July 2023
Welcome to EFM's July Newsletter!
EFM: Supporting families to play, explore, and love math
News
Playing Cards on Website – EFM has four decks of playing cards in various stages of development.
Two of the decks are puzzles primarily for classrooms – one is for grades K – 3 and one for grades 2 – 5. The K – 3 deck is finished! Two other decks are activities primarily for families – one for Stages 1 – 2, and one for Stages 3 – 4.
Learn more about these decks, including seeing all the card face images, by going to the Playing Cards Page on the EFM website.
Korean Translation is Done! – Thanks to the hard work of our Korean translators, human Korean translations of all the Activities for Families and Storybooks are now complete. Enjoy!
Japanese Translation is Partially Done! - Our Japanese translators have translated Chapters 1 to 4 of the Activities for Families.
Intentional Math Fun
One of the main aims of Think Square, a website of Andrew Lorimer-Derham and Michael Briggs-Miller, is providing games and activities that create intentional fun with math. It is striking that this needs to be stated as a goal. Sadly, too many people see math as boring, tedious, isolating, frustrating, hateful work. Fortunately there are a lot of people doing their best to change this and help people see math as playful, adventurous fun that should be enjoyed together. Other sites promoting playfulness such as Maths Play, Math for Love, Love Maths, and Let's Play Math come quickly to mind, and of course there are many more.
This month I will cover five of the games and activities from Think Square. I hope you and your children enjoy playing with them together and have lots of intentional fun!
Algebra See-Saw
These puzzles use the lever principle to create multiplication and addition puzzles.
The lever principle states that the force of a weight on one side of a lever is its weight multiplied by its distance from the fulcrum. For example, the lever below balances because the 2 weight on the left is 4 units away from the fulcrum, and that balances the 4 weight on the right that is 2 units away: 2 x 4 = 4 x 2.
The levers in these puzzles have a defined maximum length (usually 5), and that constrains the possible solutions. The puzzles are simple enough to state: Given a group of weights, place them on either side of the lever, no two weights on the same spot, so that the lever balances.
Once you’ve found one answer, can you find others – how do you know that you’ve found them all? In the case of placing 2 and 4, a second solution is to place the 2 weight 2 units from the fulcrum and the 4 weight 1 unit away.
With larger numbers, it can be a bit more thought provoking: Where would you put 12 and 16? Using prime factorizations can make this easier to do.
Vary the difficulty of these puzzles by introducing more than two weights and by lengthening the lever arms.
Sudo-Clue
The object of these puzzles is to fill an empty grid of boxes using the numbers from 1 to the number of boxes. The basic size to use is a 3 by 3 grid and fill it using each of the numbers from 1 to 9 once.
The only requirement for filling the boxes is that the numbers satisfy the clues that come with the puzzle. These clues can be as simple or as tricky as you like, and they can emphasize any particular topic your child may be interested in at the time. Your child can also have fun creating a set of clues for a puzzle for you.
Fill this 3 by 3 square following these clues:
The diagonals are odd numbers.
The top row is entirely square numbers.
The center number is the average of the bottom two corners.
The sum of the first column is as small as possible.
The sum of the third column is as large as possible.
Notice that these are similar to a crossword puzzle with numbers. That observation leads to the creation of any shape of criss-crossing numbers, but there is something very satisfying about these dense, rectangle-shaped ones.
Mathematic-Tac-Toe
This game is the same as EFM’s Math Tic Tac Toe game on page 14 of Stage 4.
This 2-person game uses a Tic Tac Toe board. One player, The Attacker, uses only the odd numbers, and the other player, The Defender, uses only the even numbers. Each number may be used at most once. The Attacker goes first, and the first move may not be in the center square. The Attacker wins if any three numbers in a line add up to 15. The Defender wins if that doesn’t happen.
Tumbling Towers
This is a two-digit ordering challenge. Start with three empty slots stacked vertically and a deck of cards with the numbers from 0 to 9 (treat queens as 0’s). Select two cards at random – say 2 and 7. You can choose to use this as 27 or 72. Once you make a choice, you must select an empty slot and place it there (it cannot be moved once it is placed). Your goal is to fill the slots in ascending order, with the smallest on top and the largest on the bottom. If you successfully fill all three slots, you go on to the next level, which uses one more slot (in this case 4 slots). If you get stuck and cannot place a number that comes up, then you go to the previous level, which uses one less slot (in this case 2 slots).
There is no natural endpoint to this game. You can challenge yourself to reach some number of slots, or you can simply enjoy the ebb and flow of the levels as you have good fortune or face setbacks.
Because this is an activity of chance, there is not necessarily a best move to make at any given moment. That makes “failure” an accepted part of the game and helps to destigmatize it. It also opens the door for fun discussions about possibly better and worse choices for moves.
Instead of using two-digit numbers, this can be played using fractions. In this case, drawing 2 and 7 creates the choice of placing 2/7 or 7/2 in one of the empty slots. In all other ways, the fraction version is the same as the two-digit version.
This is naturally a solitaire activity. Two people can play together and discuss ideas for how to move. Two people can play a game against each other by having the same number of slots and using the same random cards, and see which person is more successful with their choices.
Who is the Spy
You are given four things, often arranged in a 2 by 2 array, and your mission is to identify The Spy, the item that is the least like the other three. Just as in the real world of spies, it can be tricky figuring this out. This activity has the players compiling evidence about how each of the four things doesn’t fit in – how it is different from the other three. After all the evidence is gathered, the item with the most differences is deemed to be The Spy.
Similar to Tumbling Towers, one of the strengths of this activity is that there isn’t necessarily one right answer. There is lots of room for different answers and for discussions about the persuasiveness of various lines of thought.
You can use any four items you like, numerical or otherwise. Here are two numerical puzzles. I have listed some reasons that make each entry different – you may come up with other reasons, or you may decide some of mine are not reasonable (I won’t be offended, it’s part of the game).
2 – the only even number; the only number with an even digit; the smallest number
31 – the largest number; only number one less than a power of 2
9 – the only composite number; the only square; the only number whose sum of digits is odd; the only number that is one more than a cube
17 – the only number that is one more than a square
6/4 – the only fraction with a composite denominator; the only fraction where both numbers are even; the only fraction where the sum of the numbers is even
6/5 – the only irreducible fraction; the smallest of the fractions
10/5 – the only fraction that does not have 6 in the numerator; the only fraction where the top and bottom are multiples of 5
6/3 – the only fraction where the top and bottom are multiples of 3
If you have any questions or comments, please send them my way. I would enjoy the opportunity to chat with you. Also, if you are interested in collaborating with us or supporting us in any fashion, I would love to talk with you about ways we can work together!
Chris Wright
July 18, 2023
Chris@EarlyFamilyMath.org
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Early Family Math is a California 501(c)(3) nonprofit corporation, #87-4441486.