I was recently contacted by a former colleague, Dawn, regarding what manipulatives a grade one classroom might need to have on hand to support effective learning math. It seems a friend of Dawn’s is in a classroom which really has nothing for the children to use for hands-on math learning and they were wondering what was needed.

First off the classroom needs **counters** — counters in different shapes, sizes, etc. They can be **purchased ones** (such as mini plastic teddy bears) or ones **gathered from home** (such as bread tags, but†ons, etc.). But the need to be abundant and available.

Students need a way to count efficiently, especially in tens and ones. **Egg cartons** cut down to 10 holes, **blank 10-frames** printed on paper or card stock, or commercially produced 10-frames can all be used. I even like using cookie sheets (non-aluminum) and marking them with coloured tape as a giant 10-frame for use with magnets.

**Base 10 blocks** are also great for young students. These a generally in the form of small 1 cm cubes for “ones”, sticks for the “tens”, and flats for the “100’s”. I do want to make a critical point here: **students may be engaged in a game of trading 10 cubes for a stick, or 10 sticks for a flat with every appearance of understanding the “ten-ness” of our base-10 number system. But be careful here. Student can be following your rule of trading 10 for 1 without that understanding.** They might be just as happy to trade 8 for 1 or 12 for 1. The manipulatives give a opportunity for students to develop that important base-10 understanding, but** moving blocks around correctly does not necessarily indicate that the understanding has been built in the student’s mind.**

I think a grade one classroom needs **“pop cubes” (multi-link cubes)** — those blocks about 1inch in each dimension that can be attached together. I like to store them sticks of 5. If students need a particular amount for an activity, say 18, we discuss how many sticks each student will need, and then go get them. I also use these in many quick number-sense building activities. If I have students hold up a certain number of blocks, I want them to do so to model a ten frame. If I ask for 9 blocks and a student were to hold up a single stick of 9, I, as the teacher, cannot tell from a distance if the student is holding 8, 9, 10, or 11 blocks. But if he holds up a five stick beside a four stick, I can tell at a glance that he has the correct number. Pop cubes can be used in a multitude of math activities and should be on-hand for regular use.

Another must-have in my book are **pattern blocks**. They are particularly great for patterning activities for exploring symmetry, not to mention the creativity factor! I love them!

There are a number of things that I think should be in the classroom that are “make-able” such as **dot cards, dot plates, printed ten-frames, even printed dominoes** (click for more info on these)— all useful in exploring numbers, in building number sense, and in helping students develop the skill of subtilizing. Students need to SEE the numbers in math, and these materials can help develop that “seeing” in the children.

Of course there are many other things that are fun to have in the math classroom, such as **dice, dominoes, blocks, playing cards, geoboards, plastic coins, bingo chips, square tiles, Cuisenaire rods, and two-colour counters,** to name a few. But lots of math learning can take place with some thoughtfully crafted lessons and activities and just the basics.

I hope you will focus on the math understanding with whatever materials you have at your disposal!

Mathematically yours,

Carollee

I would disagree with using base ten blocks in first grade. There is a lot of research to support this. At this age, when learning about place value, the manipulatives must be seeable and countable. Base Ten Blocks are not as countable as adults might think. Children look at the rod and see one,not ten, in most cases. I suggest using ten frames instead. The idea that a ten frame is a group of ten ones and also one ten (frame.)

Thanks for commenting. I agree that the base ten blocks are certainly not as countable as adults often think they are, thus my cautions about children exchanging them by a rule (which might just as well be for trading some other number but 10). Building the idea of “ten-ness” necessary for our base 10 system is hard work and takes time. Lots and lots of exposure with ten frame activities (and Rekenreks as another reader commented) is certainly recommended. I would not start out with those blocks early in the year, but they are another way for students to explore “ten-ness”.

I completely agree that children need lots of opportunities to work with concrete manipulatives to help them understand the abstract world of mathematics. I would also add Rekenreks (also known as MathRacks) to your list…they are my favorite.

Yes, Rekenreks are a great tool, too. Purchased ones are handy, but they can be made with beads and pipe cleaners is the classroom budget is tight.