## extending counting collections: making math to math connections

Posted on: January 3rd, 2017 by jnovakowski

Counting collections has become a regular mathematics routines in many of our classrooms in Richmond. One of the important aspects of a routine is that students have opportunities to revisit and extend their mathematical thinking experienced through the routine over time. Although counting collections are kept “fresh” for the students over the year by introducing new materials to count, teachers have been asking me for ideas for other ways to use the counting collections they have accumulated. Counting provides such a fundamental understanding of number, that counting connects to so many other mathematical content areas. Extending counting collections is one way of making math-to-math connections.  Inspired by a tweet about a blog post by Tracy Johnston Zager and a personal passion around the importance of problem-posing, I want to encourage teachers to create opportunities for students to pose mathematical problems, inspired by counting collections.

I visited the grades 1&2 class at Garden City Elementary again at the end of November. Since my last visit, the class had continued to engage with counting collections and I talked to Cheryl Burian, the classroom teacher, about extending counting collections with problem posing. I read the book Cookie Fiasco with the class (from a  great new series of Elephant and Piggie books) in which some animal friends find different ways to share some cookies. During the story, we paused and considered what new problem emerged and the students discussed different ways to solve the problem. I explained that this sharing context was one type of math problem that could be considered with a collection of some sort.

The students counted some collections and recorded their counts on a math graffiti board or chart. During our debrief, we spent some time analyzing the counts.

The students then chose one of their collections to inspire a math problem to be solved by their classmates. The gold pirate coins were a common source of inspiration and many students also drew upon the sharing context from the story to inspire their problems.

Another way to play with the idea of counting collections is to see the “units” counted in different ways. The grades 3&4 class at Grauer Elementary counted some new collections the day before the holidays (which was also pyjama day at the school – just to explain some of the photographs!). The class has been learning about multiplication and thinking about different ways to represent the concept of multiplication such as in grouping and arrays. Although the students used the term “skip counting”, I introduced the term multiples to them. The question I asked them to focus on as they engaged in counting collections was: “What is the connection between counting and multiplication?”

One pair of students decided to practice their 7x tables (their words…) and so grouped their glitter balls in groups of 7 on paper plates. As they began to count, they  noticed since they had organized their plates in two rows that they could visually see a ten-frame and decomposed their total number of plates into a group of ten and then a four. The video below has them explaining their thinking.

Counting by 7s

Some of the collections I brought to the class were specifically curated to inspire students to think about multiples. I had bought several strands of holiday beaded garland and cut them into groups of 2, 3, 4, 5 etc beads. I anticipated that the students would either count them by 1s (each strand) or by multiples (the number of beads in each strand).

Here are two videos of students’ counting of the collections:

Counting by 5s

Counting by 10s

Other pre-grouped collections that could be used are items like packages of crayons (I have seen them in 8s and 12s) or geometric shapes where the number of sides could be counted as multiples. In both cases, the item (or shape) can be counted as a singular unit or a multiple unit, creating different entry points for students as they engage in counting collections.

Richmond teachers (and others!) – if you give one of these ways to extend counting collections a try with your students, let me know and send some photos and insights along!

~Janice