This counting collections activity engages students in finding the number of studs on a Lego (or similar) baseplate.
A collection presented as an array can be estimated, organised and grouped strategically for an efficient and accurate count. Arrays are useful for building multiplicative thinking. They can be used to explore calculations such as 13 x 5 where the array can be split into useful chunks. This means that children can use their known number facts to work out calculations. Students can represent their strategies and counts with numbers, symbols, words and diagrams.
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. This task promotes multiplicative thinking through presenting a collection to be counted as an array. An array enables students to form useful mental pictures to support the generalisation of number properties (e.g. commutative and distributive properties). The task provides students with opportunities to partition the array strategically to make the count easier, to work collaboratively, to record their strategies and to share and justify their counts and strategies 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.
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 particular solution or counting methods to 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://nzmaths.co.nz/resource/covering-our-bases at 6:06am on the 26th April 2024