This page is a stub for educational material on counting with a target audience of K-8 (age 5-13).
Counting and the Organization of the number system
Making connections between and number names and the concept of quantity. This can be taught by tagging or touching an item while saying the number word it goes with, for example, saying the word "One" while touching a singular item, let's say a cube, next saying "two" while touching two cubes. By changing the items they are counting with, the student will gain understanding that it is not the item they are touching with the name "one" but the amount of items they are touching, and it is the concept of "one" that they are naming.
Unitizing is the ability to think about the exact number in a group of things while also thinking about how many groups of things there are simultaneously. This is best exemplified when counting groups of things, such as, a group of ten cubes. Depending on how the student is able to arrive at the total number, they will either be adding, multiplying or dividing. The example below is a potential dialogue between a teacher and student.
- "Sam has one group of ten cubes. How many cubes does Sam have?" (10 cubes) - in this example, if the student tags each cube as he/she counts this is adding (1 + 1 + 1 + 1 and so on) if the student is able to conceptualize that one group of ten or (1 x 10) they are multiplying.
- "Now Sam has two groups of ten cubes. Now how many cubes does Sam have? (20 cubes) - similarly to above, if the student tags each cubes as he/she counts this is adding, if they can conceptualize that 2 groups of ten or (2 x 10) to arrive at the answer, and are able to skip count from ten to twenty, they are multiplying.
- "If Sam has 30 cubes, each in groups of ten. How many groups does Sam have?" - in this example, if the student begins by grouping the loose cubes into groups of then and then counts the number of groups, they are using adding to attain the answer. If they student is able to conceptualize that thirty cubes could be grouped into three equal groups, they are dividing.