Tuesday, April 14, 2015

Makin' It Math Mid-Month Linky -- April

Welcome to this month's Makin' It Math mid-month linky!  If you are a blogger, feel free to join us by adding your link at the end of this post.  Check out the details here!

This month, I put together two sets of task cards for measurement and geometry.  I also updated my money task cards to include QR Codes. AND since I usually include at least one freebie in my make-it posts, I will be giving away three sets! If your name is drawn, you pick the set you like best!  Just enter the rafflecopter to win...




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We hope you will share your made-its by linking up below!

All the best--

Monday, April 6, 2015

Unifix Cubes: The Elevation of a Common Math Tool

When updating my hands-one algebra product over spring break, I was reminded of a great tip for organizing a common math tool many of us use.  Several summers ago, Courtney and I attended and in-district 3-day workshop with Angela Andrews.  Angela is an expert in early math and offered an abundance of useful information and strategies. 

Just want to share a great tip Angela gave us for organizing a math tool many of us use with students, Unifix cubes (or linking cubes).  Angela suggested not only putting Unifix cubes in groups of ten (which many of us already do), but she also suggested using two different colors to show groups of five (see picture below).  The reason for this is quite simple, yet powerful.  

As students progress in their understanding of number, the tools must progress with them.  When Unifix cubes are separated and stored in a tub all mixed together, students who want to use them for modeling must count them one-by-one.  For example, a second grader may choose Unifix cubes to represent a "situation", but when he/she has to count them individually he/she is reverting back to an earlier stage of development. By organizing cubes in groups of five (two different colors) to make up ten, that second grade student can easily see five and add on. In this way, when he/she wants to show a value such as 12, using Unifix cubes/linking cubes, the use of this tool becomes much more appropriate and efficient.  

Organize cubes into groups of ten with two different colors (5 of one and 5 of another).  This will eliminate one-to-one counting of cubes that may not be desired and requires students to use their understanding of 5 and 10.

Here's a great missing addend activity that was shared in the same workshop! Students work in partners.  All that is needed is a group of ten Unifix cubes organized as shown above.  One partner holds the ten Unifix cubes behind his/her back.  Then he/she makes a break and shows his/her partner one group while keeping the other group behind his/her back.  The other partner must then tell how many cubes are hidden. He/she must also "prove" it by counting up or back or by stating what he/she knows. 

A student might respond, "I see six, and I know there are ten altogether.  I need four more to make ten with six, so four are hiding."

I hope you find these suggestions useful!
Here is the product that I was updating when  reminded of this organizational system I use with my Unifix cubes.  This early algebra hands-on math center requires modeling of known addends to help figure out the missing addend/s.  Unifix cubes, or ten frames, can be used as show below. 

Like what you see?  Enter to win one of two copies of Out of this World Algebra for your students!

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AND don't forget--If you haven't already checked out my book review of Fluency Through Flexibility and entered the giveaway of the materials shown below, click on the pic to do so!


Good luck, and all the best for a wonderful week--

Wednesday, April 1, 2015

Book Review: Fluency Through Flexibility: How to Build Number Sense (Numbers 0-20)

Good day from sunny Illinois! What wonderful weather we are having here for our spring break!

Today I come to you with a book review of an outstanding teacher resource written by one of my fellow math bloggers, Christina Tondevold, The Recovering Traditionalist.  Her new book is titled, Fluency Through Flexibility: How to Build Number Sense (Numbers 0-20), and it is perfect for new teachers and seasoned teachers alike.

Thank you to Christina for sending me a copy of her book and some wonderful materials to accompany the activities included.  Most of all, thanks to Christina for making such a positive contribution to our profession.

