The units are color-coded which provides additional visual cues for children. If you look carefully at the above photo, you can see that the units of 1 are white and the units of 2 are red, units 3 are green and so on.  When using them with children, you can refer to the lengths by their unit number as well as their color.

Unlike Unifix cubes, traditional Cuisenaire ® Rods do not attach to one another (although there are sets that do attach).  This provides a different set of possibilities for children as their uses may be less obvious and may require a bit more ingenuity.

A few weeks ago, I wrote about the “trading game” that is played with the family bear counters. Well, a more developed “trading game” can be played with the rods since each of the rods has a specific value.  White is worth 1 and red is worth 2 and green is worth 3.  In order to get a green rod, children must trade 3 whites, or 1 white and 1 red.  Give this a try and tell us what you think.

After the children have had ample time to explore the materials independently, you can begin introducing simple activities that explore mathematical concepts with them.  Unifix cubes are one of those materials that children will play with independently for ages.  They provide endless possibilities for young creative minds.  That said, they are also designed to  support many mathematical concepts including counting, patterning, sequencing, grouping, sorting, etc.

One way that children love to use Unifix cubes is to see how long they can make them.  They put them together until there are none left in the basket.  They want to see if they will go from one end of the room to the other, or from one end of the rug to the other.  Even though this may seem unrelated to math, this is a great opportunity to talk about length (longer and shorter) and  quantity (a lot, a little) .

I have often seen young children use Unifix cubes as guns, but that is a discussion for another time.

Encourage the child to make sets with moveable objects.

Hmmmm.  Here Kamii says that focusing on one set of objects limits our ability to explore number with children.  If you present a group of objects to the child, i.e., a small basket of apples, and then ask, “How many apples are there?” There is one right answer and the child knows that.  Asking a child to count objects is not a good way to help them quantify objects.

Children are better served if we find ways for them to observe sets and make judgements about them.  For example, if you put 6 apples on the table and 3 oranges, and then ask the child to make observations about the 2 sets of objects, the child is presented with more options for thinking about number.  The child determines which has more, which has less, or if they are the same.

However, the above example is still not as useful as having the child make his own sets.  Ask the child to bring enough fruit so that every child in the group gets one piece.  The child then has to start at zero and use one-to-one correspondence to provide 1 fruit for every place setting.  The child has to decided when to stop, when he needs more, or if there is not enough.

Again, the teacher needs to understand the that there is a vast difference between a child putting one piece of fruit on every plate and the child knowing how many pieces of fruit are needed in relation to every plate.  It is the child’s mental construct of that relationship that supports the ability to quantify.

She goes on to criticize materials that are already grouped in sets that cannot be taken apart.  There are manipulatives that come in predetermined sizes representing 1, 5, 10, 100, etc.  However, the child only sees each of these objects as “1” even though the adult sees that the 5 unit is actually 5 ones put together.  The 10 unit is 10 ones put together.  However, if the child cannot manipulate those units on his own, they can only represent a unit of 1, regardless of their lengths.

Children can take these units rods and put them in order from shortest (unit of 1) to longest (unit of 10).  However, according to Piaget (as cited by Kamii, p. 39) children are using their spatial knowledge of creating a “stair step shape” to put them in order rather than their understandings of number.  This is observable.  They line them up and move them around until they form the shape you see above.  The logic-mathematical construct that the 2 Unit is made up of 2 individual 1 Units and the 5 Unit is made up of 5 individual 1 Units, etc., is an internal, and therefore non observable mental activity.

The way to know if this is true is to present the young child with a set like the one above and have him put 10 unit rods in order.  Then present the child with a box if individual Unifix cubes (all of which are 1 Units) and see if he can make 10 rods with lengths that differ by one cube each.  Not as easy as it looks.

Work with numbers 11-19 to gain foundations for place value.

• CCSS.Math.Content.K.NBT.A.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

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If you are not a math person, haven’t studied math in many years, or have any amount of “math fear” the words BASE TEN may be one of those things that make you sweat and tremble.  In general, I would venture to guess that many of us have heard about Base Ten, but have little to no idea what it really means.

Base Ten is the number system that we commonly use that describes the place of each number (ones, tens, hundreds, thousands, etc.).

Take a look at a number like  4,352

The 2 is in the one’s place, the 5 is in the ten’s place, the 3 is in the hundred’s place and the 4 is in the thousand’s place.  Each of those number is 10 times the value to the right of it (thus the idea of Base Ten- each place increases by a multiple of 10).

One of the common ways that teachers are currently teaching Base Ten is by introducing Base Ten Blocks like those below.

For the most part, I think these manipulatives are too sophisticated for pre-k children but they will be introduced to these in kindergarten and will probably use them quite extensively.

If I remember correctly, ones are called “bits”, tens are called “rods”, hundreds are called “flats” and thousands are called “blocks”.  Children begin to create a “rod” by putting 10 bits together, a “flat” by putting 10 rods together and so on.  There are all sorts of interesting and innovative ways teachers are incorporating these into their math teaching.

How can we support the early concepts associated with Base Ten for younger children? The best way we prepare children to understand place value is to reinforce counting, cardinality, ordinality, and one-to-one correspondence.  There are better manipulatives for younger children (Unifix cubes, and Cuisenaire Rods, for instance) that can reinforce these concepts through exploration and play.