 10, 45, 120, 210, 252, 210, 45, 10, 1

I learned that Pascal’s Triangle holds about ten different patterns…maybe more!

I learned that the Pascal’s triangle is very useful.

The math triangles are cool. I didn’t notice the numbers in order down the triangle until they showed it.

The Pascal Triangles are harder than they look, but I can still do them.

Wow that’s complicated but I think I got it the tenth row is 1,10,45120,210,252,210,45,10,1

The triangle is going by what the numbers add up to.