Concrete Number Lines Teach The Value of Numbers

During one of my recent 20 minutes of math play sessions with my 5 year old daughter, we played around with a number line.  A number line is a really abstract thing, and without something to connect it to, it is nearly impossible for a young learner to understand. So we built this fun thing:

IMG_4775The conversation afterward was awesome! She could see that the more legos we had, the longer the line got, which meant we could talk about the value of the numbers.

That got me thinking that maybe we could build one that didn’t use similar sized objects for a number line, to help her understand that a number’s value will still be the same even if the object is a different size. That was when we came up with this one:


All of this building led to talk about sizes of things, grouping things, ordering and reordering, the value of numbers and so much more.  It was a ton of fun to make both with the number representations and actual concrete objects!


The Half Game: Teaching Division Concepts Early

I wish I had more time to post about my 20 minutes of math play per day quest. If I had the time I would post what we’ve been doing each day, mostly so that I don’t forget what I’ve done!

Anyway, here is another one that happened kind of informally. The other day, my 5 year old daughter was staring at our window in the kitchen.

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She looked at me and said, “Mama, what is half of 12?”

Always in awe of her thought process, I answered, “Six!”

She immediately shouted, “You’re right!”

When I asked her how she knew this, she pointed at the window and said that there were six squares in the top half.  How she saw this when I only see a window, I’ll never know. Tiny minds are so fascinating!

So I pulled out some playing cards and asked her to figure out half of the pile I gave her. We started small.

Teaching division at a young age.

This one was way too easy for her. So I gave her a bigger pile.  Suddenly, once the pile was bigger, she was all mixed up about how to split it up. I gave her two cups, and told her to give the same to both of the cups.

Teaching division concepts early

Her little mind started turning and this is what she ended up with in the end!

Teaching Division Concepts Early

At this point we counted both sides to be sure they were the same.  Then I showed her how to skip count, so that we could use that shortcut next time.

Math play with a deck of cards is totally endless! We’ve been trying out all sorts of different things like:

  • sorting by number and counting them
  • sorting by color and counting them
  • sorting by shape and counting them
  • putting two cards together to find the total number of shapes
  • playing war to learn about greater numbers

I forget the power of playing games sometimes, and how it can help with number sense so much. I want to think of ways I can extend this to my third graders to help them with division concepts. We started division this week and it feels like a slap in the face to many of them. I plan to share some real life division with them before even showing any symbols and numbers.

Do you have any card games you play in class? I would love to hear them!

Here are some more awesome math teachers you can connect with to learn more about real life math:

Real Life Math

A monthly REAL WORLD math blog link-up hosted by 4mulaFunFourth Grade StudioTeaching to Inspire in 5th, and MissMathDork.

Measurement and Data for Early Learners

Five year old math is SUCH fun math. My daughter and I have been doing our 20 minutes of math every day since the start of the new year.

Our latest math play fun began with counting pillows in our living room. (We have an obscene amount due to a botched couch delivery-they threw in an extra shipment of free pillows!) I quickly realized that we could sort and classify each pillow by it’s color.

That led to this little gem, which we whipped up pretty quickly with a piece of paper, some dot stickers and a marker.  Each dot stood for one pillow, and we sorted them and graphed them by color.

Math Play - Graphing for Early Learners


This really took the idea of counting up a few notches. Not only could we find out how many pillows we have total, but we could also find out our most common color, and our least common color(s). This could be done with all sorts of things in our house, and as we become more advanced we can practice some adding strategies.

Have you done any early measurement and data graphing at home? Please feel free to share!

Give the Dog a Bone: FREE Number Sense Game Online

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Give the Dog a Bone is a great little game for early learners (or for those students who struggle with number sense), encouraging them to think about patterns to find numbers on a blank number line.  In the game you need to find 10 numbers on a blank 100 chart in 1 minute. It is pretty fun and addicting!

What I like best is that the added time pressure encourages them to think about patterning, rather than simply counting one square at a time. For example, in the situation below they might count by tens to get to sixty one, rather than count 61 squares.  To get all ten bones in a minute, they’ll need to think this way!

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This game could be used as a link from school to home, as an activity in the computer lab or with small groups!

Bump and Wild to Three in a Row: A Math Play Activity

I have to say that social media has really opened me up to be a better parent and teacher. The amount of things I see on a daily basis make me a better thinker and person. I’ve been on a mission to do 20 minutes of math play with my daughter, and was inspired by these posts by Pre-K Pages and Scott’s Brick by Brick.

