A big part of developing a deep understanding of numbers in Kindergarten is to have many experiences thinking about how numbers are related to each other in different ways. One of the ways that we have been thinking about numbers lately is by grouping them together and learning to skip count. There are a few ways we have practiced skip counting: counting by fives, by tens and most recently by twos.
We use five and ten skip counting each day to count the days of school, and our students are adept at counting in these ways.
Counting by twos however, is not as easy as counting by fives or tens since the pattern is not as clear. To allow students to discover the pattern themselves, and therefore internalize it more thoroughly, we began investigation to develop the kindergartener’s ability to count by twos.
We started by reading Madeline, by Ludwig Bemelmans, which has many examples of the girls in the story in two straight lines. Next we practiced lining up two by two and counting how many people were each line, and how many in total. This led to a discovery that the number of people in each line matched.
From there we introduced a new tool, the math rack. A math rack includes 20 beads, two rows of ten where five beads are red and five are white. This simple pattern and design can be used in many ways to help students visualize quantities and relationships between numbers. We focused on seeing the groups of two with the number beads matching on each line – moving two beads at a time, one on each row, and counting by twos.
In addition to seeing groups of two, students also saw two equal groups, the top and bottom rows. This reminded them of their experience in two lines, and lead to us to represent “doubles” addition facts for students to think about.
Since then we have been thinking about what comes in pairs and using models to help practice counting by twos. Our most recent experiences have involved using egg cartons and trying to figure out how many eggs are in each line, with both lines matching, to equal, 2, 4, 6, 8, 10 and 12 – a dozen!
All of these experiences: counting, solving real problems, and using models help the kindergarteners develop a deep understanding of numbers and how they are related to each other. They are developing fluency with numbers, skip counting and grouping numbers, all of which are precursor skills for addition and subtraction. Recognizing these patterns and relationships will help them to solve math problems with greater understanding and speed than simply memorizing facts alone. What could be better than being fluent with numbers?!
Head Kindergarten Teacher