Daughter is into pickles. Like way into pickles. If I were to start a blog just for her, it would be called www.PicklesAndPretzels.com. (She’s also into pretzels.)
So when Husband grabbed two instead of one jar yesterday, it seemed natural.
Unloading the groceries, I saw the two jars a little more closely.
“Holy cow,” thought I. They’ve made ellipses (pickle ovals) out of segmenting cylinders (the whole pickles)! And they’re marketing them!
I’ve been playing with the lovely Cuisenaire Rods for a few weeks now. I made the (fortunate) mistake of creating this flower in a past article about coordinate pairs.
The mistake was that I would eventually have to come up with the coordinates for this thing. Fortunate because it gives the MathFourTicians out there something else to teach with the rods!
The center of the flower is the place to start.
Since all the “petals” are attached to the center, that’s probably the best place to begin.
I converted to something I could see.
Since everything is tiny (1 cm), I went to a bigger setup. And some of the coordinates were easy to pick out. So I put those in the big grid, too:
And then I started to do some work…
Next I considered what I was really dealing with: a square. And each side was 1 cm.
According to those crazy Pythagoreans, the diagonal measures :
So half the diagonal is :
I went back to the big grid.
When I put this information on the big grid, it looks like this:
Knowing that each corner pokes out roughly 0.2, I can calculate the coordinates:
From this I can create the ordered quadruples as described here for the petals of the flower. But at this point I’m pretty much needing a break. So I’ll leave that for next time.
Whatcha think? Fun? Share your thoughts in the comments and on Twitter:
When we crossed the street, I exposed her to undo risk by crossing at an angle.
So on our way out, I explained to her that we were walking a little further to get to the car this time. And we would minimize the risk of getting hit by a car by taking the longer route.
(Of course she’s not yet two, so she really didn’t care. But it was important for me to say.)
Crossing at an angle is shorter than going straight across.
People most often cross the street at an angle. Intuitively we know it’s shorter. Look at the tiny person in this picture. He needs to get to the front door of the store.
It’s five yards to go at the angle, while if the little guy walked straight across then up, it would be seven yards.
Suppose walking one yard takes 5 seconds. It will take the little guy 15 seconds to cross the street straight across. (And with a toddler, it does take 5 seconds to walk a yard.)
Then he has to walk the four yards along the side to the door. Which means his total time is
5 yards diagonally at 5 seconds per yard = 25 seconds
Total walking time = 25 seconds!
Crossing at an angle puts you at risk for longer.
For the pedestrian in a hurry (and wearing the shirt that reads “Safety Third”) the angled route is the way to go. But for a parent with toddler in tow, minimizing risk is a better option.
If the little guy were to cross at the angle, he’d be in front of the oncoming cars for 25 seconds. If he were to take the route that is longer overall, he’d be in front of oncoming traffic for only 15 seconds.
The car doesn’t care what angle you’re walking, it can squish you pretty easily either way.
Not to mention he keeps the driver happy.
Getting out of the driving area faster means keeping the driver happy. That might not be your goal, but adding some cosmic happy juice into the world of drivers never hurts.
Plus, if someone were to “hypotenuse you” by taking the angled route when you were driving, wouldn’t you get a little annoyed?
I noticed Daughter attempting to bejewel Husband with a strand of my faux pearls the other day. I watched, enthralled with the math learning taking place.
She held the necklace in her hands – one on each side. Just about equal. So the space available for Husband’s head was almost non-existent. Like this:
If she were to hold the necklace at two points that were closer together, she would create a “dip” in the necklace where his head could fit. Like this:
There’s an extended learning opportunity here!
This made me think of all the nifty things you can show about the relationship of perimeter to area and how you can have the same perimeter but change the area to all sorts of sizes.
If you aren’t wearing a necklace, find some mardi-gras beads. Daughter has many strands, so I’m guessing your house might be littered with them as well. If not, join the club. Go buy some.
Play with them in the bathtub or right before bed. (Make sure they give them up before going to sleep, though – it’s a strangulation hazard!)
Move the necklace around on a flat surface (or on the bed) and let your child experiment with the ways the area changes. Ask questions like:
How much “stuff” can you fit inside the shape? (If there are blocks or other toys to act as “stuff,” use them.)
How much “stuff” can you fit inside the shape after you move it around?
Is that more or less “stuff” than you could fit inside it before?
Did the distance around the necklace change? (You can introduce the words perimeter and circumference.)
Can you make it into a square? A triangle?
Be careful how much you do.
Don’t forget, activities like this should be fun. For your child as well as you. So don’t get too in depth talking the math talk if it feels weird. Go with the flow.
And let me know how that flow goes, would you? Share your thoughts in the comments.
Not only is this video about triangles that are similar, but this video about triangles is similar to other videos! (Is that fun to say or just annoying?)
Here it is:
What do you think? What other triangle things can you do with a pegboard?
Do your kids get confused between congruent and similar triangles? Do you?
In a previous post, I made this mistake when discussing right triangles on the Giant Pegboard. If a mathematician can make the error, then it is easy for a kid to, also.
In the video I said “congruent” when I meant “similar.” Two triangles are congruent if they are the same size and shape. They are similar if they are the same shape (and maybe or maybe not the same size).
One way to show that two triangles are congruent is to use the SSS Theorem or the “side side side” theorem. This says, essentially, that…
If you can show all three sides of two triangles are the same, then the angles must also be the same.
This ensures that your two triangles are congruent – or as a kid might say it “exactly the same.”
Here’s how to use the Discovery Toys Giant Pegboard to play around with congruent triangles:
What do you think? Can you use this? Give it a shot!
Check out the next post for a video discussion on similar triangles.
I hosted a Discovery Toys party the other day and ended up explaining how to use many of the toys for teaching math.
Alas, here I am now doing videos of the same. I can’t get over these toys. They are designed proportionally (the cups and weighing ones) and always with the thought “How can this be fun at the same time it’s teaching something.”
Of course, all toys teach. But the designers of these toys put the extra oomph into the thinking process so that when a kid asks “why?” there’s an easy way for the parent to answer.
Oh – and they are guaranteed for life!
So from here out, I’ll be doing occasional videos on how to use them.
The first is about right triangles on the Giant Pegboard. Notice in the video that when I say “congruent triangles” I really mean “similar triangles“.
See what you think:
Have you played with triangles and pegboards? What other ways can you use them to teach and learn?
Disclaimer: I tried to become an affiliate of these toys to help pay for this blog. Alas, they don’t have an affiliate program. The only way was to become an official consultant. These toys are so cool and helpful, that I have done it.
