I was recently doing a math lesson in a grade 3-4 classroom here in my district. The teacher told me the students had been working with place value and patterning of numbers on a 100 chart. For my lesson I decided to have students consider how number patterns would look if the patterns were marked on a 144 chart instead of a 100 chart. More importantly, I wanted students to be thinking about WHY the patterns would appear differently.
The students had already coloured skip-counting patterns on their 100 charts. They had looked at the “easy” patterns of counting by 2, by 5 and by 10, but they had also looked at the patterns of counting by 3, 4, 6, 9, and 11.
With that prior investigation in place, I gave students a sheet with 4 of the 144 number charts on it so they could colour those same patterns on the new configuration of numbers and compare the visual patterns to those on the 100 chart. The students were asked to notice things that were different between the two charts and to think about why the differences were there. In particular, we wanted the students to think about why the patterns looked like they did on the 144 chart.
The students were enthusiastic in their discussion about the number patterns and we were able to lead them into a discussion about base 10 and place value.
A great follow up activity is to colour the same number patterns on a calendar (regular or extended) and notice again how the patterns look different, asking, of course, WHY?