Playing Math with A.A. Milne

Halfway down the stairs
Is a stair
Where I sit.
There isn’t any
Other stair
Quite like
It.
I’m not at the bottom,
I’m not at the top;
So this is the stair
Where
I always
Stop.

Halfway up the stairs
Isn’t up
And isn’t down.
It isn’t in the nursery,
It isn’t in the town.
And all sorts of funny thoughts
Run round my head:
“It isn’t really
Anywhere!
It’s somewhere else
Instead!”

—A.A. Milne
When We Were Very Young (affiliate link, see details)

The Stair-Counting Game

Play on any set of stairs where you won’t get in other people’s way. Start at the halfway step.

  • Roll one 6-sided die. Go up that number of steps.
  • Roll again. This time, go down that number of steps.
  • Keep rolling the die, alternating movements up and down.

Will you ever escape the stairs?

Fill the Stairs Game

Each player draws 11 stair steps (counting the top and bottom floors) on a piece of paper. Write zero on your middle step.

Remove the face cards and jokers from a deck of playing cards. Mix the remaining cards face down in a fishing pond.

  • On your turn, choose one card. Red cards are negative numbers, and black cards are positive.
  • Write the number from your card on one of your stair steps.
  • Then mix your card back into the pond.
  • The first player to fill their stairs with numbers in order wins the game.

The numbers have to grow as you go up the stairs and get smaller going down. But you can skip numbers. For instance, you could put +2 on the stair above zero, if you like. Or you could write −4 two steps below zero, leaving only one blank in between.

If you draw a card that will not fit on your stairs, you lose that turn. Mix the card back into the pond without writing anything.

If you make a mistake — like putting +9 too close to the middle, so there’s no way to fill the higher stairs — you can use a turn to erase one number on your stairs. You don’t get to choose a new card on the same turn as erasing a number.

Fill the Stairs Variations

Help young students understand negative numbers. A stairway makes an excellent number line visual.

Download the place value version (no negative numbers) of the stairway game from Math for Love.

Or discover variations for all grade levels at Math Hombre blog. I especially like John’s Decimal Point Pickle game. And the exponential version looks like a fun challenge.

Your Turn

Do you play stairway math? Please tell us your games and variations in the comment section below.

Or share other ideas for playing math with children. I love to hear new ways to play!

More Backwards Math

[Photo by *clairity*.]

Have you ever noticed how very different little girls are from little boys, in the way they play and in the way they think about things? Princess Kitten has been playing around with Backwards Math again, and my first thought was, “None of my boys would ever have done this with numbers.”

Continue reading More Backwards Math

Math History on the Internet

[Image from the MacTutor Archive.]

The story of mathematics is the story of interesting people. What a shame it is that our children see only the dry remains of these people’s passion. By learning math history, our students will see how men and women wrestled with concepts, made mistakes, argued with each other, and gradually developed the knowledge we today take for granted.

In a previous article, I recommended books that you may find at your local library or be able to order through inter-library loan. Now, let me introduce you to the wealth of math history resources on the Internet.

Continue reading Math History on the Internet

Hit Me! (A Math Game)

Photo by paparutzi.

Math concepts: addition, subtraction, negative numbers, mental math, absolute value
Number of players: any number
Equipment: math cards (two decks may be needed for a large group)

Set Up

One player (the dealer) shuffles the math cards and deals one card face down for each player, beginning with the player on his left and proceeding in turn around the table. Then he deals one card face up beside each face down card.

Continue reading Hit Me! (A Math Game)

Backwards Math

Photo by Complicated.

Princess Kitten is recovering from her cold and getting some energy back. She came to me and said wistfully, “I wish I could do backwards math.”

I looked up from my keyboard. “Backwards math? What do you mean?”

“Umm. It’s kinda hard to explain, but I can show you.”

Continue reading Backwards Math

Negative Numbers for Young Students

[Rescued from my old blog.]

Would you like to introduce your students to negative numbers before they study them in pre-algebra? With a whimsical number line, negative numbers are easy for children to understand.

Get a sheet of poster board, and paint a tree with roots — or a boat on the ocean, with water and fish below and bright sky above. Use big brushes and thick poster paint, so you are not tempted to put in too much detail. A thick, permanent marker works well to draw in your number line, with zero at ground (or sea) level and the negative numbers down below.

Continue reading Negative Numbers for Young Students