Tag Archives: Elementary school

They’re Here! Math You Can Play Weekend Sale

Finally, the first two books of my math games series are finished and loaded up on Amazon.com (and the other Amazons worldwide). To celebrate, I’m offering an introductory sale price this weekend: US$2.99 per book, now through Monday.

Math Your Kids WANT To Do

Are you tired of flashcards and repetitive worksheets? Now your children can practice their math skills by playing games.

Math games pump up mental muscle, reduce the fear of failure, and develop a positive attitude toward mathematics. Through playful interaction, games strengthen a child’s intuitive understanding of numbers and build problem-solving strategies. Mastering a math game can be hard work, but kids do it willingly because it is fun.

Counting & Number Bonds: Math Games for Early Learners, Preschool to 2nd Grade

Counting-Games

Counting & Number Bonds features 21 kid-tested games, offering a variety of challenges for preschool and early-elementary learners. Young children can play with counting and number recognition while they learn the basic principle of good sportsmanship, to respond gracefully whether they win or lose. Older students will explore place value, build number sense, and begin practicing the math facts.

Buy now at:

Addition & Subtraction: Number Games for Elementary Students, Kindergarten to 4th Grade

Addition-Games600x800

Addition & Subtraction features 22 kid-tested games, offering a variety of challenges for elementary-age students. Children will strengthen their understanding of numbers and develop mental flexibility by playing with addition and subtraction, from the basic number facts to numbers in the hundreds and beyond. Logic games build strategic thinking skills, and dice games give students hands-on experience with probability.

Buy now at:

Don’t Have a Kindle?

You don’t need a Kindle device to read Amazon ebooks. Click here to download the Kindle program for your computer, phone, or tablet.

For those of you who prefer to buy ebooks from iTunes, Barnes & Noble, Kobo, etc.‌—‌those versions are coming soon! The epub book format takes a bit more work, but I’m hoping for time to finish it up within a week or so.

Paperback editions are also in the works.


Featured photo above by Richard Riley via Flickr (CC BY 2.0).


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Math Game: Chopsticks

Feature photo above by Harry (Phineas H) via Flicker (CC BY 2.0).

Math Concepts: counting up to five, thinking ahead.
Players: two or more.
Equipment: none.

How to Play

Each player starts with both hands as fists, palm down, pointer fingers extended to show one point for each hand. On your turn, use one of your fingers to tap one hand:

  • If you tap an opponent’s hand, that person must extend as many extra fingers on that hand (in addition to the points already there) as you have showing on the hand that tapped. Your own fingers don’t change.
  • If you force your opponent to extend all the fingers and thumb on one hand, that makes a “dead hand” that must be put behind the player’s back, out of the game.
  • If you tap your own hand, you can “split” fingers from one hand to the other. For instance, if you have three points on one hand and only one on the other, you may tap hands to rearrange them, putting out two fingers on each hand. Splits do not have to end up even, but each hand must end up with at least one point (and less than five, of course).
  • You may even revive a dead hand if you have enough fingers on your other hand to split. A dead hand has lost all its points, so it starts at zero. When you tap it, you can share out the points from your other hand as you wish.

The last player with a live hand wins the game.

When a two-points hand taps a one-point hand, that player must put out two more fingers.
When a two-points hand taps a one-point hand, that player must put out two more fingers.

Variations

House Rule: Do you want a shorter game? Omit the splits. Or you could allow ordinary splits but not splitting fingers to dead hands.

Nubs: All splits must share the fingers evenly between the hands. If you have an odd number of points, this will leave you with “half fingers,” shown by curling those fingers down.

Zombies: (For advanced players.) If a hand is tapped with more fingers than are needed to put it out of the game, it comes back from the dead with the leftover points. For instance, if you have four fingers out, and your opponent taps you with a two-finger hand, that would fill up your hand with one point left over. Close your fist, and then hold out just the zombie point. In this variation, the only way to kill a hand is to give it exactly five points.

