Using Counting Collections in the Classroom

Have you tried counting collections? 



Counting Collections: Kindergarten - a common core classroom friendly exercise from Luna Productions on Vimeo

This activity is a great opportunity for our primary students to gain a better understanding of counting and number, and with some modifications, I think it could be used, at some level, in the upper elementary classroom as well.

You will need to begin by creating some collections.  In the link above, they give some examples of objects you can gather for counting, but I'm sure you can find other items around your home or classroom that will work as well.  You will probably want them to be smaller in size so that storing them doesn't become much of an issue.  Hopefully, you can find other teachers in your classroom to join you, and then you can find a common space to share your different collections. This handout will also be able to help guide you as you plan for your collections and fine-tune the activity.

I think that these would be a great way to kick off your math habits to start the year.  You would be able to learn a lot about your students by interviewing and talking to them as they work on organizing and counting their collections.  

For older grades, I have thought that you could have them count objects in multiples or fractions to get a total.  You could also have them count by sets.  Packs of items...Can they count by 24 or 36? What if you offer them decks of cards? Can they count by 52s?  While they may not be fluent as they move through these unusual multiples, it will certainly aid them in developing mental math strategies.  Introducing fresh concepts through counting offers all students an access point, so students can practice new concepts using the math routine of counting.

Here is an example of a Counting Collection in a 3rd grade classroom:
Counting Collections: Third Grade - a common core classroom friendly exercise from Luna Productions on Vimeo.


Counting collections can adjust as your students develop their number sense. It is a routine that will allow students to think about better ways to organize, more efficient ways to count, and concepts of number. It can be used all year long.

What do you think about this?  How can you make it work in your classroom?  Please share your ideas!

I'd love to join in on the fun as your class does a counting collection!  If you are okay with that, let me know when you think you would like to do one, and I will see if I can join you.

Rethinking Homework

As we rethink the role that homework is playing in our students' learning, we should look at new ways to have our students practice their learning rather than just a set of practice problems each night.  

One idea to consider is a math reflection question for the students to respond to.   Building their metacognition through these written responses has proven to build better mathematical thinkers.  

You might decide to have a menu of questions for students to answer, or you might begin by having them all answer the same question--whatever works best for your students.

Click below to a link of some potential questions.  Reflecting on these ideas each day will help to build the types of thinkers we hope to cultivate.

Building Understanding and Developing Culture

I have done this problem with first graders for the past couple years.  The first time I offered it to students, I was surprised by how difficult they found it (due to the majority of my experiences being with older students).  When I did it subsequent times, I offered a lot of "up-front" guidance to help them think about it, and I highly encouraged them to use manipulatives and images to help them make sense. However, they still struggled...

I have decided that if  I work in a first grade classroom next year, we will again do this problem. I have been pondering some different ways to approach it.  

I think it will make a great numberless word problem that we can do with a slow reveal in hopes that students work to make sense of it rather than just trying to solve it. Using the slow reveal will offer a great way to directly instruct the students in the process of notice/wonder and making sense of the problem before trying to solve it.  This use of numberless problems should help them as we continue to build understanding throughout the year.

Doing a general overview as a class, offering the students manipulatives and encouraging them to work with a partner to solve it.  Once they think they have solved it, they must find another pair who has a solution, and each group must convince the other that their solution is correct.  I like this idea, too, as it should help to build mathematical culture int the classroom--collaboration, sharing methods, convincing others of our solution... I think that the deliberate teaching of convincing others with math talk will need to come before this lesson, so that both sets of students don't just say the answer they got and move on.  

I could provide a picture of two spotless ladybugs and then have the students work to put the spots on to match the words in the problem. This one seems very direct, but it does emphasize the importance of using visuals to help us make sense of the problem. Again, I think partner work is a great way for them to approach this.

I think the sharing out of this problem is important and recognizing the different ways that students went about solving it. Determining as a class what we think the correct answer is and acknowledging how we worked with our partners to solve it.  Maybe a gallery walk of our thinking?  

A possible follow-up activity could include students writing their own kind of problems like this and then switching problems with others.

This problem is written with 1st grade in mind.  Certainly, this type of problem could be adapted for different grade levels:
* I have six pieces of candy in my purse.  There are four more pieces of gum than mints. How many pieces of gum do I have, and how many mints do I have?
* We have 27 students in our class.  There are 5 more girls than boys in our class.  How many boys and girls are in our class?
* There are 114 vehicles in the parking lot.  There are 72 more vehicles with 4 wheels than vehicles with 2 wheels.  How many vehicles have two wheels?  How many vehicles have four wheels?
* In my closet, there are 18 shoes on the floor. However, there are 2 more right shoes than left shoes.  How many complete pairs of shoes do I have in my closet?
* I found thirty-five coins in my car.  There were four times as many pennies as all of the other coins combined?  How many pennies did I find in my car?

What do you think?  How might you approach a problem like this with your students? Do any of the ideas I shared seem to be better than the others?  I'd love to hear your thoughts.