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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More Free Math Resources


[Photo by One Laptop Per Child.]

Once again, I am adding to my Free (Mostly) Math Resources page. Here are a handful of helpful websites for teaching math…

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Diagnosis: Math Workbook Syndrome

Photo by otisarchives3.

I discovered a case of MWS (Math Workbook Syndrome) one afternoon, as I was playing Multiplication War with a pair of 4th grade boys. They did fine with the small numbers and knew many of the math facts by heart, but they consistently tried to count out the times-9 problems on their fingers. Most of the time, they lost track of what they were counting and gave wildly wrong answers.

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How to Teach Math to a Struggling Student

photo by MC Quinn via flickr (CC BY 2.0)

Paraphrased from a homeschool math discussion forum:

“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.”

Continue reading How to Teach Math to a Struggling Student

Number Bonds, Number Rainbows

Basic bar diagram

Many of us use the idea of number bonds with our young students. A number bond is a mental picture of the relationship between a number and the parts that combine to make it.

Now we have a new, colorful way to show these relationships, thanks to Maria at Homeschool Math Blog. If you teach math to young children, check this out:

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7 Things to Do with a Hundred Chart


This post has been revised to incorporate all the suggestions in the comments below, plus many more activities. Please update your bookmarks:

Or continue reading the original article…


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Game: Tens Concentration

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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