## Thursday, December 29, 2016

### Math Games for Grades 4-6 (Free Online)

I recommended this collection of math games when I was teaching fifth grade. It's a great assortment for students in 4th-6th grades.

Content includes:
• Ratios
• Multiples
• Factors
• Prime/Composite
• Multi-Digit Multiplication
• Products/Factors
If you have other games to add to the list, drop me a comment and let me know!
Ratio Blaster - In this free online game, view a ratio (example: 3 to 6) and click to shoot at the invading spaceship that shows an equivalent ratio, written as a fraction (example: 1/2).
Table Numbers - Choose a factor from 2-9, then click on one of three numbers that represents a multiple of the chosen factor.
Prime/Composite Applet - this is a great follow-up to an exploration of prime/composite numbers and reading of You Can Count on Monsters. See if you can figure out how the picture of each number relates to prime/composite.
The Amoeba Multiplication Game - practice multi-digit multiplication by splitting numbers; use partial products to solve.

MathTappers: Multiples - add this app to your mobile device to explore multiplication and division using visual models. If your student is struggling with fluency in multiplication, this is highly recommended.
Times Square - find factors as you race to get four products in a row.
Factor Dazzle- Click on the factors of target numbers set by an opponent. Use Guest Pass or register to play against students online.

Factor Game - Click on the factors of target numbers set by an opponent. Play against the computer or a friend.

## Wednesday, December 28, 2016

### Math & Literature: Time (& Related Activities!)

I'm on a holiday vacation cleaning frenzy. (Any other crazies out there?) In the process, I've made progress purging my office bookshelves, rediscovering all my kid lit/math books. It's time to revamp my Math Book List to reflect all the additions I've made in the last couple years. With the coming New Year, "TIME" seems like an appropriate place to begin. Here's the updated list for this concept. And, as always, the complete math/lit booklist can be found here.

Time  New! (12/2016)
All About Time, Jeunesse & Verdet
All in a Day, Mitsumasa Anno, et al
Bats Around the Clock, Kathi Appelt
Chimp Math, Nagda & Bickel
Clocks and More Clocks, Pat Hutchins
Cluck O'Clock, Kes Gray
Four Season Make a Year, Anne Rockwell
Henry's Important Date, Robert Quackenbush (only linked mini-version is currently in print)
How to Tell Time (older Little Golden Book)
It's About Time, Jesse Bear, Nancy White Carlstrom
Just a Minute!, Teddy Slater (Hello Math)
Maxie, Mildred Kantrowitz
My First Book of Time, Claire Llewellyn
On the Same Day in March, Marilyn Singer
Pigs on a Blanket, Amy Axelrod
Scaredy Squirrel, Melanie Watt (Review & Activity)
Telling Time, Jules Older
Telling Time with Big Mama Cat, Dan Harper
Time To..., Bruce McMillan
The Warlord's Alarm, Virginia Walton Pilegard
What Time Is It? A Book of Math Riddles, Sheila Keenan
What Time Is It Mr. Crocodile?, Judy Sierra
When This Box Is Full, Patricia Lillie

My blog also has several other activity/book entries about time:

## Tuesday, December 6, 2016

### "Presents" with Factors and Multiples!

It's time to repost this favorite from a few years ago. These little factor/multiple "presents"--and the games that follow--are great math activities to do around the holidays!

Although factors and multiples are a 4th grade focus*, they are definitely something that we fifth grade teachers like LOVE to review.

To keep my students' skills sharp during holiday break, I created factor and multiple flap books. These little "presents" require students to write the definition of "factor" and "multiple" and list 5 multiples for 2-10 and all the factors for 6,7,8,9,10,12,18, 24, 36. Blank versions are also included for teachers or students who want to use their own numbers. When these little homework assignments return from break (!), they will be added to our math notebooks.

You'll find Presenting Multiples & Factors at:

Teachers Notebook
Teachers Pay Teachers

*factors & multiples are in CCSS.Math.Content.4.OA.B.4

Looking for more factor and multiple practice over break? Below, you'll find links to some of my favorite related games:

Table Numbers - Choose a factor from 2-9, then click on one of three numbers that represents a multiple of the chosen factor.

Times Square - find factors as you race to get four products in a row. Use Guest Pass or register to play against students online.
Factor Dazzle- Click on the factors of target numbers set by an opponent. Use Guest Pass or register to play against students online.

Factor Game - Click on the factors of target numbers set by an opponent. Play against the computer or a friend.

## Thursday, September 8, 2016

### Elementary Content Specialists: Is it Time?

Over the last 10+ years, I've had the privilege of working with hundreds of K-5 teachers in math professional development. The longer I work, the more frequently a question comes to mind:

Is it time that elementary teachers specialize in subject content?

