## Monday, June 27, 2016

### Give (and Take!) Me a Great Addition Strategy

Exciting work continues in our summer math sessions!

Last week, my 10yo son and I started exploring strategies to help with multi-digit addition fluency. The "Give and Take"* strategy has given us inspiration and taken away some of our math anxiety. Here's how it works...

Let's say you're asked to add two, somewhat unfriendly, numbers.

97 + 78

Yuck. Not a great combination.

But what if you could do a little give-and-take to make it easier?

97 + 78 = 97 + (3 + 75) = (97 + 3) + 75 = 100 + 75 = 175

Which would you rather solve?

97 + 78

-OR-

100 + 75

The consensus was pretty clear around here!

443 + 289

What if we "take" 11 from 443 (443 - 11 = 432) and "give" it to 289 (289 + 11 = 300)? Is it easier to now add 432 + 300?

My 10yo explains the strategy in his math journal, in the photos you see here.

So "witch" would you rather add? :)

After journaling, to solidify the concept, he made up his own problem:

270 + 665

He took/gave 30:

300 + 635 = 935

And today, he applied it to a story problem where he had to add 275 + 168. He took/gave 25 to end up with 300 + 143. He bubbled with excitement ("MOM!!!!!"), telling me how great the give/take strategy works!

I hope this gives you a little inspiration to take back to class!

P.S. This also works well with decimals!

*The Bridges Curriculum calls this the "Give and Take" strategy.

1. I love your catchy phrasing of the strategy. However, you can't forget to help the child understand why it works. In some very comprehensive training I've attended in the last few years, the use of the number line helps students to visualize why "Give and Take" works. Copy a number line that goes from 0 to 40. Model using 27 - 19. Cut a strip that is the distance between 19 and 27 and place it on below the number line. What is the difference? Then ask move the strip and ask, what is 26 - 18 and 25 - 17. Notice what happens to the answer to all three. (The difference is the same distance each time. Why?) Move the strip forward on the number line to 28 - 20. Now what is that difference? Why? What are you noticing? What can you determine is the reason it works? Does it work with any numbers? Investigate. I hope this makes sense. It made perfect sense from the mathematics presenters I've had the honor to hear and work with during my 35+ years in education and elementary math. This actually is a way to help a child who isn't good at borrowing, to learn to be more flexible with numbers...compose and decompose...throughout their schooling.

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2. Absolutely! We did exactly that, but before this particular lesson in the Bridges curricula. Both with paper and with the (free) Number Line App.

http://catalog.mathlearningcenter.org/apps/number-line

Here's an example, though with a different strategy:

http://www.mathlearningcenter.org/blog/constant-difference-number-line-app

Thank you for your thoughtful reply! It sounds like you've had some great professional development!

Thank you for leaving me a message. I love comments almost as much as I love chocolate! And I do LOVE chocolate. :)

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