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!

How about:

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.

Multiplication Strategies: x2, x4, x8

Over the past week, my son and I have made tremendous progress with multiplication. (Intro post here.) Each day, we add to his fluency toolbox by looking at specific strategies. The (related) strategies for 2s, 4s, and 8s, have been especially fruitful. Let's look at why...

2s...Dare to DOUBLE!
Twos are easy-peasy. Just a matter of doubling. We can see an example in this array.

If you multiply something by 2, you only need to double. Instead of 1 group of 6, you have 2 groups of 6; you just double 6.












4s...Double-Double
In Bridges in Mathematics, the strategy for multiplying by 4s is called Double-Double. It's easy to see why.

We already doubled when we multiplied by 2. To go from 2x a number to 4x a number, we double. So we double, then double again.

6 is doubled to 12 (x2)
12 is doubled to 24 (x4)

I bet you can guess what's coming next!





8s...Double-Double-Double
We call the strategy for 8s Double-Double-Double.

For 8x, we double 3 times:

6 is doubled to 12 (x2)
12 is doubled to 24 (x4)
24 is doubled to 48 (x8)

Can you see it in the model?

This is not a multiplication "trick" but rather a strategy with meaning behind it. Children need to see the visual model and understand what "Double-Double-Double" means. Once they understand the concept, they can apply it in wonderful ways.

I asked my son (just developing fluency with single digit multiplication) to consider these problems.

8 x 15 = ?

He doubled 15 and got 30. He doubled 30 (60). And doubled once more to get 120. So 8 x 15 = 120.

4 x 13 = ?

Double 13 to get 26. Double 26 to get 52. (Of course he then wanted to keep going and figure out 8 x 13. Double 52 and get 104!)

25 x 8 = ?

50, 100, 200, done! This problem was also a great opportunity to talk about another strategy. Do you know what it is? Leave your ideas in the comments below to start a RICH exchange.

Hope you're having a double dose of summer fun!

Credits:
Little Girl Graphic from: www.mycutegraphics.com
Number Frames (free app) from: http://www.mathlearningcenter.org/web-apps/number-frames/

Fraction Fun with Number Lines

Studying fractions?

You won't want to miss the new, free activities from the Math Learning Center. The materials are complex...

...a number line (free pdf)
...a paperclip

I've used the paperclip/number line with students and love, love, love the way students can see and move fractions on a line.

A free "I Have, Who Has" game is also included. For a complete description and links to the free pdf, visit the MLC blog.

Supports:
CCSS.Math.Content.3.NF.A.1
CCSS.Math.Content.3.NF.A.2
CCSS.Math.Content.3.NF.A.3

Clothespin Fractions

Order and compare fractions on a number line with these simple materials from the Dollar Store.

Materials Needed:
clothespins (pack of 36 for $1)
hanger
Sharpie

Directions:
1. Use a fine Sharpie to label clothespins with the fractions you wish to explore.
2. Place clothespins in a Math Station or Workbox, along with a hanger.

3. Ask kids to clip the clothespins to the hanger--the "number line"--in order. Differentiate with varying numbers of clothespins. Change the range of the number line by removing larger or smaller numbers. For example, the number line could include clothespins from 0-1 or from 0-1/2. When students find equivalent fractions, they may clip them to fractions of the same value in a vertical line.

Additional Option: You could number or letter the back of the clothespins so that students could check their own work. (Label a set from A-Z, for example.)

Clothespin Fractions provide a powerful model for discussion. My ten-year-old son, an eager test subject, jumped right in to order the clothespins. His dad checked answers. I wish I'd recorded the ensuing dialogue. My husband, a guy with a ton of math smarts, tried to figure out the answers using percents. Since this is something he regularly uses at work to create documents, he felt like it was an efficient method. In contrast, I relied on common denominators. My husband helped my son to make a couple order changes but finally admitted that in one case, my son's original answer was actually correct. (Talk about making a kid's day!) We then talked about how my method was easier the merits of using percents vs. common denominators. I felt a fraction wee bit smug. 

But more importantly, we all had a fun, productive Math Talk!

Want more ideas for teaching fractions? (One of my favorite topics to teach!) Click here! :)

CCSS Standards in Grades 3-4: 

CCSS.3.NF.A.3a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

CCSS.3.NF.A.3b Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.

CCSS.4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

CCSS.4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2.

Circle Fractions & the Number Line Model

As I've mentioned, when I was a 4th grader, fractions were a big, hairy monster in my otherwise happy little mathematical world.

I'm still trying to heal the fractional parts of my 4th grader self. Over the last few years I've made progress:

• Ten + years ago: fractions made me slightly nauseous, rendering me unable to think.
• Five years ago: although no longer causing nausea and palpitations, fractions did require a rather strong antiperspirant
• Today: while deoderant still comes in handy, a little voice in my head now does a mini "wahoo" when I hear someone utter the word "fractions."

So whenever I see a clever lesson, one that helps fractions to make some visual sense, I take note. A free lesson from The Tutor House, Pizza Pie and the Number Line Freebie, helps kids to see the relationship between the circle "pizza" fractions we use so often and the fractions on a number line. Since the number line fraction model is such an integral part of the Common Core State Standards, this is a particularly valuable tool.

Credit: Clip Art of the 1/2 fraction man (above) is provided by Phillip Martin. His site has GREAT, free math clip art!