Wednesday, August 5, 2015

Making Sense of Math: Reasoning Strategies

I am hosting again for our Making Sense of Math Series and this weeks topic is 

Reasoning Strategies

This one can definitely be a tough one for our kindergarten students. Many are still just learning the concept of numbers and grasping the basic understanding of what comes next. So how do we teach them strategies that will help them with problems?

First of all

Build a DEEP understanding of Number Sense
Marilyn Burns says,
"Number sense essentially refers to a student's "fluidity and flexibility with numbers."" (Gersten & Chard, 2001)
Students with a strong number sense can "think and reason flexibly with numbers, use numbers to solve problems, spot unreasonable answers, understand how numbers can be taken apart and put together in different ways, see connections among operations, figure mentally and make reasonable estimates." (Burns)

Sounds like a lot doesn't it!

Here is a video I found that shows how great it is for students to learn about numbers in a variety of ways. 

This is just a simple glance at what we can do to show our students different ways to learn.

This video is one that I can't WAIT to try this year. What a great way to make number sense fun!

Again, these are just simple ways to help develop number sense.

As number sense grows, you will see students vocabulary and discussions about numbers improve. I love Number Talks and they are so much more meaningful when the students are providing the answers and guiding the discussion. But we have to be there with logical questioning to keep things moving and to get their mind to think about other things.

Guess what they do when they have to switch gears like that - REASON!

I love to model my reasoning for students from day one and eventually give it to them to explain their reasoning for their answers.

It all starts in kindergarten and remember reasoning can be as simple as something inductive like what number does not belong? what number does not make sense?

Wednesday, July 29, 2015

Making Sense of Math: Estimation

Last week, I completely bombed in the blogging world. That last Sunday, we threw my mom a surprise Retirement Party! She was completely shocked. After that, my niece and nephew stayed with my parents and we had fun filled days every day! It was a great week. 

Now, back on track....

This week, the focus of our discussion is Estimation.  Why is estimation important for number sense? 
Estimation is a higher level skill that makes students conceptualize and mentally manipulate numbers.

This is HARD for these little ones to understand.
Kids (not just in kindergarten) are so accustomed to finding the CORRECT answer, that they have a hard time letting go of the factual and rearranging their thoughts to the conceptual.

I will even admit that I cringe a little when working on estimation. 
At one point, I used to incorporate it daily into my calendar time like this:

This kids would have to estimate how many and give their answer. In the beginning this was good, but soon they caught on and started counting instead of guessing. So I switched methods.

We still do it as a part of calendar time, but instead, I have a jar like this (click pic for link to Post-It idea):

Our week goes like this:
 Monday - pass the jar around to have a look. What do you see? Is the jar a little full or a lot? Think about how many might be in there.

Tuesday - show the jar again and count out a small amount (if you have 20 only count 3 or 4, if you have 50 count out about 10....just so they get an idea of what a small amount looks like)

Wednesday - students write their guess on our estimation chart. I've done this two ways and I like the 2nd the best. My chart is laminated so I had them write on their jar with a dry erase marker. This was good, but you would have some who liked to copy what they saw from others. So I got the small Post It notes and had them write their answer at their seat, then go put it on their jar.

* I label their jar by number but you can also write their name on their jar. 

Thursday - we count out a few more and I ask if anyone wants to change their answer. Some might and some will keep their answer.

Friday - we reveal the answer and see who is the closest. This is a great time to talk about more and less, we use the 100's chart to see how far off their guess was. 

We do this WEEKLY and it really helps build their skills. 

You will still have yours who always guess 100, but sooner or later they get the idea. 

Estimation is not a tested skill for our district. However, this is such an important skill to help with number sense that I feel it needs to be taught in kindergarten. Tying it in to calendar time makes it simple and easy and less cringe worthy.

What are your ideas for estimation? Come see others at 

Thursday, July 23, 2015

Product Review: Conectaballs

I was recently given the opportunity to play with a new "toy". And I must say I LOVE it. The possibilities are endless!

It is a wooden puzzle toy that has a stretchy string. There are 8 wooden balls on each string and they can be twisted and connected in many different ways. 

This toy is in kick starter mode and only has 5 days left! I plan on backing it because I want MORE for my math center and possibly even a literacy station! I'll share my ideas in a moment. Here is their Kickstarter video.

So what do you think?

They come in this cute burlap bag.

Inside is an introductory pamphlet and 6 rods. They are either color or natural wood. I love the primary colors. 

Here are some shapes that I made. There is a 2d square and a 3d pyramid. 

