For the last few weeks, every other night, our 5 yr-old and I do a couple of bite-sized "lessons" about ideas in math or science. They take us about 3 minutes each, and are fun. He's come to ask, "is tonight lesson night?" Since he's getting a kick out of it, I'll post our first 11 lessons in case your'e looking for ideas of doing the same.

I hope our five year old won't mind that I'm putting this online, forever in Google's memory banks...

Preliminary: We reserve a special 6" x 9" spiral-bound notebook for these, and we dutifully label the top of each page with the lesson number and name. (Honest, this is part of the fun.) We assume you already are doing stuff like multiplication of single-digit numbers, and have watched some sciencey stuff like They Might Be Giants's DVDs about atoms and DNA and things.

**Lesson 1: length, area, volume**

- Draw three short lines: 1 inch, 2 inches, 3 inches, ticking off the inches. Draw another line. How long is it?
- Draw rectangles composed of many 1 x 1 squares. How many squares is each rectangle? What if you multiply the length of one side by the length of the other side?
- Write "one-dimensional" by length, and "two-dimensional" by area. Write "three-dimensional." Can you guess what that is? Draw a cube of cubes, etc.

**Lesson 2: adding bigger numbers**

- Add two two-digit numbers, in which carrying is never needed. (E.g., 23 + 34, added vertically.) Your child does some in their own handwriting.

**Lesson 3: adding big numbers with carrying**

- E.g., 78+94 = ... (but do it vertically of course)

**Lesson 4: "place value"**

- My wife had already shown him this Kahn Academy video: http://www.khanacademy.org/math/arithmetic/multiplication-division/v/place-value-1
- Pick a quick example, e.g. 9654, and label the places (ones, tens, ...)

**Lesson 5a: Perpendicular**

- Two lines that make a "T" shape are perpendicular. I like the near-miss form of learning: draw a couple of examples of perpendicular lines, and then provide counterexamples, saying "these are NOT perpendicular lines."
- Draw a line, and put a dot along it, and ask your child, "draw the perpendicular line that starts here."
- Try to teach the notion of angle. If the lines are perpendicular, the angles are the same on either side of the perpendicular line. The lines are not perpendicular, one angle will be larger than the other.

**Lesson 5b: how to know where a laser beam would go if it hits a plane (flat) mirror**

- My son likes lasers, and kids hear about them in movies like Toy Story, so...
- Draw a line segment, with hashmarks on one side to indicate it's the cross-section of a mirror. like this, but without the Thetas. ("normal" is just the physics word for "perpendicular, but in any number of dimensions")

(picture from this site)

- Draw the laser beam coming in
- Draw the dotted perpendicular line where the laser hits the mirror
- Draw the reflected laser beam, such that its angle with respect to the perpendicular line is the same as the incoming beam's angle to the perpendicular line
- Do a few examples, letting him or her draw the lines and arrows and neat stuff like that

**Lesson 6: half**

- Draw a line. Where's half?
- Write a number, like 10. What's half?

**Lesson 7: Number patterns**

This was kind of a long one, which I used just to let some words of math wash over him. I don't know how to do subscript in Blogger, so I'll use brackets.

- "What numbers come next in the pattern?" 0, 0, 0, 0, ... ?
- 1, 2, 3, 4, 5, ... ?
- 0, 2, 4, 6, ... ?
- 1, 1, 2, 3, 5, 8, 13, ... (talk them through this) - and tell them about sunflowers, etc
- 1, 3, 5, 7, ...?
- Now explain that people who really like math have a secret key that lets them describe these patterns with just a few little special marks on their paper. First, let's give these numbers special names. Let's call the number we're interested in x[n] ("x sub n"). That's the number we're trying to figure out. Let's call the guy before it x[n-1] ("x sub n minus 1"). That's the guy right before it. And what might we call the number before THAT? (... x[n-2] )
- Here's the magic way that we can re-write these
- x[n] = 0 is shorthand for the pattern {0, 0, 0, ...}
- x[n] = x[n-1] + 1 is shorthand for how we count! {1, 2, 3, 4, 5, ...} (I didn't bother saying that you also need a rule defining the starting point, I figured it's overkill.)
- x[n] = x[n-1] +2 is the magic key for things like odd or even: {1, 3, 5, 7, ...}
- And that weird last pattern, the Fibonacci guy, his pattern is: x[n] = x[n-1] + x[n-2]

BONUS: Vi Hart did a few YouTube videos doodling about Fibonacci numbers, e.g. http://www.youtube.com/watch?v=ahXIMUkSXX0

**Lesson 8: shape pattern**

This is why we asked "What's half?"

