Tag Archives: Addition

Math Game: Thirty-One

Math Concepts: addition to thirty-one, thinking ahead.
Players: best for two.
Equipment: one deck of math cards.

How to Play

Lay out the ace to six of each suit in a row, face up and not overlapping, one suit above another. You will have one column of four aces, a column of four twos, and so on‌—‌six columns in all.

The first player flips a card upside down and says its number value. Players alternate, each time turning down one card, mentally adding its value to the running total, and saying the new sum out loud. The player who exactly reaches thirty-one, or who forces the next player to go over that sum, wins the game.

31-Game

Variation

For a shorter game, use only the ace to four of each suit. Play to a target sum of twenty-two.

History (and a Puzzle)

Thirty-One comes from British mathematician Henry Dudeney’s classic book, The Canterbury Puzzles. According to Dudeney, “This is a game that used to be (and may be to this day, for aught I know) a favourite means of swindling employed by card-sharpers at racecourses and in railway carriages.”

Dudeney challenges his readers to find a rule by which a player can always win: “Now, the question is, in order to win, should you turn down the first card, or courteously request your opponent to do so? And how should you conduct your play?”


Dudeney, H. E. The Canterbury Puzzles, Thomas Nelson and Sons, 1919 (originally published 1907); available at Project Gutenberg or the Internet Archive.
http://www.gutenberg.org/ebooks/27635
https://archive.org/details/canterburypuzzle00dudeuoft


Addition-Games600x800

This post is an excerpt from my book Addition & Subtraction: Math Games for Elementary Students, available now in bookstores all over the Internet.


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Addition Games with Cuisenaire Rods

Education Unboxed has posted some playful addition games for young learners. If your browser has as much trouble displaying Vimeo content as mine does, I’ve included the direct links:

Six is Having a Party! – Math Facts with Cuisenaire Rods

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PUFM 1.3 Addition

Photo by Luis Argerich via flickr. In this Homeschooling Math with Profound Understanding (PUFM) Series, we are studying Elementary Mathematics for Teachers and applying its lessons to home education.

The basic idea of addition is that we are combining similar things. Once again, we meet the counting models from lesson 1.1: sets, measurement, and the numberline. As homeschooling parents, we need to keep our eyes open for a chance to use all of these models — to point them out in the “real world” or to weave them into oral story problems — so our children gain a well-rounded understanding of math.

Addition arises in the set model when we combine two sets, and in the measurement model when we combine objects and measure their total length, weight, etc.

One can also model addition as “steps on the number line”. In this number line model the two summands play different roles: the first specifies our starting point and the second specifies how many steps to take.

— Thomas H. Parker & Scott J. Baldridge
Elementary Mathematics for Teachers

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Triangular Numbers: Sum from 1 to N

Kitten and I covered triangular numbers a couple months ago in our Competition Math for Middle School book, but I think it’s time to revisit the topic. I like the method James Tanton gives in this new video:

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Game: Target Number (or 24)

[Photo by stevendepolo.]

Math concepts: addition, subtraction, multiplication, division, powers and roots, factorial, mental math, multi-step thinking
Number of players: any number
Equipment: deck of math cards, pencils and scratch paper, timer (optional)

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Mental Math: Addition

[Photo by woodleywonderworks.]

The question came from a homeschool forum, though I’ve reworded it to avoid plagiarism:

My student is just starting first grade, but I’ve been looking ahead and wondering: How will we do big addition problems without using pencil and paper? I think it must have something to do with number bonds. For instance, how would you solve a problem like 27 + 35 mentally?

The purpose of number bonds is that students will be comfortable taking numbers apart and putting them back together in their heads. As they learn to work with numbers this way, students grow in understanding — some call it “number sense” — and develop a confidence about math that I often find lacking in children who simply follow the steps of an algorithm.

[“Algorithm” means a set of instructions for doing something, like a recipe. In this case, it means the standard, pencil and paper method for adding numbers: Write one number above the other, then start by adding the ones column and work towards the higher place values, carrying or “renaming” as needed.]

For the calculation you mention, I can think of three ways to take the numbers apart and put them back together. You can choose whichever method you like, or perhaps you might come up with another one yourself…

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Cute Math Facts for Visual Thinkers

numberwalk[Photo by angela7dreams.]

A forum friend posted about her daughter’s adventure in learning the math facts:

She loves stories and drawing, so I came up with the “Math Friends” book. She made a little book, and we talked about different numbers that are buddies.

Continue reading Cute Math Facts for Visual Thinkers