In reading the introduction, I especially appreciated the background Christina provides for what fluency means when it comes to students learning addition facts.  Fluency involves:

  • Efficiency - a speedy way to get the answer
  • Accuracy - getting the right answer
  • Flexibility - having another way to approach a problem when it can't be figured out

Christina goes on to stress the importance of flexibility.  If students are not yet able to recall a fact, they need to use what they do know to help make the problem easier.  This is something my second graders are able to do, yet it needs to be instilled in children through much exploration. An example of flexibility would be a student who cannot yet recall the sum of 8 + 9 but can use his/her current knowledge of number to create relationships between numbers.  He/she might choose to:

  • use doubles, "I know 8 + 8. That's 16.  9 is just one more than 8, so 8 + 9 is 17."
  • use tens, "Well, one more than 9 is ten, so I can move one from 8 to make a ten.  Then 10 + 7 is 17."
  • create landmark/benchmark or "friendly" addends, "I can think 8 + 10, and that's 18.  18 - 1 = 17."

When a student has flexibility, he/she is able to think in this way.  Without flexibility, Christina stresses, students will "revert back to counting on fingers."

Number sense is SO much more than simply memorizing basic facts.  This book will help you provide valuable experience for your students to explore numbers and discover relationships that lie within.  Activities are organized into four areas, and these areas coincide with what students who have good number sense understand.

They understand:
  • Spacial relationships - recognizing how many without counting (subitizing)
  • One and two more, one and two less - knowing which numbers are one and two less or more than a given number
  • Benchmark of 5 and 10 - knowing how numbers relate to 5 and 10
  • Part-Part-Whole - seeing numbers as being made up of two or more parts

Christina provides a detailed description of each of the above areas in her introduction, and goes on to give suggestions for using the activities included.

Various tools are also used with the activities and some can be downloaded or purchased on Christina's website, Mathematically Minded. Tools include subitizing cards, number paths, and the MathRack (rekenrek). It would be well worth your time to investigate Christina's rationale for using a number path vs. a number line for kindergarten and first grade students.  

What do I like about this book?
  • Christina's introduction that provides sound rationale for using the activities included
  • the variety of activities for use with students at different stages of development
  • suggestion for what to "Look For" when observing students work within an activity
  • suggestions for "Reuse" depending on how students are developing
  • the adaptations/extensions that can be made to activities based on student need 

How will I use this book? As a teacher who uses guided math, I can pull various activities from this book to use in small guided groups based on need, and the activities can also be done independently during station work.  I did not have Christina's book at the beginning of the year, so it will be a wonderful added resource as I help my new second graders develop fluency through flexibility.

What have I tried?  My second graders explored one of the part-part-whole activities, Number Search (Numbers 11 to 20).  I presented the activity one way with two game boards (one for each player) in plastic sleeves using dry erase markers.  Students wrote a sum in the center of the game board and each took turns circling addends to add to the sum while saying the combination aloud, "10 plus 3 equals 13."  The player with the most combinations circled was the winner.  Natural questions arose.  "Can we overlap?", "What about the other person who can see what you just circled?", "If the sum is 19, you can't hardly circle anything.", etc.  Their questions and suggestions led to some variations in game play that they created.  They tried using one game board with two colors of markers, and they definitely wanted to overlap.  Sums that yielded fewer combinations became games where three addends could be circled. The kids loved it! Number Search is also an activity I will be sending with the kids for at-home practice along with their math tool bags.

Do you like what you've read? Well, you can enter to win a copy of Fluency Through Flexibility, a MathRack, and Savvy Subitizing Cards--all donated by the author!  How do you earn the most entries into this giveaway? Share your thoughts about Christina's new book in a comment--What sparked your interest?, What do you like?, How could you use it?, etc.  Good luck!

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Keep in touch with Christina, her publications/materials, and professional development opportunities on her blog and website:

The Recovering Traditionalist
Mathematically Minded

Also--don't miss Christina's free webinar this coming Wednesday, April 8th.  Click here to register!

AND, in the spirit of giving, the Easter Bunny has arrived early with a FREEBIE for you! Feel free to download this fun jellybean math activity Courtney created to use with her kids this year--Jellybean Taste-Off: Jellybean Math Fun!  Simply click the pic to download!


Happy Easter to you and yours!