Why?

Sheer Amount of Content
New standards change and increase the amount of math and language arts standards that each grade level teacher must know. With new standards comes new curricula, hopefully of high quality (check yours on EdReports) and hopefully with plenty of supportive PD.

For some, new curricula (or good curricula!) is not purchased and teachers piece together their own. (For a recent statement on this trend, read a reflection by NCTM President, Matt Larson.) If one is to learn even one new set of content area standards--and a new, related curricula--it takes time to develop proficiency. Add in another major content area (or 2, 3, 4...) and you have a recipe for overwhelmed teachers.

Depth of Content
Over the last 10+ years, I watched many standards appear to come down a grade level (example: what was in 4th is now in 3rd.) Then it seemed to happen again. Much of what we learned when we were kids is now taught 1-2 grade levels earlier. I routinely work with 4th and 5th grade teachers to learn how to teach math content that they first encountered when they were in middle school.

Please Note: I fully believe teachers capable of learning the mathematics. (See Jo Boaler's work.) But they don't always have the TIME to learn it.

If K-5 elementary teachers specialized, they could focus, teaching one subject (or a major content subject and related subjects) twice a day. For example, a language arts specialist might team up with a math content specialist, sharing a class that rotates between two locations. Each could add related subjects like social studies or science, or another specialist could take a third area. Teachers could focus professional development time, standards, and curricula on a single subject.

Students would benefit from teachers who not only understand the content, but know how to teach it well. Teachers would be trained in developmental stages in a given content area, allowing them to deeply reflect on current student understanding and what individuals need in order to advance.

Completely self-contained classrooms and all the related advantages would disappear. However, if paired well, teachers could work together to establish common expectations and similar classroom climates. Students would still only see two teachers per day. And with today's emphasis on constant change of focus (thinking of video games and t.v....always quickly changing), perhaps it would even help to keep student attention?

What do you think? Are you or your teachers overwhelmed? How can we help teachers to learn all they must know to be successful?

## Friday, July 22, 2016

### Tears to Cheers! (Perseverance!)

If you were a fly on the wall in my house this morning, you would have heard this coming from my 10yo during math...

[sniff, sniff]

[sniff, sniff]

[sniff, sniff]

Background: At the beginning of the summer, I noticed that my son struggled to solve multi-digit subtraction problems. So, for the last several weeks, we've been adding strategies to his toolbox. He's caught on fast. Yesterday, as we discussed one strategy he grinned and said that this made sense!

Fast forward to today.

He's working on a problem. I ask him to call me over when he's ready to talk about it. When he does, my heart sinks. (More on that later!) I immediately see that he attempted to apply the strategy from yesterday. But it didn't work. Basically, he tried to make the strategy into a series of rules. He tried to follow "the rules." He forgot "the rules." And when it didn't work, he just accepted whatever answer came from the procedure. He forgot that math MAKES SENSE.

My gut reaction? I wanted to immediately jump in and show him where he went wrong. I sorta did. That was sorta terrible on my part. Luckily, it was short-lived and he went back to working on the problem on his own. He struggled. And struggled. And struggled.

[sniff, sniff]

Then he got it. Sorta.

At this point, you might say his knowledge was shaky. He did figure out the problem. He did use his strategy. But it was very unclear as to whether he really "got it."

So he continued to the next problem. Wherein my heart sank again. (Yeah, yeah. More on that later...) He used the same strategy in the same, wrong way. This time, I asked him to talk me through what he'd done on his visual model. His words made sense, but he couldn't show it on the visual model. I repeated what he'd said, but explained that I couldn't see that on his model. He looked at the model, obviously perplexed. He KNEW that it didn't match what he was saying. It was dawning on him that this DIDN'T MAKE SENSE! I asked if he could revise his model to represent what he said and told him to call me back when he was ready.

[sniff, sniff]

[sniff, sniff]

Now here, folks, is where I'd usually jump in with two never-let-my-child-suffer feet. I mean the kid is CRYING! (Or at least sniffling!) Who wants to see their kid in agony?

I wanted to intervene. I wanted to get-him-back-on-the-happy-track. Maybe ask a good (pointed!) question. Or suggest an avenue that might lead him to discover where he'd gone wrong. I wanted bunnies. Pink ponies. And rainbows.

But today, with every-ounce-of-my-being, I kept my mouth shut.

Guys, it was SO HARD!

Time passed. It felt like FOREVER. I think it must have been at least, what, TEN MINUTES! An eternity!

