June 2021
Welcome to EFM's June Newsletter!
Chapter 5 - I Can Count to 100!
Chapter 5 and its Bonus Material are now available for download from the site. Have fun doing the many new games, puzzles, activities, and investigations with your family.
In other news ...
Annotated Storybooks: The Beginning Verbal level of storybooks is complete. The third level, Beginning Story Line storybooks, is now halfway done. Enjoy reading all these new books with your children!
Translations: Dutch and Chinese (Traditional and Simplified) have finished translating Chapter 1 and the Printables file. If you know someone who would like to volunteer to help us bring Early Family Math to more communities, please put them in touch with us.
New Activities to Enjoy!
Chapter 2 – Barrier Game – An activity from Michael Minas
Make a barrier between the two players so they can’t see each other’s work. Each person has a piece of paper and the same set of colored pencils, crayons, or pens. One person draws shapes (such as circles, triangles, squares, and rectangles) in colors and groups in distinctive positions on their paper. That person then gives directions for the other person to follow to make the identical drawing. At the end, the barrier is removed and the two drawings are compared (usually with lots of laughter). The players compare ideas on which spoken directions worked and which did not.
This can be a 3D activity if each player has the same set of stackable items (such as Lego bricks). In this case, one player makes a stack in some interesting way and then gives a sequence of directions to the other player.
Chapter 3 – Skyscrapers – A puzzle from Julia Robinson Math Festivals
These puzzles practice spacial and logical reasoning. Start with a 3 by 3 square. On each part of this square, place a number that represents a “skyscraper” that is 1, 2, or 3 stories high. Each row and each column should have exactly one skyscraper of each height. At each end of each row and each column place a number that is the number of skyscrapers you can see looking in that direction – a taller skyscraper blocks the view of a shorter skyscraper located behind it. To make a puzzle out of this, remove all, or almost all, of the skyscraper numbers, and maybe remove a few of the viewing numbers around the outside. For a beginning player, having a set of uniform stackable blocks is helpful for visualizing what is going on. You can also start with a new player by putting in all the numbers in the 3 by 3 square and asking what the viewing numbers would be.
In this example, if you only put in the two 3’s that are viewing numbers, that would still be enough to determine all the other numbers.
To provide more of a challenge in your puzzles, remove many of the viewing numbers on the outside of the puzzles you make. Also consider using 4 by 4 or even 5 by 5 puzzles.
Chapter 4 – Tumbling Towers – A game from Michael Minas
A “tower” is a list of empty slots for 2-digit numbers to be filled in. The “height” of a tower is the length of the list. The challenge during a player’s turn is to fill in a tower without making it “tumble over” – it will only stay upright if it is filled with numbers that increase in size from bottom to top. Play starts with one player having to fill a two-story tower. To fill a tower, use Number Cards from 0 to 9. Each time a new number is to be filled in, two cards are selected and the player chooses the order the digits will be used to create the two-digit number and which empty row in the tower to put this number in. When a player finishes successfully filling a tower (and doesn't get stuck), the next player must fill a tower one story higher. The last successful player gets as many points as the height of their last tower. Points are totaled over several rounds and the person with the most points wins.
For more advanced players, select three Number Cards and use slots for 3-digit numbers.
Chapter 5 - Check out the great new activities in this new chapter!
Chapter 6 – I'm Thinking of a Number - Remainders – A game from Chris Wright
This is a remainder game my children loved to play when we traveled. The Puzzler announces an appropriate number range, say 1 to 100, and then thinks of a mystery number in that range. The Questioners get to ask questions of the form “What is the remainder when you divide your number by n?” - where n is a number from 2 to 9.
This uses the beautiful mathematical idea that if you know the remainders when you divide by two numbers that are relatively prime (that means they have no common factor larger than 1), then the remainder is determined when you divide by the product of the two numbers. For example, if you know the remainder is 3 when you divide by 5, and the remainder is 2 when you divide by 8, then the remainder must be 18 when you divide by the product 5 x 8 = 40.
After each question, the Questioners can announce how much more they know about the number after hearing the latest answer. In this example, if the number is between 1 and 100 and has a remainder of 18 when divided by 40, then the number must be 18, 58, or 98. Asking what the remainder is when the number is divided by 3 will determine which of those three numbers it is.
If you have any questions or comments, please send them my way. I would enjoy the opportunity to chat with you.
- Chris Wright
June 18, 2021
chris@kitchentablemath.com