Playful Invitations: A Tour

Playful Invitations: Inspiring Ways to Teach Early Mathematics, is a blog written by Dorie Ranheim. Its goal is “to inspire parents, caregivers, and educators of preschool children to intentionally teach math using natural materials.” By using “loose parts”, backyards, playgrounds, and parks become great places for teaching and learning math. As described in the blog’s about page,

“My playful invitiations to learn math eventually extended beyond our home to our backyard and nearby park. During our time outdoors I realized I could showcase the beauty of real, natural materials and how inspiring, meaningful, and relatively easy they are to acquire. Overall, I hope to share ways adults can intentionally teach preschool math using these beautiful natural materials.”  – Dorie Ranheim

In this tour, I will summarize some of its most recent posts. Many of them can be used as guided activities, and Ranheim provides a helpful guide on how to use her blog posts.  One of the aspects I appreciate about the activities is that they are all centered around play. Many of the posts consist of three parts: Prepare, Invite, and Play, and some include reflections and extensions to the activities.  As she remarks,

“The blog posts are simply suggestions. There are MANY ways to develop these math skills. My hope is that reading the blog will inspire you to find opportunities in your daily life to teach math to preschool children.If it is playful, meaningful, and reasonably challenging then chances are the learning will stick!”


In this post, Ranheim shares some of the ways that during last Spring, she and her children became more entune with nature and spent some time thinking of long-term projects.

We watched the bare branches bud and blossom, now we celebrate trees bursting with bright green leaves. […] Here are a few ways my children have explored math during this time at home:

  • Practice number identification and formation using loose parts.

  • Write numbers on river stones using water and brushes.

  • Pattern using various colored rocks. Sometimes the simplest activities and materials seem to hold their attention the longest!

I found it related a lot to what I’ve done since the quarantine. In a very similar what, I discovered patterns in one of my hikes.

My own exploration of patterns at the beach.


Invite: Today I thought we could trace our bodies so we can see how big we are. (After tracing one or more bodies) I wonder whose body is the tallest/longest?

This invitation is inspired by the following quote,

To compare objects, children begin by using nonstandard units (“My table is more than four hands long”) and then move to using standard units (“The table is almost three feet long”). Comparing fairly is an important concept for young children. – Juanita Copley, 2010

This made a lot of sense to me! Once you learn the standard units of measurement it’s easy to forget all the other intuitive ways we make sense of measurements. If anyone has ever tried to learn a family recipe, you’ve probably encountered many non-standard ways of measuring yourself. In this activity, each child lays on the ground and draw a chalk outline of their body, afterwards they use natural loose objects of similar size (e.g. leaves, rocks, etc.) to lay them side by side and compare the lengths. Some fun extensions include introducing rulers, or filling the outline of the body, and talking about the area.

Puzzle and Spatial Position

Invite: “I’m trying to put this leaf back together! Will you help me find the perfect match to make my leaf complete?”

As a big fan of tangrams as a kid, I love that in this invitation, you introduce the idea of fractions at a basic level by transforming leaves into puzzles.

It is a great way for children to play with the idea of a “whole”. You can start by cutting leaves in half and trying to find the match, or you can extend the activity by adding more different types of leaves or cutting them in four pieces instead.  Ranheim advises that before using the leaves for learning math, they should explore their properties.

“It would also be beneficial if the child has explored the property of leaves before being asked to use them for math learning. Observe a small pile of leaves and the attributes before taking them apart.”

A personal project that has brought me great joy during the pandemic, has been to gather seeds and start my balcony garden.  I could see all the fascinating (and often subtle) ways math seeped into my gardening.

The joy of learning and caring for my small garden.

What drew my attention to this blog, were my conversations with my best friend and early-childhood educator, about the ways math should be tied into how we experience nature around us. I would have loved these activities as a kid!

Also, it reminded me of one of my favorite books Braiding Sweetgrass: Indigenous Wisdom, Scientific, Knowledge, and the Teaching of Plants” by Robin Wall-Kimmerer (I can’t recommend it enough).

“The land is the real teacher. All we need as students is mindfulness.” – Robin Wall Kimmerer, Braiding Sweetgrass

Have an idea for a topic or a blog you would like for me and Rachel to cover in upcoming posts? Reach out in the comments below or on Twitter (@VRiveraQPhD).

About Vanessa Rivera-Quinones

Mathematics Ph.D. with a passion for telling stories through numbers using mathematical models, data science, science communication, and education. Follow her on Twitter: @VRiveraQPhD.
This entry was posted in Blogs, Math Education, planet math, Recreational Mathematics, Sustainability, Uncategorized and tagged , , , , , . Bookmark the permalink.