Math Workshop

Themes & Holidays

My Classroom

Math Tools and Models to Support Numeracy and Math Literacy


How many of you have gotten this response when your math curriculum asks your students, "Solve this problem and show me your thinking."? If you're raising your hand and laughing... you're not alone! Even I have gotten my fair share of those answers and as cute as they are- because my word they are too cute and one of the many reasons I love the primary grades :) - what are we going to do about it?

When conferring with students in math workshop, one of my favorite questions when they are working is "pick your tool or model show me how you're using it." This requires students to use a conceptual understanding of the math skill in order for them to demonstrate whether they know how to use the tool or model. This is ultimately the mathematical literacy we are all now striving to achieve in our classrooms. It also encompass many of the CCSS Standards for Mathematical practice. 

I'm not sure about you but I am always looking for a way to spice up my math workshop games and centers! Math tools and manpulatives are an easy and effective way to support engagement and mathematical literacy. Math is a subject that is so important to foster a positive growth mindset at an early age. Over the years I've collected some fun and engaging tools that support my math instruction that I'm excited to share with you!!

Before I do, there is something I would like to share with you that I learned after recently attending a Mathematics in the City summer institute in NYC. The presenter brought to my attention something that has completely transformed the way I think about math manipulatives. Ultimately, there is a difference between math tools and math models.  A math tool is a physical object that a student can manipulate to help them solve a problem. I like to think of this as your typical math manipulative. For example, dice, calculators, pattern blocks, base ten blocks, money, etc. 

Here are some of my favorite math tools and where you will be able to purchase them!


One of my personal and kid favorites are my jumbo double dice from Lakeshore! They are a great way to differentiate your centers. I have purchased a few sets of double dice before and this is my favorite because both sets of dice are large enough for not only our tiny finger in primary land but also so that both sets of dice are large enough to see. :) You can find them here


 A calendar favorite is definitely our magnetic tens frames to build the calendar date each month. We also use the green and blue dots to make various partterns each month throughout the year. It is the perfect way to build fluency with composing numbers through 30-31. These particular colors are discontinued however, they still have them in red and blue. You can find them here.

We also have magnetic money and base ten blocks. Each day we add one penny and one "one." Their magnetic ability makes it easy to manipulate on the board during our discussions when we may need to regroup or make a different combination of coins. Plus lets be honest, anything magnetic is more fun!  You can find them here.
I also keep quite the collection of Target Dollar spot erasers so that they can be changed from season to season. At the start of the year, they may simply be used as counters to represent numbers. Then we transition to becoming fluent composing and decomposing numbers 0-20 and eventually we link this to addition with two or more addends. Tens frames and counters also make a great visual for subtraction.  


 Two math manipulatives that are always such a hit are magnetic numbers and magnetic dominoes! They grew to become so popular that they turned into indoor recess games rather than just "math centers." :) The magnetic numbers can be used at the beginning of the year to order and compare numbers when counting. Eventually we used them to make up our own addition problems to solve on the white board. This is a great center than can be easily differentiated based on the numbers given to the students or the number of digits to add (ed. double and/or triple digit addition). Its important to teach into the concept that these are a TOOL not a TOY. Ha! I won't be shy in admitting that we usually need this reminder more than a *few* times. :)  They can be purchased here.

The magnetic dominoes are my newest addition and I'm still coming up with some effective ways to use them in my classroom. If you come up with any ideas, don't hesitate to comment below! As of now we use them to compare numbers, part-part- whole addition problems as well as to build fact families! You can find these on Scholastic Reading Club and purchase them with your teaching points. :) 


Unifix cubes are a great tool for one-to-one correspondence as well as a visual aid for addition!


Foam dice in an assortment of sizes are a teacher favorite because of how quietly they roll. Ha! These pictured here can be found at Five Below. I have also purchased smaller versions at the Dollar Tree. I am currently on the hunt for dice with dry erase sides... wish me luck!


 These number cards here are a part of our tool kit from Everyday Mathematics. They are a great tool for subitizing. I have also purchased tens frames cards from Lakeshore that can be seen here. It is also easy to print pictures of tens frames on card stock, cut and make your own cards if you are looking to be savvy with your money. :)
Jenga and cup stacking is not necessarily a math tool but a great way to practice math facts.  If you are looking to see how I use these games below in math centers, please read my previous post here

I love providing students with ample opportunities to practice using manipulatives in an engaging way. While there may be times where students interact with manipulatives without a worksheet, I believe sometimes it is important to have an accountability piece. I have created a Math Games Bundle aligned to the CCSS for first grade that allows students to practice math skills with manipulatives. These are the perfect centers to use all year long! They can be found in my TPT store here


Now that you are up to date on math tools, lets transition to math models. A math model on the other hand shows structure. It demonstrates student thinking in an organized way. For example, tens frames model numbers and have a structure of ten. Math racks or rekenreks are another great math model that can be purchases with different structures based on what grade level you teach (structures of 5, 10 and 20). Number bonds and part-part whole models various number compositions. Tallies, dots, number lines and hundreds grids model number space. They are focused on the distance between numbers- which is less and which is more.   

I have created math maths to be used as reusable math models to build math literacy in the classroom. I plan to print them on card stock, laminate them and place them in pocket protectors. When I teach a specific skill, I will teach into each model as a strategy to solve and model one's thinking. Then I will add them to our math center in a place where students can access them whenever they need during math workshop. 

                      
This is the perfect mat for students to organize their base ten blocks when adding two digit numbers. It will allow them to organize and visualize the different places and their values.









Tens frames are perfect for subitizing, number recognition, combinations of ten, decomposing numbers, adding two or three addends, modeling subtraction and of course modeling numbers and their value.

Open number lines are perfect for modeling adding and subtracting single and two digit numbers, comparing numbers, skip counting and finding the distance between numbers.

Number bonds are perfect for number composition which eventually leads to addition and subtraction. They can be filled with numbers or manipulatives in order to help with one-to-one correspondence, hierarchical inclusion of a number (aka 1 and 2 fits inside 3- think of the Russian dolls :) ). This is a great tool for numeracy and that numbers have values when connected to real objets or measures





You can find these in color and black and white in my TPT store HERE

When teaching math in the primary grades, it's important that we must remember the math is not in the tool or the model. Therefore, we can not just give students a tool or model and expect they know how to use it. We must provide opportunities for students to mathematize the tools and models. This is just a big fancy word for teach into the math. Then you must provide opportunities for them to contextualize it. In other words- When is it appropraite to use this model? In what context? 

In order to do this, I spend time in the beginning of the year exploring the tools by asking questions, "what do you notice?" or "What do you see?" Then once students are using them to solve problems, I move to asking, "Did anyone do/see anything different? or "How could that help you?" I also create anchor charts for the different tools/model we can use to solve addition and subtraction problems. Eventually these questions and strategies will lead your students to be able to respond to the "show me your thinking."  



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