# Counting Collections

Counting Collections promotes number sense and can challenge students from level 1 through to level 5 of the curriculum.
Number sense is an essential foundation for students to be successful mathematicians.

 (show text) Counting collections promotes number sense and provides challenge for students from level one through level 5 of the curriculum. Number sense is an essential foundation for students to be successful mathematicians. I love doing counting collections with my class and I find it extremely successful with mixed ability groups. Counting collections provides rich opportunities for children to practise their oral counting and to develop efficient counting strategies. It promotes also child agency in choosing their own system for counting the collections. I’m glad that I did counting collections and that I got to choose what to count and how to count it and how we recorded it. We got to count cool stuff like Lego, Pokemon cards, stickers and sports equipment. At its most basic it is counting all but counting progresses from counting in ones or groups to applying proportional relationships to estimate the size of a collection when only a sample of the collection can be counted. I like grouping collections because I like counting big numbers like up to one thousand. I like counting collections cos I like putting stuff in groups and then counting groups I like counting big groups. It’s important for teachers to step back and allow their students to approach these tasks in their own way through observation and questioning teachers will be able to recognise and identify and reflect on students’ mathematical thinking and number sense. As I walk around the classroom, I find that the children have chosen many different types of strategies to count their collections; some of these are expected and some are unexpected. First we did them in tens and then if we don’t have enough room we put another ten into each one so there’s twenty. Students are encouraged to collaborate to choose their own methods to count, group and record collections. First we estimated how many there were but sometimes there were too many to count so we measured out a smaller amount and then we worked out how many there would be in the whole collection. I can use what I hear to build up a really good knowledge of their thinking and their number sense in general. It was hard for me not to jump in and tell the kids how to do things but after a while you could see that they were starting to work it out on their own. They also are encouraged to give feedback to each other and challenge each other for more efficient strategies and to look for and make use of patterns. When we were asked to work out how many squares were on a hundreds board we thought this would be easy but it was actually quite complicated. We noticed patterns we could use so we didn’t have to count we used this pattern to solve other problems like how many squares are on a chess board. I have found that the children learn beautifully from one another and they can challenge each others’ thinking. It is important to give students time to communicate their understandings and justify their thinking. I made sure that there was always time and the end of each lesson that the students could share their counting strategies and recording those solutions and strategies allowed for that reciprocal learning to be more concrete. Through allowing students to participate in counting collections you will build on their current mathematical thinking and number sense. The perseverance and success that they showed was really great. There are many benefits from counting collections and I hope you enjoy doing them as much as I do.

## Years 1 to 3

I wonder

Cars, cars, cars

Count it (years 1-3)

## Years 4 to 6

Covering our bases

How many pieces? (years 4-6)

Count it (years 4-6)

## Years 7 to 10

Counting squares

How many pieces? (years 7-10)

The handshake problem

References for Counting Collections

Schwerdtfeger, J. K., & Chan, A. (2011). Counting Collections. Teaching Children Mathematics, 13(7), 356-361 (click to purchase article).

Gibbons, L., & Lomax, K., (2016). Counting Isn’t Just for Primary Grade Students. Blog post on www.nctm.org.

Boaler, J. (2008). Promoting ‘Relational Equity’ and High Mathematics Achievement Through an Innovative Mixed Ability Approach. British Educational Research Journal. 34 (2), 167-194