Here is the pyramid up close.

I will admit that I had a hard time with the pyramid. I had to watch a youtube video about 5 times before I got it. But once I got it, I thought, well that was too easy. My brain just couldn't wrap around the idea. 
Here is the tutorial to different shapes:

My ideas for this awesome toy:
Math centers - making shapes or just creating. Even adding could be done..I don't know how yet, but I'm working on it.

Literacy centers - Making letters, sight words. It can be done! 

So please, click HERE and pledge to back this product. There are even rewards for the amount that you give.  I've already done it and can't wait to get the rest of mine for my classroom.

Wednesday, July 15, 2015

Making Sense of Math Series: Mental Math

It's week three of our Math Series and this week I am your hostess with the mostest. =)
My topic this week is Mental Math. 
And no, this is not the "mental" that some of us teachers become when working with our kids on math.
Mental Math is almost like fluency. It's recognizing numbers, patterns, how many and eventually computations quickly without really having to think about it. Then when they understand the meaning behind it, fluency takes place.

On the Kindergarten Common Core Math Wiki Page, they give these ideas for having successful and effective practices of Mental Math.

"In order to be effective Mental Math sessions should:
  • occur on a daily basis (5-10 minutes per day)
  • encourage ‘having a go’ on the part of all students
  • emphasize how answers were arrived at rather than only whether they are correct
  • Promote oral discussion
  • allow students to see that there are many ways to arrive at a correct answer rather than one correct way
  • build up a dense web of connections between numbers and number facts
  • emphasize active understanding and use of place value"

With the occurring on a daily basis, I would set aside time to actually do Mental Math. Possibly after Calendar Time. In the beginning focus on number recognition. Show cards with numbers written in different fonts. Like these cute ones from Lettering Delights.

You can start with just 0 - 10 and then gradually move into the teens up to 20.

Even when doing something so simple as recognizing a number, you can talk about it. 
"What told you that was 4?"
"Is there another way to write a 4?"
"Could you count on from the number 7?"

You could eventually start taking two numbers like 4 and 7 and put them together to see what students would say. Start talking about place value or adding them together. So many possibilities.

Work on counting forward from a number other than one. You can do this with small numbers like four and seven or go even higher. They need to be able to count to 100 right?

Another favorite thing that I love to do with my kiddos in SUBITIZING!!
You've heard me say it before and to me it's a big key in Mental Math.

This summer, my former TNCore Coach, Jennifer, made some great cards that I will be printing off to use with the kiddos this year. She has not published this that I know of which is why I marked it with my website. 

She has different dots on 10 frames, dot patterns, dice patterns, animals and different ways to subitize one number. 

My favorite game to play with subitizing cards is Snapshot. 
I prep the students by telling them I am going to hold up a card with dots on it (or animals, or ten frame etc). I am only going to hold it up for 5 seconds (then later to 3 and even 1). Look really hard at the dots and think about how many you see. When you have an answer, give me a thumbs up under your chin. 
Then I hold up a card for 5 seconds, I count in my head so I don't mess up their counting. Then I put the card down. I look to see who has their thumb up and then ask what does everyone see. 

Here is a video from the Teaching Channel that shows the game.

Now, with this game, yes some are using their fingers and counting and not seeing the number right away, but that's okay. To me, Mental Math is a learning process and the more we practice, the better it will be. 

After working with number recognition and quantity with subitizing, I like to move in to 1 more and 1 less. This is great with the 100's chart. 

I use something similar to this, but in the beginning I have the 10 more and less closed. Then when I feel they are getting the hang of it, I introduce them. It's so great when they can see the patterns in the 100's chart to figure out number relationships!

So there are a few Mental Math ideas for you. I'd love to hear your comments and ideas so please link up as well and follow the other teachers who are helping out with the series.

Tuesday, July 14, 2015

TPT Seller Challenge: Follow Frenzy

At the end of last week, we were asked to share our new friends that we have followed. 
I would love it if you would follow them as well.

1. Brigid from Bits of First Grade
3. Diana from My Day in K
4. Chrissy from First Grade Found Me

1. Antoinette from Shoelaces and Sugar Cookies
2. Sam from Fun with Firsties
4. Emily from Elementary Times

I really enjoyed the #tptsellerchallenge
I started following some new faces and got some new follows in return. 

Thanks for hosting from these four:

Sparkling in Second
Peppy Zesty Teacherista

Monday, July 13, 2015

Math Monday: Organizing Centers

This week I'm on the hunt for new ways to organize my math centers. I have found some pretty awesome ideas and wanted to share other posts with you. I hope you find something you like as well.

