22 April 2012

(parenting) Bite-sized math/sci lessons for 6! yr-olds (12-27)

Hello -

More ideas on little 5-minute lessons after storytime. I received lots of great feedback and encouragement here and on Facebook - thanks! In continuation of the previous post, here goes!  (Toby turned 6, so now this is "for 6 yr olds.")

Lesson 12: Review of addition
Do some addition of 1-, 2-, and 3-digit numbers, with or without carrying.

Lesson 13: What's inside?
Draw a cross-section of some common mechanical device, like a ballpoint pen. Your child might want to draw it, too.

Lesson 14: Vectors
(I don't know what I was thinking here, but it worked out okay.) If you know what vectors are already this will be really simple:

  • A "vector" is an arrow that you draw. Its length and direction are important.
  • Length: draw a small vector and a long vector pointing in the same direction
  • Direction: draw two vectors of the same length, pointing in different directions
  • Show how to ADD vectors (put the tail of the second vector at the head of the first, and...)
Lesson 15: Some Angles
Show him or her what an angle is. I did it by drawing a series of increasing angles, e.g. 30, 50, 90, 95, 120, 175... And for fun, 1 degree.
  • 90 degrees has a special name
  • Draw a protractor and label some angles, make tick marks every 10 degrees
Lesson 16: Types of 4-sided shapes
I think this one might've been a bit much.
  • Make a table of 4 columns: {angle, lengths of sides, name, picture}
  • We had rows that ended up like this. I know, I know, I could have done this a lot better, but at sleepytime this was the best we could do:
  • 90 degrees; 2 short, 2 longer, or all the same, "rectangle," picture
  • 90 degrees; all the same; "square," picture
  • parallelogram (oh, my, what's parallel?)
  • ...trapezoid
I convinced myself that for a kindergartener maybe it's sufficient for them to realize that plenty of different shape-types have 4 straight sides.

Lesson 17: Parallel
Two lines are parallel if they never touch if continued forever
I still like the "near-miss" method of teaching, so I drew a bunch of parallel lines and then a bunch of "not parallel" lines.

Lesson 18: Beginner's fractions
We draw a bunch of pies with 2, 3, 4, and 5 pieces. We colored in 1 or more pieces of each. We labelled them with words and numbers, e.g.:

  • half  1/2
  • third  1/3
  • two thirds  2/3
Lessons 19, 20, 21: Smart people telling us interesting things
I punted and relied on YouTube one evening:

Lesson 22: Math - Parentheses
Show them that putting parentheses around parts of an expression tell you to calculate the stuff in the parentheses first.

First, I showed that sometimes, the order of evaluation matters.

  • An example where it doesn't matter:
  • 1 + 2 + 3 = ?
  • 1 + 5 = 6
  • (or, 3 + 3 = 6)
  • An example where it does matter:
  • 1 + 2 x 3 = ?
  • If you do "1 + 2" first, you get: 3 x 3 = 6
  • If you do "2 x 3" first, you get: 1 + 6 = 7
Oh my goodness! Luckily, people agree that you should do things in this order: PEMDAS (etc etc).

So you don't need parentheses for: 1 + 2 x 3 if you mean 1 + (2 x 3)
But you do need them if you meant: (1 + 2) x 3

Lesson 23: "Topology"
I recall my father or grandfather teaching me this when I was about 5, sitting on the bed, wondering how on earth "a donut is the same as a coffee cup." I figured it was time to teach Toby.

  • Let's play a game with pretend Silly Putty. You can smoosh the Silly Putty all you want, but there are two rules: you can't make new holes, and you can't seal any holes up.
  • (0 holes) A blob "is" a snake "is" an egg
  • (1 hole) A donut is a coffee cup
  • (2 holes) Um.... I don't know. A pair of eyeglasses is... ummm... we gave up.
Lesson 24: Simple electrical circuit
Show them the schematic symbols for: wire, battery, light, and switch.
Draw the circuit that connects them together. Explain closed and open circuits.
Let them draw it too.
Consider showing them what series and parallel mean.

Lesson 25: Subtracting big numbers (without borrowing)
Y'know, 875 - 321, 9748 - 1211, etc. Then they do a couple.

Lesson 26: Subtracting big numbers (with borrowing)
E.g., 21 - 15, 46 - 37, 52 - 16, 32 - 15.
Some get weird, like 80-79, because they'll want to do 7-7 in the tens column and get 0 but you don't write that down.

Lesson 27: Drawing a cube
Show them how to draw a wireframe cube.
Show them how to draw a solid cube, and put the sun up in the background, and show them how to shade it. Let them try too.

Enjoy!  As always, your feedback is invited.


02 April 2012

(parenting) Bite-sized math/sci lessons for 5 yr olds: # 1-11


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"
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.)


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.