Lessons about Pi

Are you wrapping your mind around Pi this week?
March 14 was Pi Day! Here's a sign we made to celebrate: Happy Pi Day! 
#WeAreProblemSolvers
I apologize that I am a day behind on this entry, but I wanted to include some new activities that we enjoyed together this week.

Start with the Math
When you have a circle, you can quickly measure its diameter. Diameter is the imaginary line across the middle of the circle. Find a circle! Anything will do! 
This oatmeal cookie is pretty round. It even had a dimple in the center.
We measured across the middle. It was just a bit less than 3 inches across.
We then measured around the cookie - the circumference. It was about 9 inches around. 
This is consistent with the formula 

Circumference = π × diameter

We used a metal tape measure for this activity. It would have been easier with a fabric tape measure.

Beads
With our 2 year old, we love measuring with strings of beads. This is because we use strings of beads to develop number sense and learn to count. Here are strings of beads that a child organized from one to ten.
So, now that we've played around with beads for a while, here's a video that I made which explains a way of visualizing pi using strings of beads.
And a little picture of it, too.

Estimating Circumference
Measure diameter with a measuring tape, ruler, or even strings of beads, then estimate circumference. In these exercises we simplify the math by using 3 for π (pi).

Here is what our table looked like for this activity.
Find any circle around your house and measure the diameter. I'd you have a calculator, you can multiply that diameter by pi to find the circumference. 
Or, you can round pi down to 3. Here's a photo of our girl estimating circumference. She measured the diameter and then counted by 3 to see that the circumference would be about 6.
Here's a video to practice skip counting by 3.
Here's a video where our daughter teaches us how to multiply by 3.

Art with Pi
We set up this activity for them to do some art of their choice around pi. We provided cardstock paper, watercolor, and crayons. They had fun tracing circles with crayons and watching colors pop as they painted over the wax crayon with watercolors.
I wish I had taken photos of them working, I only have my notes and this photo from that lesson. I will come back to edit this entry when I repeat the lesson.

Using Pi with Rockets

For this series of lessons, we started by reading the book Rocket Science for Babies by Chris Ferrie.
Here is a link to a video of me reading this book:
We learned the words
Lift
Thrust
Velocity
Angle
Air Density

To calculate lift, we need to measure angles. We also need to have a general concept of pi. Here are a few quick lessons our children enjoyed on each of these topics.

Mat #1: Understanding and writing pi with beads, by measuring diameter and circumference (we did this earlier).

Mat #2: Introduction to measuring angles. We did this with a paper guide indicating 0°, 45°, 90°, 180°, and 360°. We also had colorful paper cutouts of triangles that we could hold up to the guide to determine what angles were present. 

Here are another couple of mats with lessons.
Mat #3: Art meets angles! Matching more angles to their outlines. She even had fun coloring and cutting out her own triangles and other wing shapes to measure.

Mat #4: The lift coefficient is different for different shaped objects. And you need to know the lift coefficient before you can begin to measure lift (lift involves velocity and air density, too). Here's our simple formula for the lift coefficient: 2 × π × angle. 

We enjoyed feeling each part of the equation by writing in crayon and moving around blocks and sandpaper numbers as we solved these equations. When we rounded pi down to 3, we realized we could quickly estimate the lift coefficient for a wing that we designed ourselves.
This formula is simplified because we're supposed to use the angle in radians rather than in degrees. We aren't ready to introduce radians yet.

Want to play around more with lift and aerodynamics? Check out the lessons in this blog post: http://steamma.blogspot.com/2021/11/ball-play.html

Making a Pi Pie
We had a lot of fun measuring out and mixing up our whole grain flour, sugar, butter, and water to make pie crust.
Do you want an excuse to talk about fractions? Break out those baking tools!

We explain fractions through our measuring scoops in this little video:

And here's a more active continuation of this lesson where we went outside with water and filled up our cup measure with a bunch of smaller fractions.

We added berries and bananas to our pie crust and put it in the oven to bake. Here is what it looked like in the oven.
Our end result?
Well, Ma thought it was scrumptious. These children just preferred eating fresh berries.

Berries for Spaceflight?
Did you know that horticulture scientists at Kennedy Space Center have been growing strawberries so astronauts can someday grow them in space?
Here's a photo of hydroponically grown strawberries at Kennedy Space Center in 2004.
(photo from images.nasa.gov)
And here is a strawberry that was grown more recently (personal photo).
Other Pi Day Resources
Our friends at "Surviving Math" made a simple video about pi and circumference. check it out! https://youtu.be/2O3AxtnuaQs?si=w21kNnD6IX63ZzV0
And here's a cute picture they made to wish folks a happy Pi Day 

Comments

Post a Comment

Popular Posts