## Friday, June 18, 2010

I talked with a math teacher friend today about how she teaches adding and subtracting integers to her 7th graders. She mentioned the following type of method, and I decided to put it to pictures. I'm going to try it next year with my high school kids who STILL mix things up. Maybe this will do the trick.

1. Anonymous1:54 AM

Not a bad idea - I tend to use temperature as a context for integers, so a vertical number line would suit my students better.

Any ideas for models / contexts for negative times negative?

2. I JUST had that discussion with another math friend. I'd never thought about it before, just knew the rule, but our conversation made me come up with my own reasoning (which is probably not new).

If you think of multiplication as repeated addition, then say -3 * -5, means you are "adding" -5 three times in the "opposite" direction, or you're subtracting -5 three times.

So going back to the "star" model here. You start at 0 (facing right), and you're "subtracting" -5 three times. So 0 - -5 - -5 - -5. The negative on the 5 makes me turn 180 degrees to face left, and the subtracting moves backwards (so to the right). Boom, 15.

3. Off topic, but do you use twitter? There's a group of math teachers that I follow and every day I learn something from them. I love your blog and just wondered if you tweeted as well.

4. Hmmmm, I actually signed up for a twitter account, and then I didn't explore it past that. What are some you "follow" (is that the terminology)? Maybe I can figure out how it works by lurking.

5. Anonymous10:47 AM

Probably the best way to get a list of math people to follow would be to read Sam Shah's "Favorite Tweets" on his blog:
http://samjshah.com/

Can't wait to see you there!!!

6. Anonymous11:07 AM

I'm jealous of your worksheet making skills. Mine always look boring. Yours are quite polished and fancy. This one is AMAZING! I'm hoping to use it in my classroom next year as conceptual knowledge of adding integers is always difficult.

7. Thanks, Jalzen! You made my day. I'm glad someone else can get use out of them. Hopefully, this one will catch more high school kids up on adding and subtracting integers.

Thought you guys may be interested in KenKen, its a logic/arithmetic puzzle. Tons of teachers use/play them and they work really well to develop math skills.

9. hibyscus3:28 PM

These sheets are FANTASTIC! I always struggle with teaching subtracting intergers and I just learned about this method the end of last year. I plan to have them physically do it but I just LOVE the sheets as well....

10. Anonymous11:13 PM

11. You would HOPE that the students would have this skill down before the 7th grade (or high school), but sadly, many still struggle with it.

12. I have tried a number of visualization things with students, but they often get confused when they then have to work with decimals and fractions, particularly with algebraic equations. Now, I use those at the start of the year with 7th graders or with kids coming for help after class.

With older students, I try to focus on fast rules:
1. Look at the symbols (or implied symbols) in front of the digits. Are the symbols the same or different (ie, -2-5 both have minus signs in front, whereas 3-7 have different signs).
2. If the signs are the same, add the digits and keep the sign.
3. If the signs are different, subtract the smaller digit from the larger. Keep the sign from the larger digit.

It's such a battle!

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