Number Sense and 10
Nov 18, 2021
By Brenna Watson, Lower School Teacher
It’s not uncommon that a special education teacher is led to the profession because of their own struggles in school. For me, it was math. I remember feeling so ostracized when my entire class grasped a concept that made no sense to me. To this day, my parents still talk about the stress and tears induced by math homework most nights. Ironically, math is now my favorite subject to teach. I’m very thankful for the shift in math instruction that’s been unfolding throughout my career.
One of my favorite “best practices” is fostering a solid sense of ten. Students who develop “ten-ness” are more successful with place value and mental computations. Math, even with large numbers, is simply easier if ten can be used flexibly. My students are well aware of my favorite number within the first few days of school. We do big celebrations when I see ten being used for efficient computations or to explain math thinking.
There are two building blocks to conceptualizing ten. The first is subitizing, or the ability to see a number without counting. We first foster this skill with dice patterns and 10-frames, then progress the skill to irregular dot patterns. The students should start to recognize quantities that are shown in different ways without counting. For example, in an irregular pattern, a student might see a group of five and a group of three and know that it’s eight without counting.
The second building block is mental composition (bringing together) and decomposition (breaking apart) of numbers. I recently had students compute 48+7 mentally and without counting. The hope was that they decomposed the 7 into 2 and 5 and turn the problem into 50+5 in order to subitize to add. I had one student think of it differently: they knew that 8+7=15 and used that to add 40+15. In both scenarios, the students with a strong sense of ten could subitize and decompose successfully. My relationship with math would be significantly more positive if I would have been taught with the best practices we know today. Because of this, my students are developing a more healthy and optimistic relationship with math.
If you’re interested in activities that foster number sense and ten-ness, a quick Google search will bring up many resources. Here are some that I find helpful:
What is Subitizing and Why Teach It by The Moffatt Girls
Quantity Cards by I See Maths
Greg Tang Games (Greg Tang’s resources are a personal favorite)