Counting is an essential skill for all mathematicians, but not just for the ability to know how many of something there are. Counting around the room is an activity that helps students build fluency, identify number relationships, and look for and make use of patterns and structure. This activity is easy to execute as timing is flexible and it requires no materials! To execute this activity at its simplest, have students sit or stand in a circle and count one after the other.
While the focus of counting around the room does not need to be speed, the frequent practice of it helps students become more familiar and flexible with the ways they count. Students will start to develop a fluency with numbers and feel more comfortable with what numbers come next in a sequence, as well as what numbers may come before. Furthermore, students will begin to count objects in different sized groups. For instance, if a student always counts objects (such as blocks) by 1, counting around the room by different amounts may help them become more confident in grouping objects into sets. Ideally, students will become so fluent in counting by different amounts that they will have the flexibility to choose an appropriate multiple to count by for any given situation. For instance, a student may count people in an auditorium by groups of 10 or 20, but count a dozen cupcakes by 2. Another aspect of counting around the room that helps build fluency is that different amounts of people (if a student is absent, or if you’re working with a smaller group) helps to maintain authenticity of the counting instead of letting students just memorize what number comes next.
Identifying Number Relationships
The ability to identify relationships among numbers is an integral piece of a mathematician’s success. One way to help highlight student’s developing understanding of multiples and factors is to slightly alter counting around the room and play the game buzz. The game works by choosing a specific number (say 3) and any time a student would be saying a multiple of the number 3, they say buzz instead. For example, 1, 2, BUZZ, 4, 5, BUZZ, 7, 8…and so on. You can still play by skip-counting also. For example, you could have students count by multiples of two, but “buzz” on multiples of three. 2, 4, BUZZ, 8, 10, BUZZ. This helps students gain an understanding of common multiples and least common multiple.
To show the connection between factors and multiples, you can play backwards. Start at 100 (or a different number) and have students count in reverse, still “buzzing” on factors of a certain number. Students may start to recognize that (except for the number itself) no one “buzzes” until they reach half of the given number. For example, you can start at 100 and count in reverse by ones. The first “buzz” would be at 100, then at 50, then at 25, then at 20, etc…
Making Use of Structure
To get students to begin articulating these patterns that are developed, consider asking the following questions.
- Can you make a conjecture about what number you will say before it gets to you? If so, how? If not, why not?
- What if three people were out of the circle? Does that change what number you will have? How does it change it? Does it matter which three people are removed?
- What do you notice about every 3rd (or 4th, or 5th…) person’s number? How are they related?
- When counting around the room by a larger number, why do the numbers increase much faster?
- Can you identify any relationships when we count by different numbers? For example, what do you notice when we count by 5 versus when we count by 10?
- If counting by 2, is each person counting up by 2 the same as every other person counting by 4? Why or why not?
These questions help students solidify the ideas that are fostered by counting around the room. Questions like this develop a deeper understanding of number sense, as well as proportional relationships which will be imperative for students in later years.
For more information visit http://investigations.terc.edu/library/curric-math/qa-1ed/counting_around.cfm
Elizabeth Masalsky is a 6th, 7th, and 8th grade mathematics teacher at Battery Park City School in Manhattan. She has a post-baccalaureate in mathematics from Brandeis University and her master’s in secondary math education from Bard College. Elizabeth is a Math for America Master Teacher and continues her professional development through workshops with Math for America, Metamorphosis and Math in the City.