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Sunday, January 15, 2012

Power of Math Manipulatives

Practicing subtracting with regrouping
A couple of my students were having difficulty mastering subtraction with regrouping (a skill they have been practicing since the younger grades).  It was clear they did not understand WHEN they should be regrouping and WHY they were doing so. The concept was too abstract and I knew I needed to make it more concrete.

Grabbing my bins of base ten blocks, I sat down and started using them to instruct and SHOW the meaning of subtraction.  Reviewing the idea of "trading" the tens for ones and hundreds for tens was the first step.  I then gave the students a number to 'build' with the base ten models.  From there we came up with a number to subtract. I modeled how we would use the blocks.  It was then the students turn to use the blocks to subtract (they were NOT writing yet, but I was recording each step on a white board for them to see.)  In this way, we continued through many, many problems until the kids were comfortable with the idea of subtracting and regrouping with just the manipulatives.

Eventually, I heard the words I had hoped would come,"OHhhh, I GET IT!" The math tools had worked - they students were able to make that connection between the concrete and abstract! The students were now ready to move onto the next step of using the manipulatives and recording the steps on their own to just using the algorithm. 

Base Ten Blocks, Pattern Blocks, Money, and Square Tiles are just some of the math manipulatives that are helpful to use in classrooms to help children explore the sometimes abstract  world of math.  

For teachers who don't have these types of tools available there are many Virtual Manipulatives available on line.  The following are some of those sites that help bring abstract concepts come to life.

NLVM: National Library of Virtual Manipulatives.  Manipulatives for use with PreK - Grade 12 students in the areas of Numbers and Operations, Algebra, Geometry, Measurement & Data Analysis.

Math Playground: Contains manipulatives for fractions, Algebra, angles, percents and more.

Teacher LED: A site to use with an Interactive Whiteboard to help with mathematical understanding.  (not just virtual manipulatives)

Shodor Interactivate: A site with lessons, manipulatives and activities.

How to Make the Most of Math Manipulatives: An article in Scholastic by reknowned Math Educator, Marilyn Burns with other helpful links.

Manipulating Math: Concrete Vs. Abstract:  Blog post in Teach Hub by the author of Thinking Outside the Box Blog

The Use of Manipulatives in  Math Instruction: An article in LDOnline by Louise Spear Swerling which discusses the pros and cons of using these tools.

Learning Mathematics with Virtual Manipulatives: by CITEd (Center for Implementing Technology in Education) includes an article and resources.

Subtraction with NLVM site
I have witnessed first hand the power of using math manipulatives.  When students finally grasp the meaning of those concepts that might otherwise remain abstract for years it is proof to me that those tools have a valued place in any math curriculum.

(Managing these tools can be challenging  and I find that sometimes I do not use these tools because they can be cumbersome and difficult to distribute.  I welcome your ideas on best practices with the storage and distribution. Feel free to leave your ideas in the comment section below. Also, please let me know of your success or concerns with using different math tools. 


  1. Where were you while I was in school. I had big trouble with telling time and math.

  2. Maybe I should have used a question mark after my first comment.

  3. Some tips from a 2nd grade teacher: One idea for managing manipluatives is to have ziploc baggies pre-assembled for each student. This works well with base ten blocks, specially those tiny bits! Toss all the baggies in a tub or basket for easy distribution. I have also used small plastic trays (recycled from an old science kit) to pass out bigger manipulatives to individuals or smaller manipulatives to a group of students at a table. I used these trays for connecting cubes, and always laid them out on the tray in sticks of ten. Stack the trays up for the next day. Have a class job "Materials (or Manipulatives) Manager", that student can help distribute and collect. Hope these tips help!

  4. @Anonymous - Thank you. I wish they had used manipulatives when I was in school. They did have access to cuisenaire rods as they passed them out to play with during indoor recess!

    @Terri - Thanks for the suggestions. I have seen that people are successful with baggies but I have never taken the time to organize that way. Perhaps I will try it. Also, LOVE the idea of having a class job: Materials Manager! I know the kids would be great at it and take it seriously! Thanks for sharing.

  5. Hi Nancy. I agree with Anonymous! So nice to have a teacher that can come up with alternative ideas and methods when they see someone struggling. Nice read!

  6. @ Carol Ann - Thank you for the kind words.

  7. Hi Nancy,

    I too used ziplock bags that were ready to hand out to kiddos. For bulkier manipulatives, I had storage tubs. For unifix cubes, I had a crate of them, and I cut the gallon jug of milk to make a scooper to scoop out bulks of them onto their tables. The kids then just shared as needed. When it was time to clean up, they found creative ways to return them all (using scoops made from hoodies, etc.)

    I'd have one student from each group go get a set for the group. I always made sure we talked about how they looked when we got them, and how having the set ready for us helps us manage our learning time. We made sure we talked about how we'd clean up and put things back the way we found it. I never had a problem with it because the kids respected that and wanted the responsibility of cleaning up so we'd be ready to learn the next time.


  8. Hi Tracy,
    Thanks for your ideas. It seems that the consensus is to use ziploc baggies. The milk jug scoop is a great idea for pattern blocks and bulkier manipulatives. I think the kids would love helping with that too.
    I need to get beyond the management piece and really focus on finding better ways to incorporate them into my lessons on a regular basis.
    In the past I have used fraction tiles to help with fractions but I think I'd like to try using the pattern blocks instead...or maybe both.
    If you know of any good resources on the topic, please pass that information along. I think the kids really learn so much more through the use of these 'tools'.
    Thanks for taking the time to comment.

  9. Hi Nancy,

    I loved teaching math. In fact, when I had my own class, I taught it twice a day. During some years, we'd group for math, but I still taught my homeroom an extra math time. During that extra time, or the regular lesson, I thrived on the hands-on.

    If my kiddos had prior knowledge for computation, then I'd give them the manipulatives and ask they prove it or show it a different way. This was my formative assessment -- my proof that they understood how it worked and why.

    Here's an example of how I taught math. Note, this wasn't my class, but rather it was Shauna Hamman's class and we were team teaching for a lesson.

    I hope that helps.

    Kind regards,

  10. Hi Tracy,
    I loved that lesson you presented to the kids. It was great how the students learned two ways to show how many degrees in an angle. They really had to have a good understanding of the different types of angles. Using those tools (and the mirrors) really helped solidify the concept. Thanks for sharing.

  11. Just practicing finding the comment box and writing a comment.

  12. Tracy, I found that when children used manipulatives they grasped math concepts far quicker and at a much deeper level. If you would like a free copy of my cuisenaire rods software app please visit My 5 year old grandson and I love using them together. He has already saved an art galleries worth of his creations!


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