A Puzzle for Palindromes

If you haven’t seen the meme going around, this is a palindrome week because the dates (written American style and with the year shortened to ’19) are the same when reversed.

Here’s a math puzzle for palindrome week — or any time you want to play with math:

  • Print a 100 chart.
  • Choose a color code.
  • Play!

What do you think: Will all numbers eventually turn into palindromes?

Links

You can find all sorts of hundred charts on my Free Math Printable Files page.

Read about the history of palindromes on Nrich Math’s Palindromes page.

Find out more about the Palindromic Number Conjecture in Mark Chubb’s article An Unsolved Problem your Students Should Attempt.

Or play with Manan Shah’s advanced palindromic number questions.

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. Then the second player turns down a card, adds it to the first player’s number, and says the sum.

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

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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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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)

Set Up

All players must agree on a Target Number for the game. Try to choose a number that has several factors, which means there will be a variety of ways to make it. Traditionally, I start my math club students with a target of 24.

Shuffle the deck, and deal four cards face down to each player. (For larger target numbers, such as 48 or 100, deal five or six cards to each player.) The players must leave the cards face down until everyone is ready. Set the remainder of the deck to one side.

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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

Contig Game: Master Your Math Facts

[Photo by Photo Mojo.]

Yahtzee and other board games provide a modicum of math fact practice. But for intensive, thought-provoking math drill, I can’t think of any game that would beat Contig.

Math concepts: addition, subtraction, multiplication, division, order of operations, mental math
Number of players: 2 – 4
Equipment: Contig game board, three 6-sided dice, pencil and scratch paper for keeping score, and bingo chips or wide-tip markers to mark game squares

Set Up

Place the game board and dice between players, and give each player a marker or pile of chips. (Markers do not need to be different colors.) Write the players’ names at the top of the scratch paper to make a score sheet.

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30+ Things to Do with a Hundred Chart

[Photo by geishaboy500 (CC BY 2.0).]

Are you looking for creative ways to help your children study math? Even without a workbook or teacher’s manual, your kids can learn a lot about numbers. Just spend an afternoon playing around with a hundred chart (also called a hundred board or hundred grid).

My free 50-page PDF Hundred Charts Galore! printables file features 1–100 charts, 0–99 charts, bottom’s-up versions, multiple-chart pages, blank charts, game boards, and more. Everything you need to play the activities below and those in my new 70+ Things to Do with a Hundred Chart book.

Download Free “Hundred Charts Galore!” Printables

Shop for “70+ Things To Do with a Hundred Chart” Book

And now, let’s play…

Continue reading 30+ Things to Do with a Hundred Chart