The ziploc quilt is extremely easy to make and the building of this game was an entire 20 minutes of math problem solving for one day alone! We made our quilt out of stuff that we already had around the house:

  • colorful duct tape
  • ziploc bags
  • paper
  • masking tape
  • giant duplo blocks

All we had to do was make a simple array. While we were making it we talked about skip counting by three. I made mine with 12 ziplock bags and made a “quilt” by laying them onto the sticky side of the duct tape. Then we covered the sticky underside with masking tape so it wouldn’t stick to the floor.

Math Game

The object of the game? Simply get three of your game pieces in a row horizontally, vertically or diagonally.

For our first game I made a deck of cards for the draw pile of three types to be played in the following way:

  1. Numbers 1-12 in standard form: Find a matching representation of that number on the board.  (If your number is already taken due to a bump or wild card, you lose your turn.)
  2. Bump card: bump someone’s piece off and replace it with your own.
  3. Wild card: place your game piece on any open space.

Math Game

Then I made 12 cards to slip into the ziplock bags for the game board.  I mixed the representations up and made tally marks, word form and dots to make the standard form cards. I wanted to make five and ten frames but I wasn’t sure I could draw them evenly enough (and our printer is out of ink!). I’ll probably try that next time.

Playing with three players made each game both quick and fun.  We were totally addicted.  I think the three of us played for an hour straight. The game wasn’t purely about matching, but included thinking about where to put a wild piece, as well as which piece would be the best to bump. My five year old began picking up strategies and we were amazed at her thinking!

The possibilities are endless for what can go in the quilt!

I think I am going to see if we can make these in my third grade classroom for the kindergarten mentors we work with!  Making them will mean that they’ll need to use their multiplication skills to make the quilt.

This is a great after school play activity!

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Even and Odd: The Importance of Conceptual Understanding

I can’t tell you how many times I learn through the eyes of my five year old.  She asks amazing questions, especially when it comes to numbers.  While we were doing some daily math play today, I thought about introducing her to the concept of even and odd numbers.  I was taught even and odd by being told to memorize the numbers: 2,4,6,8.  As a tiny child I don’t think I truly understood why a number was even vs. odd.

So we built the numbers 1-10 (in hindsight I wish I had included zero) with unifix cubes. Then I told her to put them in pairs. We put the pairs together, and lined everything up. During this process she was uncomfortable whenever one was left over, and wanted to pair it up with one from another number set! This is how it looked once we had it all situated.

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Then I asked her what she noticed.

“There is ‘ones’ all by itself!”

We pointed out which numbers had an “odd one out” as I put it. That was when I introduced the words odd and even.  I think it is essential to introduce the vocabulary to kids after they have explored the concept, so that they have a way to name what it is they are seeing.

She then noticed that every other number was odd.  So we looked at and extended the pattern: odd, even, odd, even….until we got to the 10. I then asked her what she thought 11 would be, odd or even?  She shouted out “odd!” without even thinking about it.

I still have a few third graders that are struggling with this concept (can you even believe that?). I am going to try to see if this could help them understand this very basic concept.


Math Play: 20 Minutes a Day

I really think it is amazing that as a society we have really been pushing new parents to read to their children for 20 minutes a day.  We all know that this helps a child in a myriad of ways to become better speakers, writers and readers.  I am blessed with a five year old that learned to read completely on her own at age 4, and I believe that reading to her every day of her life has been the reason this happened.  The cool thing was, we didn’t have to teach her to read, it just happened on it’s own (trust me, we were shocked and humbled by this development!).  Whether that is the norm or not, it got me thinking about math.

Why don’t we as a society promote 20 minutes of math play each day, the same way we promote reading? Imagine if children could authentically develop number sense from an early age by counting or playing with numbers DAILY. I bet we wouldn’t see as many students struggling with some of the simplest concepts like even vs. odd. I still have a few third graders who aren’t sure of the difference!

This is my daughter “building” numbers today. All we needed was a little paper and some unifix cubes which you can pick up at any educator supply store. I want her to see that numbers aren’t really all that abstract.  We’ll be adding many different number representations to our papers each day.

Building Numbers

I plan to add math play to my 5 year old’s day, the same way we read each day.  If you already do something like this, I hope you can share some of your activities with me!

Last, this also gets me thinking about my third graders. Is there a way that I can have math play be homework? Hmmm….I’m on it!