[sniff, sniff]

[sniff, sniff]

But then, tentatively, he calls me over. He talks me through his visual. He explains why it makes sense. And it DOES! It REALLY DOES!

So here's what I said to him: "You know what was cool today? You persevered. Do you know what persevere means? [no] It means you kept going. You stuck with it. And look what you did! You kept going until it MADE SENSE." I cheered!

Herein, the child grins. Tears falling, while grinning.

Guys, he GOT IT! And I ALMOST, with my Momma-doesn't-want-to-see-you-suffer-mentality, TOOK THAT AWAY FROM HIM!

So back to my heart sinking...

When I see a child make a mistake, my natural reaction is to cringe. It's in me. I admit it. I want to FIX IT! But we know that mistakes grow the brain. We have to let kids make mistakes. Toss, turn, and roll in their mistakes. Until they discover that MATH MAKES SENSE.

You know what would have happened if I'd intervened today: a few less tears and a whole lot less learning.

Obviously, I don't want math to hurt. Shoot, no one wants to see kids in pain. But sometimes there is a little pain in perseverance. And if we never let them persevere? Well you know what would happen then... (Eeesh.)

Our job? We must also persevere...by letting them struggle. We must allow them to bask in moments of disequilibrium. For it's in those moments, those oh-how-I-want-to-save-my-child-moments that real learning happens.

Persevere!

Update p.s.
The first week of school this child came home and related an assessment he'd just taken in math. "I used that strategy, Mom! It worked!"

## Wednesday, June 29, 2016

### Chalk, Animals, & Tile: Summertime Fun with Area & Perimeter

On my summer reading list: Jo Boaler's Mathematical Mindsets: Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching.

Yesterday, I read her challenge to teach math content using a question rather than following a procedure. (p. 78) She offers this suggestion:
"Instead of asking students to find the area of a 12 by 4 rectangle, ask them how many rectangles they can find with an area of 24."
And voila...we have a summer afternoon activity for a slightly bored child whose siblings are all at camp!

I posed the situation this way...

A farmer has pens that each contain an area of 24 square units. The farmer wants to know how many different rectangular pens he can make.

Then we got out the chalk, tile, and animals.  The first pen he built, 4 x 6, was for the cows:

I asked what other pens fit the criteria of 24 square units. He thought for a bit. "6 x 4?" We agreed that since this had the same dimensions, we wouldn't built it. He soon thought of another: 3 x 8.

He asked if this farm could have penguins. Sure, why not? The next pen took a bit more thought, but after some think time he built a 2 x 12 for the pigs.

I asked if this included all the possibilities for pens with an area of 24. He wasn't sure, so we made a list. (Ideally, he would have played around with 24 tile, exploring how many different rectangles could be made, but the farmer was getting tired.)

Although he didn't want to make the 1 x 24, he talked about how LONGGGG that one would be.

The farmer needs to buy fencing for each of the pens. One section of fence covers one side of a tile. Which pen has the cheapest fencing? Which has the most expensive?

At first he predicted that the "biggest" pen would have the most fence. (At this point, in his mind, the 4x6 pen was "biggest." After all, it did contain the cows! Later on, I asked about pen size and he was able to say that they are all the same.)

His findings:
4x6 area = 20 sections of fence
3x8 area = 22 sections of fence
2x12 area = 28 sections of fence
1x24 area = 50 sections of fence

His eyes got really big when he heard it would take 50 sections of fence. He remarked that the chunkier pens have less fence because more of the edges are in the middle. I asked if he knew another name for the "fence" or the distance around. He named it perimeter.

Thanks, Jo, for a great summertime exploration!

p.s. Try making your own farms with pens of 36, 100, or other areas!

## Tuesday, June 28, 2016

### Student Notebook Strategy Posters

This quick, easy idea is one that works well for student notebooks. When I work with students on strategies, I often create a classroom anchor chart for the wall. I like to record the name of the student who used the strategy, along with a title that clearly describes the strategy. Kids love to see their own names in print and when they're asked to name what happens in the strategy, they often delve into rich mathematical thinking and discussion to define exactly what it is that they've done.

To give students greater ownership in the process, I invite students to make their own posters to go in their math notebooks or journals. I give each child an 11" x 17" paper, folded near (but not on) the halfway mark and 3-hole punched on the left. This way, the poster can be folded and added to their math notebooks as permanent reference.

Today, we made posters for Addition Strategies. If you click on the photos, you can see that we depict and name a variety of strategies. You'll also notice that this exercise is appealing to the artists in the crowd.

## 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...

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.

## Wednesday, June 22, 2016

### 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/

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