This counting collections activity engages students in finding the number of squares of any size on a chessboard.
When a count forms a pattern, students can be encouraged to generalise. A generalised pattern supports students to reason algebraically (develop a rule) for the further counts in the pattern.
Counting collections promotes number sense, and is an essential foundation for students to be successful mathematicians. Recent literature (e.g. Boaler, 2008) suggests that flexible grouping practices best supports equitable opportunities for student learning.
It is important to share the mathematical focus of the task with students. Provide them with opportunities to find patterns within their count, to work collaboratively, to record their patterns and strategies and to share and justify their mathematical thinking using a variety of representations. The progression in the sophistication of students’ thinking when asked to count a collection of objects goes from counting in ones, to counting in groups, reasoning additively to reasoning multiplicatively. When the count forms a pattern (e.g. how many squares or the handshake problem), students should be encouraged to generalise and reason algebraically (develop a rule) for the nth count in the pattern. Consider the mathematical language your students are likely to use when grouping and counting and the language you want to develop.
Student agency is promoted if students have choice over their own counting and recording methods. Rather than suggesting a particular solution or counting method to the students teachers can use enabling prompts to support students who require assistance. Extending prompts can be offered when students have completed the task to build more sophisticated strategies and understandings.
The wondering for this mathematical inquiry is:
Considerations when planning for the task introduction include:
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/counting-squares at 8:54pm on the 26th February 2024