I visited the grade three class at Garden City Elementary twice in February, focusing on ways to teach mathematics through the big ideas in BC’s new curriculum.
Teacher Stella Santiago asked that we do some work around patterning together and we began with a class discussion around the question: What makes a pattern a pattern? The students shared their developing ideas about patterns, which included many examples of patterns, and then the students were provided with a choice of materials with which to investigate different types of pattens with. We asked them to push their thinking about what patterns were and to investigate different types of patterns and what makes them patterns.
The students mostly began with repeating patterns but used different formats for their patterns such as going around the circumference of a table instead of just in a straight line. Blank grids were provided for students to investigate and some students engaged with those.
Students also explored using different shape frameworks to create patterns with.
And they played with seeing patterns in three-dimensions, from different perspectives.
About half an hour in to the work with materials, we asked the students to pause and walk around and notice what other students were doing – to be inspired, to capture an idea, to make connections.
As the students created their patterns, I recorded the questions I was asking them during their investigations, meant to provoke their thinking about what makes a pattern a pattern.
It was these questions that I came back to in the end as students shared their findings about patterns. We were able to come to consensus as a group that a pattern is predictable and generalizable, that there is regularity in it. Big words for a big mathematical idea.
On my next visit to the class we connected the idea of patterns to the students’ current study of multiplication. We began with a number talk, using a grid to support students in visualizing the patterns in multiplication. We played with the idea of decomposing numbers to support us in calculating multiplication questions. After our number talk, the students were provided a choice of materials and tools with which to investigate the focus question: Where do patterns live in multiplication?
One of the tools provided to students was a 100 chart and students used gems to cover multiples of different numbers on the chart to investigate what visual patterns might emerge.
Some students started with their understanding of multiplication – equal groupings of objects and then used the materials to create different visual patterns with these groupings.
Some students connected the idea of growing patterns with multiplication and used different materials to represent this connection.
The students were very curious about the geoboards, as they are not a regular item in their classroom. One student wasn’t sure where to start with the geoboard and I showed him how to stretch a band to make a square. He made another square and then I added a third. By then, he was making his own connections and began an investigation of square numbers.
Another student used the geoboard to create arrays. She played with the idea of halving and doubling the arrays, including using diagonals to create triangles.
A group of three students chose to use the magnetic grids to play with patterns and multiplication, using alternating colour patterns.
The students again had an opportunity to walk around the class and see what other students were doing to investigate patterns and multiplication and then go back to their own materials, adding new ideas if inspired to do so.
We met together as a class in a “math congress” to report out our findings and make connections between what we had found out about patterns and multiplication. Students used the terms growing and increasing but identified the regular-ness of the patterns involved in multiplication. Some students focused more on the spatial relationship of arrays and how those change as factors increase or decrease.
As the students continue to study multiplication and division, I am looking forward to hearing what relationships and patterns they find.