Let’s Play Math!

[Photo by SuperFantastic.]

Keith Devlin’s latest article, It Ain’t No Repeated Addition, brought me up short. I have used the “multiplication is repeated addition” formula many times in the past — for instance, in explaining order of operations. But according to Devlin:

Multiplication simply is not repeated addition, and telling young pupils it is inevitably leads to problems when they subsequently learn that it is not.

I found myself arguing with the article as I read it. (Does anybody else do that?) If multiplication is not repeated addition, then what in the world is it?

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Photo by paparutzi.

Math concepts: addition, subtraction, negative numbers, mental math, absolute value
Number of players: any number
Equipment: math cards (two decks may be needed for a large group)

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Photo by MC Quinn.

Help! My daughter struggles with arithmetic. I guess she is like me: just not a math person. She is an outstanding reader. When we do word problems, she usually has no trouble. She’s a whiz at strategy games and beats her dad at chess every time. But numbers — yikes! When we play Yahtzee, she gets lost trying to add up her score. The simple basics of adding and subtracting confuse her.

Since I find math difficult myself, it’s hard for me to know what she needs. What’s missing to make it click for her? She used to think math was fun and tested well above grade level, but I listened to some well-meaning advice and totally changed the way we were schooling. I switched from using workbooks and games to using Saxon math, and she got extremely frustrated. Now she hates math.

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Photo by Mike Licht, NotionsCapital.com.

The cold came back and knocked me flat, but there are compensations. The downtime gave me a chance to browse my overflowing bookmarks folder, and I found something to add to my resource page. Princess Kitten and I enjoyed exploring these games and quizzes from Ambleweb.

Math games by elementary students

Each game was designed by (or at least with the help of) 4th-6th grade students at Ambleside CE Primary School.

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Math concepts: addition and subtraction within 100, logical strategy
Number of players: 2 or 3
Equipment: printed hundred chart (also called a hundred board) and beans, pennies, or other tokens with which to mark numbers — or use this online hundred chart

Set up

Place the hundred chart and a small pile of tokens where both players can reach them.

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The ability to solve word problems ranks high on any math teacher’s list of goals. How can I teach my students to solve math problems? I must help them develop the ability to translate “real world” situations into mathematical language. In two previous posts, I introduced the problem-solving tools algebra and bar diagrams. These tools help our students organize the information in a word problem and translate it into a mathematical calculation.

Working math problems with Poor Richard

This time I will demonstrate these problem-solving tools in action with a series of 3rd-grade problems based on the Singapore Primary Math series, level 3A. For your reading pleasure, I have translated the problems into the universe of a well-written biography of Ben Franklin, Poor Richard by James Daugherty.

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The ability to solve word problems ranks high on any math teacher’s list of goals. How can I teach my students to reason their way through math problems? I must help my students develop the ability to translate “real world” situations into mathematical language.

In a previous post, I analyzed two problem-solving tools we can teach our students: algebra and bar diagrams. These tools help our students organize the information in a word problem and translate it into a mathematical calculation.

Now I want to demonstrate these problem-solving tools in action with a series of 2nd grade problems, based on the Singapore Primary Math series, level 2A. For your reading pleasure, I have translated the problems into the universe of one of our family’s favorite read-aloud books, Mr. Popper’s Penguins.

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Are you looking for ways to unschool math? You and your children can learn a lot by playing around with a hundred chart (also called a hundred board). Here are a few ideas to get you started:

(1) Use it as a number line to do addition and subtraction beyond what your child can handle mentally. Develop mental math skills by showing how to add or subtract the tens first (counting up or down) then the ones (counting left or right.)

(2) Look for addition and subtraction patterns. 5+7=? Now go to 25+7, 35+7, 65+7. What do you notice? What do 13-6, 23-6, 53-6, etc. have in common? Find other patterns.

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Egyptians wrote in hieroglyphs, a type of picture writing, and in hieratics, which were like a cursive form of hieroglyphs.

Hieroglyphs came first. They were carved in the stone walls of temples and tombs, written on monuments, and used to decorate furniture. But they were a nuisance for scribes, who simplified the pictures and slurred some lines together when they wrote in ink on paper-like papyrus. This hieratic writing — like some people’s cursive today — can be hard to read, so we are only using hieroglyphic numbers on this blog.

Download this page from my old newsletter, and try your hand at translating some Egyptian hieroglyphs:

Hieroglyphic addition and subtraction (pdf 47KB)

Then try writing some hieroglyphic calculations of your own.

Edited to add: The answers to these puzzles (and more) are now posted here.

:: :: :: :: :: :: :: :: :: :: ::

• The Secret of the Pharaoh’s Treasure, Part 1
• Alexandria Jones and the Thief in the Night
• Egyptian Math Puzzles
• The Secret of Egyptian Fractions
• Egyptian Geometry and Other Challenges

Math concepts: addition, number bonds to 10, visual memory
Number of players: any number, mixed ages
Equipment: math cards, one deck

Set up

Each player draws a card, and whoever choses the highest number will go first. Then shuffle the cards and lay them all face down on the table, spread out so no card covers any other card. There are 40 cards in a deck, so you can make a neat array with five rows of eight cards each, or you may scatter them at random.

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[Rescued from my old blog.]

A number bond is a mental picture of the relationship between a number and the parts that combine to make it. The concept of number bonds is very basic, an important foundation for understanding how numbers work. A whole thing is made up of parts. If you know the parts, you can put them together (add) to find the whole. If you know the whole and one of the parts, you take away the part you know (subtract) to find the other part.

Number bonds let children see the inverse relationship between addition and subtraction. Subtraction is not a totally different thing from addition; they are mirror images. To subtract means to figure out how much more you would have to add to get the whole thing.

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[Rescued from my old blog.]

Would you like to introduce your students to negative numbers before they study them in pre-algebra? With a whimsical number line, negative numbers are easy for children to understand.

Get a sheet of poster board, and paint a tree with roots — or a boat on the ocean, with water and fish below and bright sky above. Use big brushes and thick poster paint, so you are not tempted to put in too much detail. A thick, permanent marker works well to draw in your number line, with zero at ground (or sea) level and the negative numbers down below.

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