Memory Plus: A Play and Practice Card Game

One of the things that is important (I think!) in being strong at what we call Mental Math, is being able to see, in your head, the "partner numbers" that add up to, say 10. 10 is particularly important, being the base for the number system we use.

This card game is based on the old standard, Memory. In the original game, a deck of cards is dealt face down on the table, and players take turns trying to turn over matching pairs. It might be numbers, or pictures, or some other representation on the cards.

In this game, we use a standard deck of cards, but only the numbers from 1 (Ace) to 9, so 36 of the 52 cards. Players try to turn over two cards whose values add up to 10. It's a great way to become comfortable with knowing that, for instance, "if I have a 3, I need 7 to get to 10".

Once working with 10 as your total becomes too easy, try taking out the nines, and turning over pairs that add to 9. Do the same for 8 or 7, by taking out all cards of a value equal to or higher than the total you are working with. Note that the number of cards on the table becomes a bit small for a good game as total gets lower.

 I have created an instruction sheet for Memory Plus if you need it.

 Enjoy!

Poetry in Math

My niece, Heather presented me with a math equation recently, which she had found and thought was rather fun.

Here it is:

[12 + 144 + 20 +  (3 x square root of 4)] / 7 + 5 x 11 = 9 squared + 0.

It does equate - both sides are 81.

You probably know that 12 is a dozen; But here are a couple of others:  144 is a gross; 20 is a score.

And so, if we put math into verse, we get:

A dozen, a gross and a score
Plus three times the square root of four
Divided by seven
Plus five times eleven
is nine squared and not a bit more!

Math in Limerick form.    Thank you Heather!

Puzzling Through Trig Identities

Proving trig identities is a bit like solving a puzzle:  if it doesn’t work this way, try that way . . . !

As was said of the Grinch:  “he puzzled and puzzled ‘till his puzzler was sore.” (Dr. Seuss)

When you are studying trigonometry in your math course (grade 11 or 12 ?) you likely have to  practice proving trigonometric identities.  And you don’t want to keep on puzzling and puzzling ‘till your puzzler is sore, so some strategies to aid you in your puzzling might not go amiss.

There is no one RIGHT way to prove a trig identity.  There are usually many ways to get from start to finish.  And there are many tips and tricks to help you along the way.  Try this Tips and Tricks sheet, and see if it helps at all.  Happy Puzzling!  

ADDEMUP! A Play and Practice Card Game

I often invent little games to play with students, to try to turn practice into play.  I find that many students need to work on their ability to add and subtract or multiply and divide numbers in their head.  "Mental math" it is often called.  The thing is, practicing once a week doesn't quite get us where we want to be (or so my piano teacher once told me!).  My hope is that if I can create a fun way to practice, maybe students can do it with their parents, siblings or friends at home.

Here is a game I created recently with a grade 5 student to practice adding and subtracting numbers up to 10, in your head.  We call it Addemup!

ADDEMUP!

Set-Up

Use a regular deck of 52 card deck of playing cards.  Remove the 12 face cards.
Pick a number between 1 and 20.  This number is the Game Number for the current game.
Shuffle the deck well.  Deal eight cards, face up, in a two rows by four cards.  This is the game grid.

Object of the Game

Each player tries to collect as many cards as possible, by picking up sets that total the Game Number, using addition and subtraction.

Game Play

This game can be played with two or more players.  Play is done by turn, until the entire deck is used.

On a turn a player attempts to make as many sets as possible, from the game grid, for his or her set collection.  A set is made up of a number of cards that total the Game Number, by adding or subtracting the value of each card.  The player must state what their calculation is as they pick up the cards. For example if the Game Number is 12, Player 1 may pick up 6, 9, 2, 1, in that order and say:

“6 plus 9 is 15, minus 2 is 13, minus 1 is 12”; or
“6 plus 9 is 15, 2 plus 1 is 3, 15 minus 3 is 12”.   

As a set is completed it is removed from the game grid and added to the player’s set collection.

At the end of a turn, cards from the deck are dealt to fill the spaces left in the grid by the removed sets.

The game ends when no cards are left to be dealt and the player whose turn it is can make no more sets.

The object is to collect as many cards (not sets) as possible.  A set with four cards is therefore more valuable than a set with two cards. 

Variations

·         Instead of a 4 x 2 layout of cards try 3 x 3 cards, 3 x 2 cards or 4 x 3 cards instead. 

·         The red cards are negative integers and the black cards are positive integers, with addition and subtraction allowed, but if you have a red 4, you must subtract -4 or add -4 to get your final result.  For this variation, your Game Number may be a negative integer.

·         Instead of choosing a Game Number prior to the start of the game, for each turn, after filling the grid or face-up cards, flip the top card of the deck over and place it on top of the deck – this becomes the Game Number for this player’s turn.  For the next player’s turn, this card becomes the first one placed in the grid to replace the cards removed as sets.