I have to admit, I ran out of ideas (or STEAM [hah hah hah]) on little 3-minute lessons here at Chez Favingham. We've been distracted by longer night-time stories, various construction toys, and life in general.

On the 0.002% chance that I have a readership, I present to you a giant backlog:

**28: Number lines**

**Draw a number line of integers from -3 to 3. Something about it lets a bunch of concepts "click" at once.**

**29: Multiplication table**

**We did a table from 1x1 to 5x5. The parent fills in almost all of it, your child can do a couple too.**

Extra: ever wonder what the curves are when you connect equal answers? They're solutions to xy = C. Yes, hyperbola. Or as my teacher used to say,

*degenerate hyperbola*, which sounds vaguely naughty.

**30: Computing miles from a map**

(We had a road atlas with one of those giant tables in the back that kind of looks like a multiplication table but isn't.)

Anyhow, it's a good source for your kid's first word problems - connecting practical questions to arithmetic.

"How far is it from Portland to Boston to New York City?"

**31: Drawing noses**

Our 6-yr old took a turn and taught me a nice lesson in drawing noses on stick figures.

And also:

**32: How to tell if a cheetah is 10 months old**

I have no idea if this is true:

- Babies under 10 months have a white stripe
- Over 10 months, they have spots.

**31 (back to my numbering): M C Escher**

Kids like Escher.

Then we practiced drawing cubes again.

**32: Logic**

I honestly was reaching pretty deep here. I thought "it'd be a good idea for him to see what circuits and logical statements look like."

Reversed photo, I know, I know. |

**33: Area of a rectangle**

This was a more abstract recap of Lesson 1, in which we constructed rectangles out of arrays of squares, and the area = the number of squares.

*a*=

*xy*

(Draw a 3-by-10 rectangle. The area is:

area = 3 x 10

= 30

etc.)

**34: Quadrangles II**

Hmm. All I drew were some parallel lines. Not sure where I was going with this.

**35: 3-dimensional shapes**

Draw a cube. Label: vertex, edge, face

**36: Statistics**

Teach: minimum, maximum, and range.

Pick a friend and write down, I don't know, how many glasses of water she drank each day.

Josie: 4 10 1 7 12

M T W Th F

Min: 1

Max: 12

Range: 12 - 1 =

**11**

Then, let your child do one.

Then, we decided to graph something.

**37: Parts of a Robot Arm**

I mean, kids love robots, right?

(from Articulated-geometry.jpg)

**38: Base**

I thought that maybe if I showed him what "base 10" meant, I could somehow more easily explain how to tell time. Not sure I succeeded. But, realizing that we have 10 digits (that coincidentally map to our 10 fingers) might be a kind of a-ha! moment. Maybe there are number systems with 2 digits? Or 16 digits?

NUMBER: 7 2 6 0

(and then, "digit" with an arrow to each)

Base 10 has 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9

I drew three cylinders, like your odometer wheels, with the numbers on them, to show how the one all the way on the right moves through every digit and then the wheel one step to the left advances by one, etc.

And then imagine: what if each odometer wheel only had THREE numbers on them? That's base three! It would only have: 0, 1, and 2.

Maybe three-fingered aliens would count like: 0, 1, 2, 10, 11, 12, 20, 21, 22, 100, 101, 102, 110, 111, 112, 120, 121, ...

What if aliens had 16 fingers? That's hexadecimal!

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1A, 1B, ...

**39: Potential energy + kinetic energy**

Explain what each is.

Draw fun looking ramps and hills. Imagine pushing a boulder all.. the way.. to the top... "filling it" with potential energy. If you let go, where does it roll? What's the highest point it could reach on the other side? Does it roll forever? Where does that energy go? Does it become heat?

I know you love the backwards photos. |

**40: Coordinates in the Cartesian plane**

'nuff said

**41: Review of carrying**

We did a bunch of multi-digit addition exercises.

**42: Compass rose**

Draw a pirate treasure map with a compass rose.

**43: Lift (i.e. of an airplane wing)**

Draw a free-body diagram in which a down arrow (gravity) and an up arrow (lift) act on an airplane. What happens when the up arrow is longer? Where does the airplane go?

**44: Electronics II**

Draw an atom: nucleus & electrons.

Complain about Ben Franklin setting a counterintuitive standard for arrows depicting current flow in the "wrong" direction on circuit diagrams.

Draw a circuit with a battery and a light bulb. Show which way the electrons run through it. Show the way the absence of electrons (the "holes" kind of) go the opposite way. That's current.

Draw the "soda in a soda bottle with a little bubble in it" analogy. When you tilt the bottle, the soda follows gravity and the bubble goes the opposite way.

**45: TAKE APART TIME!**

Take something apart, like a digital camera. Products are made out of subsystems that work together. People like us designed them, and other people made them, and then they were put together. A camera has:

- small screws
- magnets
- viewfinder lenses
- LCD
- image sensor
- gasket
- capacitors
- (etc.)

**46: Pi**

Draw a circle, label diameter and circumference.

For some

*crazy reason*, if you take any circle and multiply its diameter by a number that's a little more than 3, you get its circumference.**47: Area of a circle**

Whew! I'll pause here. We're up to 60. Soon...

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## 3 comments:

This is fantastic, Gregg. Thanks so much for taking the time to share it. Stuff most of which (not all!) can do with my kid, yet I wouldn't have thought of on my own. Would be curious to know which lessons have most intrigued T.

E. is learning Mandarin in school, and one of the first units has included learning to write the numbers in Chinese characters. In my 3-minute exposure to the material at a prof dev workshop with E.'s teacher, I gathered that it's sort of the equivalent of base 10 -- there are 10 different characters used in writing numbers -- combined with a Roman numeral-style cumulative approach to representing large numbers. It's not exactly like Roman numerals, though: While XX = 20 and XXI = 21, in Chinese it's 2/10 (i.e. those characters written side by side in that order) = 20 and 2/10/1 = 21. It made me wonder fleetingly whether E.'s exposure to that system could be used to give her some concept of what base 10 means. Still not sure. Thoughts?

I am saving these for when I need them in 3-5 years.

For the parallelogram, slice off the overhanging part and put it on the under-hanging side. Area remains height by width, just like in a "normal" triangle. Height just means height, not length of the side.

GEB - E's learning Mandarin? Wowzers. I bet E already has an innate grasp of Base 10 - but it's sure easy enough for you to illustrate if you're... bored?... or just think it's fun.

Sheryl - Oh, yeah! I should add that, thanks!

Google - HOLY COW, I keep failing the CAPCHA.

-g

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