The first is from School is a Happy Place. I really like the way this one is organized. She does Daily 3 for math and these are her "Math with Someone" centers. Students have to mark off their name after they play and can't go back that week. Brilliant!

Next is one from Third Grade Thinkers. She organized her drawers by math strands with a few games in each drawer. 

I like these next two. They are pretty similar. The first is from First Grade Critter Cafe. I highly recommend visiting her page and seeing the additional pictures for organizational ideas.

The other that is similar is from Differentiated Kindergarten. She has hers organized the same way, but in her boxes are three different levels of each center so that students can play at their ability label.

This is one from Simply Skilled in 2nd. Everything in one place and it doesn't take up too much room. Students also have a sign in sheet to mark off what they have and have not played.

Denise from Sunny Days in Second Grade has her stations set up to follow the BUILD strategy. This is one I'm interested in looking at. I like her organization too.

The whole post at Tunstall's Teaching Tidbits is well worth the read. This is her updated board and she gives a lot of tips for centers and guided math time.

The last is from Sweet Seconds. It's a little busy for me, but I love the organization.
I hope some of these were helpful to you. If you have a great idea, please link up. I'd love to see how you organized your centers.

Tuesday, July 7, 2015

Making Sense of Math: Modeling Different Computing Methods

I'm excited to join my good friends again with the 2nd part of this link up series. This time Heidi, from Mrs. Samuelson's Swamp Frogs, is hosting. Click her button to see other great posts.

Modeling Different Computing Methods

This is an excerpt from

""Marilyn Burns describes students with a strong number sense in the following way: “[They] can think and reason flexibly with numbers, use numbers to solve problems, spot unreasonable answers, understand how numbers can be taken apart and put together in different wayssee connections among operations, figure mentally, and make reasonable estimates.”"

We have to help build this number sense by showing different ways that answers can be found. 

We have so many different manipulatives that we use with our students:

10 Frames
Dot Cards
Subitizing Cards
Number Lines
100's Chart

These are just a few examples that we use. We should be teaching our students how to use each of these correctly to show that we can use different ways to solve a problem.

If you've followed my blog for awhile, you know that I LOVE 

This is a great way to teach number sense and to lead in to addition and subtraction. I believe that this skill is the foundation for helping with computations.

If taught correctly, students can see how numbers go together to make other numbers. 
This is a packet that I use when beginning Decomposing numbers 1-5.

Now I am slapping myself on the wrist for not taking more pictures last year. 
That way I could show you my kiddos decomposing numbers and working problems out in small groups and on their own.

I've talked about my journals as well. The big part of our journal time is coming together afterward and having a Number Talk.
Since I didn't take a picture, I've made a replication of one of my charts from this past year so you can see what we do.

The prompt is taken from Deanna Jump's Math Journal Prompts.

The prompt is written ahead of time. The first thing we do is read the problem and highlight the MATH words. That word EACH is a biggie. We worked really hard on the meaning of that word last year.

Next, I ask every child for their answer. I only write the ones that are different. At this time, students can see that they may be wrong when they hear many of their friends say an answer different from theirs. 

Then, I ask for students to share what they did and I write or draw it out for others to see. I usually call on those who gave a correct answer. As we go through the correct answers, I am constantly asking questions to the rest of the class:
"Do you agree with what Johnny did?"
"Can you repeat what he said?"
"Did Bill have a different way, but get the same answer?"
"How are Bill and Susie's answers to the problem similar?"

I then circle the correct answer and do nothing to the wrong answers.

The friends who got the answer wrong have a chance to go back and fix their answer. I usually speak to them when others go back to their seats to put their journals away, but the best moment is when they realize it themselves. They raise their hand and said, I see what I did wrong, can I fix my answer. If they are brave enough to take the risk to tell us they were wrong, I ask them what they did wrong and how they fix it. They are proud that they figured it out for themselves and owned up to their mistake. 

Can they do this at the beginning of the year...ummm probably 5% can. That's why when we begin decomposing numbers I begin modeling ways to break down numbers. I show them different ways. As we go into numbers 0-10, I start adding in the problem solving problems and we work through them as a class with me modeling and showing how it works.

We always do the following:

Highlight the Math Words
Write Everyone's Answer (but don't write 8 sixteen times)
Draw a Picture that represents that Problem
Show the Different Ways to Solve


Next week, I will be hosting Mental Math! I hope you'll join us again.  Please visit Heidi's blog to see what other bloggers have to say about computing methods.