We have been counting in second grade all year: waiting in line, backwards and forwards, by 2s, 3s, 5s, 10s. Sometimes we start in the hundreds, other times the teens… So, why am I observing students struggle to cross decades when counting in the midst of double digit addition and subtraction?!?! For example, working on adding multi-digit numbers, I stumble upon a student heading toward the wrong answer. I listen to her explain her thinking, realizing when she counts from 19 to 20, there is a question mark in her voice and she looks up for reassurance. From 38, 39 she heads to 60 with the same inflection and eye contact. Unfortunately, she’s not the only one.
Consequently, this is a symptom of more serious issues, one of which is patterning in base ten… and conceptualizing the magnitude and difference of numbers.
Activities to Improve Counting and Number Sense
1. First, I’ve been doing an activity we call Sound of a Number for a few minutes each day. The kids love it and they are exercising an important part of their math brain. For this activity, I hide behind a cardboard study carrel with a pile of base ten blocks. Students listen hard to attempt to identify the value of the blocks I drop. We begin each lesson with a quick review. First, I drop each of the pieces: unit, ten rod and hundred flat; a student identifies each by sound and explains some of the different ways each could be made. For example, we could make a hundred flat with ten ten rods or 100 unit cubes etc. This helps to deepen the concept of base ten.
Next, I drop different quantities (while hidden behind the carrel) and students listen intently to try to name it. This feels like a game and I learn a lot about students’ thinking. For example, when I dropped 21 (two ten rods and one unit cube), a wrong answer of 23 or 25 was different than 201. Most answers are accurate though, during this quick activity.
2. Here’s a counting center I threw together that my students love! Bonus… it practically differentiates itself and gives me great information about students’ thinking.
At the center, students have three dice, white boards, markers and socks (for erasing). First, students decide on their own if they want to roll two dice to get a 2-digit starting number, or three dice to get a 3-digit starting number. I was impressed with the choices students made for themselves.
I circulated and checked students’ work as they made their number lists. Some of my strugglers needed the scafffold of hearing me ‘count on’ when they seemed stuck, and then were able to continue on their own. I asked some students to use another marker color to identify patterns or talk with a partner about patterns. This was great as students articulated patterns in the ones place throughout their lists. I challenged some fast finishers to roll a new number and count backwards by 2. I plan to keep this center going for a while and mix up what students are ‘counting by.’
Games to Improve Counting & Number Sense
These games have also helped us deepen our understanding of base ten: