ory correctly. Rational counting is matching each number name to an item in a group. In order for rational counting to take place the learner must master one-to-one correspondence, stable or- der, cardinality and order irrelevance. While some people may feel that one-to-one correspondence is easy, it actually takes a while for learners to grasp it. Learners need to coordinate words to physical movement and the eye along a line of items, match- ing one number word to one item until all the items are used up. Here are some activities or tools to try: The use of number lines to teach stable order, board games where you count spaces going down a path to teach one-to-one correspondence, put- ting items in different groupings to teach order irrelevance, and lastly labeling a group after counting them to teach cardinality. The math learning center has a virtual number line that you can adjust the spacing, the number sets, and many other various tools. If you have students with visual concerns, you can create tactile number lines. To get your learners up and moving, create a number line on the floor for the learners to walk on. Another great resource for online manipulatives would be: National Li- brary of Virtual Manipulatives
are sorting and then use the stamps for the sorts. Learners could choose which stamp collection they would like to sort. This app also has the capabilities of changing the background color to black which may be beneficial for learners with a visual disability. The second topic area is Number Sense , which is a key building block of learning arithmetic. Number sense connects counting to quantities, solidifies the concepts of more and less, and helps learners estimate quantities and measurements. The first math concept within number sense is numbers are used in many ways. Numbers may be categorical or nominal, referential, cardinal or ordinal. The second concept is quantity is an attri- bute of a set of objects, and we use numbers to name specific quantities. The last concept is quantity of a small collection can be perceived without counting. This concept is also known as subitizing. As a learner I can look at a group of items and know “how many” without counting the items. Providing opportuni- ties, to observe and manipulate quantities and change in quan- tities builds on the learners natural sensitivities and interest. Providing language enhances these experiences. Here are some activities or tools to try: Life-size activity, feet, would be to take painters tape and make five frames or ten frames on the floor. Have the students be the manipulatives within the frames; make sure the frame sizes are large enough if you have a wheelchair user in your classroom. You can modify this to make a frame on a table and use paper plates to be the manipulatives.
A number line on the floor for the learners to walk on.
The fourth topic is Comparing and Composing Numbers this topic may also be considered Number Operations. The math concepts within this topic area are: sets can be changed by joining items or by separating items, sets can be compared using the attribute of numerosity and ordered by more than, less than, and equal to, and a whole can be decomposed into equal or unequal parts: the parts can be composed to form the whole. Number operations are the tools that we use to find the answers to the questions like: “How many fewer?”, “How many more?”, “How many now?”, etc. When we are first teaching math, there is no need to focus on the math symbols or arithmetic. The learners need many opportunities to think through the relation- ships between how quantities work in their everyday life before they can think of using addition or subtraction. When we hur- ry our learners through memorization of rote facts, we lose the time the learner has to understand why the fact is true. We need to provide time for the learners to problem solve and multiple opportunities to make sense of the problem. Allow the learn- ers to draw, use manipulatives, or act out the problem. Experi- ences encourage explorations and appropriate talk of parts and whole in many contexts. Manipulating and grouping all kinds of objects builds foundations for parts and wholes from which all
Frame on a table and paper plates.
The National Council of Teachers of Mathematics has an Illu- minations website where the learner can do online interactive Ten Frames. Interactive Ten Frame The third topic is Counting . Even before they can count, chil- dren learn that number, or counting words are special. Experi- ence hearing others count, or name quantities provides foun- dational experiences with number words and the idea that they refer to quantities and can be ordered. The math concepts with- in counting are: counting can be used to find out “how many” in a collection and counting has rules that apply to any collection. Counting is very complex as it includes rote counting and ratio- nal counting. Rote counting is reciting the numbers from mem-
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