History

Finger-counting games are common in eastern Asia—and they must be contagious, since my daughters caught them from their Korean friends at college. Middle school teacher Nico Rowinsky shared Chopsticks (which is simpler than the version my daughters brought home) in a comment on the “Tiny Math Games” post at Dan Meyer’s blog.


Counting-Games

This post is an excerpt from my book Counting & Number Bonds: Math Games for Early Learners, available now in bookstores all over the Internet.


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The Math Student’s Manifesto

[Feature photo above by Texas A&M University (CC BY 2.0) via Flickr.]

Note to Readers: Please help me improve this list! Add your suggestions or additions in the comment section below…

What does it mean to think like a mathematician? From the very beginning of my education, I can do these things to some degree. And I am always learning to do them better.

(1) I can make sense of problems, and I never give up.

  • I always think about what a math problem means. I consider how the numbers are related, and I imagine what the answer might look like.
  • I remember similar problems I’ve done before. Or I make up similar problems with smaller numbers or simpler shapes, to see how they work.
  • I often use a drawing or sketch to help me think about a problem. Sometimes I even build a physical model of the situation.
  • I like to compare my approach to the problem with other people and hear how they did it differently.

(2) I can work with numbers and symbols.

  • I know how numbers relate to each other.
  • I’m flexible with mental math. I understand arithmetic properties and can use them to make calculations easier.
  • I’m not intimidated by algebra symbols.
  • I don’t rely on memorized rules unless I know why they make sense.

(3) I value logical reasoning.

  • I can recognize assumptions and definitions of math terms.
  • I argue logically, giving reasons for my statements and justifying my conclusion.
  • I listen to and understand other people’s explanations.
  • I ask questions to clarify things I don’t understand.

Continue reading The Math Student’s Manifesto

Teaching the Standard Algorithms

[Feature photo above by Samuel Mann, Analytical Engine photo below by Roͬͬ͠͠͡͠͠͠͠͠͠͠͠sͬͬ͠͠͠͠͠͠͠͠͠aͬͬ͠͠͠͠͠͠͠ Menkman, both (CC BY 2.0) via Flickr.]

Babbage's Analytical Engine

An algorithm is a set of steps to follow that produce a certain result. Follow the rules carefully, and you will automatically get the correct answer. No thinking required — even a machine can do it.

This photo shows one section of the first true computer, Charles Babbage’s Analytical Engine. Using a clever arrangement of gears, levers, and switches, the machine could crank out the answer to almost any arithmetic problem. Rather, it would have been able to do so, if Babbage had ever finished building the monster.

One of the biggest arguments surrounding the Common Core State Standards in math is when and how to teach the standard algorithms. But this argument is not new. It goes back at least to the late 19th century.

Here is a passage from a book that helped shape my teaching style, way back when I began homeschooling in the 1980s…

Ruth Beechick on Teaching Abstract Notation

Understanding this item is the key to choosing your strategy for the early years of arithmetic teaching. The question is: Should you teach abstract notation as early as the child can learn it, or should you use the time, instead, to teach in greater depth in the mental image mode?

Beechick-EasyStartArithmetic

Abstract notation includes writing out a column of numbers to add, and writing one number under another before subtracting it. The digits and signs used are symbols. The position of the numbers is an arbitrary decision of society. They are conventions that adult, abstract thinkers use as a kind of shorthand to speed up our thinking.

When we teach these to children, we must realize that we simply are introducing them to our abstract tools. We are not suddenly turning children into abstract thinkers. And the danger of starting too early and pushing this kind of work is that we will spend an inordinate amount of time with it. We will be teaching the importance of making straight columns, writing numbers in certain places, and other trivial matters. By calling them trivial, we don’t mean that they are unnecessary. But they are small matters compared to real arithmetic thinking.

If you stay with meaningful mental arithmetic longer, you will find that your child, if she is average, can do problems much more advanced than the level listed for her grade. You will find that she likes arithmetic more. And when she does get to abstractions, she will understand them better. She will not need two or three years of work in primary grades to learn how to write out something like a subtraction problem with two-digit numbers. She can learn that in a few moments of time, if you just wait.

