Counting and Quantifying Collections
Ideas of quantity and magnitude need to be in place before we move into formal place value activities with young students. In fact, it is worth checking out what counting strategies and ideas of magnitude older students have too.
How can a child understand a system of tens and know what a hundred looks like with bundling or stacks of 10 if they have limited experiences with counting large collections of loose objects? They cannot really understand is the answer to that question.
Students need many opportunities for purposeful counting not just rote counting or one-to-one counting before we go anywhere near formalizing and using structured materials.
When students are offered large collections to count, they will need to know which have already been counted and to be systematic in some way. It is always interesting to see what happens when a student’s count is interrupted. Do they go back to the beginning and count again, do they trust the count, remember where they got to and count on from there? Or have they created equal sized groups that allow them to skip count quickly? If students know they have a large collection to count and may be interrupted, they may invent a strategy to help them get organized.
Trusting the count does not stop at 10. When a large collection of objects is contained in a plastic bag, they look different in quantity to when they are in a heap on the desk, and different again when they are spread out. As such, estimates of the actual quantity each time may be poorly informed. Students need to see collections in various configurations to begin to have informed ideas of magnitude. They need to be encouraged to look and make predictions based on what they can see.
“It looks like more than 20.”
“There’s about 10 there and 10 there and a few moreover here, so less than 30.”
Fun With Hands-on Materials
Snap lock bags and loose objects, jigsaw puzzle pieces, counters, shell etc, are all that is needed. Once the process for the following activity is established, students can create their own ‘tricky’ snap lock bag collections and challenge a friend to estimate and then check how many.
Model The Process
Show a bag of objects, pass it around so students can shake and examine it. Ask students to guess about how many. Tip them out in a heap and ask if anyone wants to change their guess and why. Encourage comments such as ‘there are 5 there and a lot here so about 40…” Ask volunteers to come and show how to check. This will offer opportunities for one-to-one counting and lining up the ones counted, or moving them into 2s for skip counting, or 5s for even faster counting and of course, two groups of 5 will lead to thinking about counting in 10s.
Let The Students Play
When the pattern of the activity is established students can continue the game on their own. As they play you will be able to notice:
- who can count one to one and how far
- who trusts the count
- who moves and organizes the ones counted
- who breaks the counting sequence to count on
- who counts in 2s, 5s or 10s
- who is beginning to make informed estimates about large quantities
To find out more about knowing what to look out for and how to create purposeful activities check out our Early Place Value materials and our Trusting the Count course. The complete Early Place Value bundle includes each of the smaller modules to create a cohesive developmental approach to place value and to create cohesive numeracy blocks in your classroom. Each individual module also stands alone and can be used to compliment or extend your existing program.
Enjoy and as always, let us know how you go with your students.