I hear these questions all the time — “What math tools should be available in my classroom?” “Which manipulatives purchase would give me the best bang for my buck?” “What math tools should I buy for my teachers so their students will be successful?”
My first thoughts probably go without saying:
- When the manipulatives stay on the shelf or in the closet, they don’t get used. They are not a good investment.
- If students don’t engage with the manipulatives in meaningful ways, the manipulative will not be a successful tool.
- If the teacher is ill-equipped to help the students use the manipulatives effectively, the impact is likely to be negligible.
My “tier one list” of math tools will help teachers stock their classrooms. The list identifies what I recommend be present in every elementary classroom.
Base-Ten Manipulatives as Math Tools
The most conventional version of base-ten manipulatives are Base-Ten Blocks. These pre-grouped blocks can often hinder students’ understanding of arithmetic because they undo place value understanding (see our previous journal entries). Instead, I prefer groupable manipulatives that help students develop a concrete understanding for the “nesting” nature of our base-ten system. By “nesting” I mean where one ten is concurrently 10 ones, one hundred is concurrently 10 tens and 100 ones, etc. KP Ten-Frame Tiles facilitate developing understanding of numbers within ten and building with tens for both whole numbers and decimals. Click here to check them out!
Counters as Math Tools
My preference is either clear colored disks or two-color counters. I prefer the two-color counters because they transition so nicely from whole numbers to integer operations. I’m not a huge fan of all the “cute” counters with which we stock our primary classrooms, such as teddy bear, dinosaur, or people counters. It’s far more meaningful for students to “pretend” that the simple counters are these other objects. Such “pretending” involves substitutionary thinking that can lay the groundwork for using variables as substitutes for numbers later on.
Connecting Cubes as Math Tools
These have been around for years. They can be used for counting, simple arithmetic, and non-standard units for linear and area measurement.
Inch Tiles, Inch Cubes, and CM Cubes as Math Tools
All of these are great for counting, early arithmetic, and transitioning to standard measurement units. I also use the 1” tiles for introducing the area model for early multiplication.
You’ll want to be sure your students have access to rulers, balance scales, and liquid volume pouring containers. Of course, using non-standard units is a must prior to introducing students to standard units and the tools that measure them.
Pattern blocks are incredibly useful from kindergarten through middle school. They can be used meaningfully for geometry, algebraic thinking, whole number work, or fraction concepts,
Proportional Coin Cards
It’s common for us to think of plastic (or real) coins as math manipulatives. However, there is nothing conceptual about coins that helps students see the proportional relationships among their values. Therefore, KP Mathematics has created a set of proportional coin cards, based on ten frames.
These coin cards help students develop an understanding of these relationships. Download a free set from our website by clicking here.
Of course, there are many, many other things out there. My “tier two list” includes things like geometric solids, unmarked fraction bars, Cuisenaire rods, and attribute blocks. However, most of the items on my “tier two list” can easily be reproduced with paper, scissors, and tape.
Now I’m wondering what’s at the top of your manipulatives list. How do you stock your math tools in your classroom? Please let us know by responding in the comments box below.
We look forward to continuing the conversation!