— Ruth Beechick
An Easy Start in Arithmetic (Grades K-3)
(emphasis mine)


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2015 Mathematics Game

[Feature photo above by Scott Lewis and title background (right) by Carol VanHook, both (CC BY 2.0) via Flickr.]

2015YearGame

Did you know that playing games is one of the Top 10 Ways To Improve Your Brain Fitness? So slip into your workout clothes and pump up those mental muscles with the Annual Mathematics Year Game Extravaganza!

For many years mathematicians, scientists, engineers and others interested in math have played “year games” via e-mail. We don’t always know whether it’s possible to write all the numbers from 1 to 100 using only the digits in the current year, but it’s fun to see how many you can find.

Math Forum Year Game Site

Rules of the Game

Use the digits in the year 2015 to write mathematical expressions for the counting numbers 1 through 100. The goal is adjustable: Young children can start with looking for 1-10, middle grades with 1-25.

  • You must use all four digits. You may not use any other numbers.
  • Solutions that keep the year digits in 2-0-1-5 order are preferred, but not required.
  • You may use +, -, x, ÷, sqrt (square root), ^ (raise to a power), ! (factorial), and parentheses, brackets, or other grouping symbols.
  • You may use a decimal point to create numbers such as .2, .02, etc., but you cannot write 0.02 because we only have one zero in this year’s number.
  • You may create multi-digit numbers such as 10 or 201 or .01, but we prefer solutions that avoid them.

My Special Variations on the Rules

  • You MAY use the overhead-bar (vinculum), dots, or brackets to mark a repeating decimal. But students and teachers beware: you can’t submit answers with repeating decimals to Math Forum.
  • You MAY NOT use a double factorial, n!! = the product of all integers from 1 to n that have the same parity (odd or even) as n. Math Forum allows these, but I’ve decided I prefer my arithmetic straight.

Click here to continue reading.

Math Debates with a Hundred Chart

Euclid game
Wow! My all-time most popular post continues to grow. Thanks to an entry from this week’s blog carnival, there are now more than thirty great ideas for mathematical play:

The latest tips:

(31) Have a math debate: Should the hundred chart count 1-100 or 0-99? Give evidence for your opinion and critique each other’s reasoning.
[Hat tip: Tricia Stohr-Hunt, Instructional Conundrum: 100 Board or 0-99 Chart?]

(32) Rearrange the chart (either 0-99 or 1-100) so that as you count to greater numbers, you climb higher on the board. Have another math debate: Which way makes more intuitive sense?
[Hat tip: Graham Fletcher, Bottoms Up to Conceptually Understanding Numbers.]

(33) Cut the chart into rows and paste them into a long number line. Try a counting pattern, or Race to 100 game, or the Sieve of Eratosthenes on the number line. Have a new math debate: Grid chart or number line — which do you prefer?
[Hat tip: Joe Schwartz, Number Grids and Number Lines: Can They Live Together in Peace? ]


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Roadmap to Mathematics: 3rd Grade

[Feature photo (above) by Phil Roeder. (CC BY 2.0 via Flickr)]

roadmap3

A frequently-asked question on homeschooling forums is, “Are my children working at grade level? What do they need to know?”

The Council of the Great City Schools has published a handy 6-page pdf summary of third grade math concepts, with suggestions for how parents can support their children’s learning:

Whether you are a radical unschooler or passionately devoted to your textbook — or, like me, somewhere in between — you can help your children toward these grade-level goals by encouraging them to view mathematics as mental play. Don’t think of the standards as a “to do” list, but as your guide to an adventure of exploration. The key to learning math is to see it the mathematician’s way, as a game of playing with ideas.

The following are excerpts from the roadmap document (along with a few extra tips) and links to related posts from the past eight years of playing with math on this blog…

Continue reading Roadmap to Mathematics: 3rd Grade