Sorting things into categories is one of the ways mathematics enters into our daily life. At “clean-up time,” children discover that forks and knives belong in one place, plates belong somewhere else, and glasses and cups belong in yet another place. As children and adults talk about what makes one set of things go together and why other things belong elsewhere, they are doing important talking… and thinking. Talking about attributes and qualities such as size, shape, texture, and color encourages children to look more closely at things. This also is a great way to develop children’s vocabulary.

Sort It Out! by Barbara Mariconda provides a great model for incorporating math into everyday activities. This brightly colored picture book shows Packy the Pack Rat trying to obey his mother’s order to put away all the treasures he has collected.

The Button Box by Margarette S. Reid could launch another exploration of a collection many teachers may have in their sewing closet. In this story, a little boy finds all kinds of stories in his grandmother’s collection of buttons. Grandma’s Button Box by Linda Williams Aber uses another approach. In this book, Kelly and her cousins help Grandma sort the buttons that spilled when Kelly accidentally knocked over the box.

All of these provide great entry points for exploring sets and sorting in everyday life. Math is, in fact, all around us.

Sharon Hogan and her preschool class at Peterson School had all kinds of fun with the way Eric Carle’s The Secret Birthday Message plays with the two main faces of geometry—shapes and spatial sense. The group made up their own treasure map to correspond with the one in the story and then brought the map to life as they set up an obstacle course. Throughout the process, the children were surrounded by two- and three-dimensional shapes and involved in recognizing, naming, drawing, and building with them.

They also got lots of practice using directional language such as “down the stairs” or “through the opening” and relative words like “near to.” Sharon knew that both first- and second-language learners need many repetitions of these terms. These words can describe a relationship between two objects that shift. For example, one person pointing left looks like they are pointing right to someone facing them, or just as a bush that might have been in front of you at one point soon is behind you as you continue along a path.

A Triangle for Adaora by Ifeoma Onyefulu is a delightful book that emphasizes several Big Ideas in geometry, including that comparing attributes of shapes helps define and classify them and that two- and three-dimensional shapes can be used to represent and understand the world around us.

Adaora doesn’t want to eat her paw-paw fruit because she loves the shape inside – a star. The conversation with her cousin that ensues sets the stage for an exploration of shape and the search for one shape in particular – a triangle. As Adaora sees that her world is full of shapes and learns the names of these shapes, we also learn about life in a Nigerian village.

As we journey with Adaora and her cousin, we see the rectangle of Uncle Eze’s robe, the circular tops of the elephant drums, and many other beautiful shapes in her world. We see the shapes, but we also see the culture and hear the life of the village. We are drawn in with Adaora on the search for the elusive triangle, and when she finds it, we are able to celebrate with her. Her exploration invites the reader to search their own world for shapes and to see that geometry is all around us.

This book is a wonderful way to connect mathematics with children’s lives. Teachers can explore the culture of the children in their classrooms from a geometric perspective by encouraging the children to identify different shapes unique to their family and discuss the shapes that they have in common. Having collected all this data, don’t forget to graph it to answer the question, “Which shape is most common in everyone’s family?” The results will be both fun and enlightening. Children may eventually be able to come up with additional questions this data can answer.

A child compares two small sets of wooden cubes.

Focus on the Child videos are taken from one-on-one interviews with individual children. The interviews are designed to elicit evidence of children’s mathematical thinking. They are not teaching episodes or formal assessments.

Teachers who go home from our learning lab with Anno’s Counting Book immediately put it to use to get their students exploring “how many?” After reading Anno’s Counting Book, Nancy Beza at Waters Elementary encouraged her preschoolers to make a list of objects that could be found in a winter scene—snowflakes, trees, etc. Each student created an object from the list to display on a bulletin board. A question posted on the board, such as “Can you find…?” followed by a list of objects and their quantities, encouraged the children to go on a counting expedition.

Ms. Beza comments, “I was surprised by the popularity of the bulletin board. Parents and students alike stop to find and count all the objects. I change the objects occasionally to make it more interesting. This has been very beneficial in motivating children to count objects independently.”

Laura Carbajal of Armour Elementary and her kindergarteners also used the book to develop a deeper understanding of number sense and number recognition using dice. Laura had each of her students roll a die and then count and identify the number of dots. Then they found the number on the number chart and wrote the numeral. Ms. Carbajal gave her students many opportunities to practice by moving the activity into the centers. The children in the classroom have a heightened awareness of numbers as they discover them in books and see their use in everyday routines. The students are enjoying counting using manipulatives in class and real-life objects at home.

Ms. Carbajal commented, “I have a different perspective and understanding about mathematical thinking at my student’s level.”

A child seriates four cups by their capacity.

Focus on the Child videos are taken from one-on-one interviews with individual children. The interviews are designed to elicit evidence of children’s mathematical thinking. They are not teaching episodes or formal assessments.