While visiting schools in our Northwest region, I am constantly reminded that students of all ages have intuitive number sense and understand how to use mathematics to solve real-world problems.
On a recent visit to an elementary school, I observed a school-wide fun run. They giggled and cheered as they circled the playground. Parents marked each lap on the back of students’ T-shirts on a circle with 36 sections. Additional laps were tallied above the circle. All students were proud of the number of laps recorded on their shirts. As the teacher and I walked her third graders back to class, we decided to ask the students to estimate how many total laps their class had run.
Back in class, students started by writing their totals on mini-white boards. Students were then given time to come up with a prediction of how many laps the entire class had run. Predictions ranged from 254 to 1,000,000! One student added, “I am sure the number is at least 54 because I ran 39, so our class laps have to be more!” I love third graders!
Next, students were asked to think of a strategy they could use to determine the entire number of laps their class had run and to share that strategy with a partner. The teacher and I traveled around the room listening to their ideas, prompting students to question their partners for details if needed. Those ideas were then shared with the whole class taking the time to listen, think and discuss the strategies presented. The range of strategies (see below) were amazing and reflected the sophisticated and developing thinking of third graders.They worked hard to precisely describe their strategy, to listen to their classmates and to reflect on understanding each strategy discussed. We wrapped up class by capturing their strategies on the white board and decided that the students’ next step would be to choose one of the strategies discussed to solve the problem of how many laps the class ran.
Some of the strategies that the third graders shared:
- Make a number line and start on the number of laps I ran (39) and add up from there.
- Line up all the students and their white boards along the wall in the classroom and make a long number sentence with the number of laps each student ran. Like 49 + 39 + 51….
- My idea was similar but I think you should add two numbers at a time and take the sums and then add them together.
- You could group each number in columns of tens and ones and add all the tens and then all the ones.
- You could add by 20’s.
- You could make groups of 100’s.
- I know that everyone in the class ran at least 30 laps so you could add all the group of thirty’s that each student ran and then the extra tens and ones.
- My idea is like that but we know everyone ran at least 36 laps so I think you could add all the thirty-six’s together and then the leftover tens and ones.
When we ask students questions around mathematics that relate to real world contexts, students are naturally engaged. The context gives students a solid connection and enables them to think flexibly about numbers. This spontaneous lesson reminded me that there is real world mathematics everywhere. I look forward to visiting more classrooms and participating in real-world math problems throughout the Northwest!