Simple math and graphing in preschool

The children absolutely love exploring our math jars and one way we explore the math tokens is to graph them…

As you can see from the photos, we have built up a wonderful collection of math tokens to keep in our estimation jars from our math bag program this year…

For graphing the math tokens, the children begin by selecting two estimation jars that they would like to explore…

Then they take the jars to a table where they will find “graphing paper” that I made on my computer and printed out….

Each child opens their first jar and organizes the tokens on one column of the graph. Then the children open a second jar of math tokens and organizes them in the second column of the graph…

Some of our math tokens didn’t quite fit into the spaces I made for the math graph. I wanted ten spaces (or cells) in each column of the graphs.  When making my own learning materials, I find that I often have to go back and make adjustments along the way….

After putting their items on the graph, I invite the children to estimate which set of tokens has more and which has less…

Then the children count and see how many are on each side of the graph. If there are more than 10 tokens in the jar, most of the children naturally stop when they run out of spaces in each column. Some of the children just start putting the tokens in any empty space. For today, the goal was simply to explore the graphing process, compare the differences between the tokens, and get a feel for how to place them on the graph so they can visually see a difference in the number of objects….

The children really enjoy any activity we do with our math tokens. They will sit and count, sort, graph, and explore the math tokens for lengthy periods of time.  Just when I think they are starting to lose interest, the children always surprise me and jump up to go and pick another jar…

I just love listening to my students as they explore the math tokens. I love listening to the counting and to the funny conversations they have about the math tokens. I think because the tokens are items they have collected from home all year long, they find the tokens much more interesting than just counting bears or blocks.  The math tokens are meaningful to the children because the children are personally invested in the process and the materials…

Oh, and because we keep the math tokens in our special glass estimation jars (baby food jars), the children view the tokens like treasure. I used to keep the jars tucked away until we had math but now that we are entering the last few months of the school year, I no longer do that. I now keep the estimation jars out in plain view at all times for the kids to explore during center time…

And at the end of the day, I walk over and straighten up the jars on the shelf and when I walk away, I look back and think to myself – “Wow, those math tokens and estimation jars are such a cool part of our math program!”

Deborah talking about Math on Fox News

You can view my Math Segment from Indiana Fox News by clicking here or see the video below…

Books on Amazon

By |2012-03-15T18:00:03+00:00March 15th, 2012|

About the Author:

Deborah J. Stewart, M.Ed. has been working and teaching in the field of early childhood education for over 30 years. Deborah currently owns and teaches in her own part-time, private preschool called The Children’s Studio. Deborah’s deep passion for teaching and working with young children is documented and then graciously shared with millions of readers around the world through her blog and other social networking communities. Deborah believes that young children learn best through play and exploration and embraces this belief in all that she does in her own classroom so that she can effectively and passionately share rewarding, real- life, tried-and-true practices with other teachers, parents, and leaders across the field of early childhood education.


  1. corrie March 15, 2012 at 6:32 pm - Reply

    Great idea. I love that the baby food jars make the number of tokens small and managable. Why do you do so much with estimation?

    • Deborah J. Stewart, M.Ed. March 15, 2012 at 7:20 pm - Reply

      Hi Corrie,
      That’s a good question. I find by having the children estimate it helps them draw connections to the materials outside of just rote counting. It draws their attention to terms like more/less bigger/small greater/less-than.

      It also helps them develop a deeper interest and understanding of mathematical concepts. If I just said – “I want you to count these” – the children would not find a reason to count other than because I said so but when I say, “How many do you think are in this jar?” and the child makes an estimate – then the child is given a reason to seek out the information – they want to find out how close they were to the correct number and through this process they find math interesting and meaningful.

      Estimating also creates awareness of the things in their world from a mathematical perspective – One of my grandparents told me that her grandson came home and said, “Grandma – how many shoes do you estimate are on the floor?” Then he counted them to see if she was right!

      We estimate all the time – it is naturally integrated into our day. We estimate/predict/hypothesize the books we read, the tokens we explore, the amount of paint we need, the glue we use, the water we pour, and so on. We estimate through conversations we have and the things we do. I want the children to view their world from a problem solving/solution seeking perspective. I hope this makes sense:)

  2. Valerie @ Inner Child Fun March 16, 2012 at 12:11 am - Reply

    Oh, I love how the children see their math jars as “treasure” because used to only come out during math time. What an effective and experiential way to learn math, Deborah! Those kiddos are SO lucky! 🙂

    • Deborah J. Stewart, M.Ed. March 16, 2012 at 12:38 am - Reply

      Yes – the baby food jars make the math tokens look irresistible!

  3. fiona thomas March 16, 2012 at 4:48 am - Reply

    Guess what i will be asking my parents with younger children to bring in !!?? Love this idea, a good challenge for some of my older pre schoolers. Thanks agian for inspiring me .

  4. YourTherapySource March 16, 2012 at 7:34 am - Reply

    I just love your blog. I find myself pinning your activities daily. Were you an occupational therapist in your past life??? haha! So many of your ideas incorporate motor skills, visual perceptual skills and sensory skills. Great job in encouraging children to learn using multisensory techniques. Howard Gardener would be very proud of your classroom!

  5. kewkew March 16, 2012 at 9:13 am - Reply

    I love this idea for using in our homeschool. Now to find someone who has baby food jars. I have lots of lids but no jars!!
    I had to pin this to my Montessori board and my math board. Thanks for sharing.

  6. C. Lorena Pina March 16, 2012 at 1:19 pm - Reply

    Very interesting idea. Not only the activity but the fact that they are ready to go for any other activity. Teaching graphing, estimation, and comparing in this manner is just another visual and hands-on approach that children at this age crave so much. 🙂

  7. Vanessa @Pre-K Pages March 16, 2012 at 1:56 pm - Reply

    As always, great stuff! Just in case anybody asks for alternatives to the jars I have used plastic peanut butter jars- but only if your school is not a peanut free facility. Other containers I have used with success in the classroom are the clear plastic deli containers used for soup and pasta.

  8. Marnie @ Carrots are Orange March 20, 2012 at 4:44 pm - Reply

    This activity is great! Thank you for sharing it with us.

Leave A Comment

This site uses 'cookies' to give you the best, most relevant experience. Using the website means you're OK with this. Ok