- Draw a Sierpinski triangle, or whatever the right name of it is. Draw a triangle. Put a dot at the halfway point of each side. Connect the sides to draw a new triangle inside. Put a dot at all 9 new halfway points. Draw 3 triangles. And so on. FOR-EV-ER!

**Lesson 9: "Daddy's Square"**

I don't know the name for this. Basically you draw an inward-spiraling square, in which the corners are a little less than 90 degrees. Like the last two figures here.

**Lesson 10a: heat**

- (Assumes you've already chatted about atoms and molecules.)
- Draw a little cartoon of ICE (ice cube) --> WATER (water in glass) --> STEAM (steamy lines) --> PLASMA (electrons and nuclei floating around)
- Heat is a kind of energy. When stuff heats up, the atoms and molecules inside jiggle around more and more. So the ice melts, becomes water, becomes steam, eventually the electrons tear off, etc etc. I like presenting it this way, around 4:30 [YouTube, Feynman].

**Lesson 10b: Important Temperatures**

- In America we have a weird way of telling the number of how hot or cold something is. It's called
*degrees Fahrenheit*. Most of the rest of the world calls it something different. Like, here we use inches or miles, and over there they use centimeters and kilometers. - Draw a number line with two ticks on it. The first third is called "ice," the second is "water," and the rightmost third is called "steam." Tick one is 32 (deg) F, and then 212 (deg) F.
- Talk about this. Have them recite, "ice becomes water at 32 degrees Fahrenheit." I know it might feel rote to rehearse it this way, but really, I think that is the most sensible thing.
- Still awake? Then say, remember how the rest of the world has an easier way of thinking about it? They call their way degrees Celsius, and the numbers are 0 and 100.
- There's actually a number way... over... there... (to the left) where if we ever got all the way over, those jiggling atoms would stop. But you can't ever get that far. You can get really close, very very close, but never all the way (etc). This is absolute zero.

**Lesson 11: gears**

- Draw two enmeshed gears
- If this one goes this way, which way does the other one spin?
- Say this has 10 teeth and the other has 20 teeth. If you spin the big one once, how many times does the little one spin?
- What if it's 10 and 30?
- What if it's 5 and 10?
- Why is this useful? Well, you know how your bike has gears here and here...?

I'd love to hear your informal bedtime lessons if you got 'em. Share! (And if you want a next installment of this, encourage me in the comments.)

**G-Fav**

ps BONUS: Cosmos is available on Netflix Instant. I've been really shocked at how much of Sagan's teachings stick with our kids. There's evidently a lot of "see that snow? it's from the STARS!" talk, lately.

## 5 comments:

greg, this is totally awesome. when i'm a parent one day, i'll want to refer to this. i may even try these with my nieces and nephews. wonderful stuff. go greg!

oops, you're gregg, not greg. sorry.

:-) Thanks, Tammy!

I'll look to you to make the lesson about semiconductors. Maybe I'll be able to understand it when I'm 45.

g

Gregg, thanks, these are terrific! More please!

Also, I have a lasting image in my head of Carl Sagan, on Cosmos, unrolling a really long strip of adding-machine paper (or whatever it was) with a googol written out on it -- a 1 with 100 zeroes. He unrolled it out the door and down the street, I seem to recall. Cosmos definitely does stick!

-Rebecca :)

RLB - Yes! Toby keeps mentioning "Googolplex" over dinner!

Awesome show. I think they're redoing it.

And I bet the episode about the library of Alexandria (was that it?) made your heart ache...

g

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