The Growing Story and Three Feet Small are two wonderful picture books that address a “math all around us” question that young children find compelling. Both of these stories are built around a question: Am I getting bigger? They also offer rich possibilities for exploring two important Big Ideas of measurement:

• Many different attributes can be measured, even when measuring a single object, and
• Isolating the attribute to be measured is an important precursor to measuring.

The Growing Story by Ruth Krauss, illustrated by Helen Oxenbury, was first published in 1947 but the story is timeless. From early spring through fall, a little boy easily can see how baby chicks, puppies, and plants in the garden grow. But his own growth isn’t nearly as easy to measure—until he finds he has outgrown the warm clothes his mother put away in the spring.

Helen Oxenbury’s warm pastel illustrations will help young readers track precisely how the chicks change in appearance and size; how the rolly-polly puppy becomes a dog; and how the apple tree goes from barren, to bud, to apples ripe for picking. The story links beautifully with an inquiry unit looking at farm animals; it invites rich discussions of how different creatures grow at different rates—a baby chick’s childhood is a matter of months while a human’s lasts for years.

Michael Rosen’s Three Feet Small, illustrated by Valeri Gorbachev, takes a different tack, but one that is equally important to little ones. The concern about getting bigger is not just a question of physical growth—it has just as much to do with how getting both older and bigger means we can do more things. The little bear who is the center of this book is just not sure that he is growing—especially when he sees all the things his older sister and his adult relatives can do that he is still too little for. However by the end of the book, he also finds that he needs new clothes and that he is beginning to do some of those things that seemed out of his reach earlier.

These books could be used alone or together to open up a wonderful exploration of the benchmarks children can identify concerning what it means to “get bigger”—either in terms of size or abilities. Rosen’s book includes at least one picture showing a measuring chart—if you don’t already have one in the classroom to mark the growth over several months, you could start one now. However, be sure to emphasize that height isn’t the only attribute that shows growth. Include discussion of other physical attributes such as weight. The most emphasis should be put on how we can measure how much we are growing our brains as well as increasing physical abilities. What are things the children know now and can do now that they couldn’t when they were one year old? How about things they couldn’t do at the beginning of the school year?

Estimation, an important skill for young children to have, can be touched on in many different activities. Benita Johnson, a teacher trained by the Collaborative, was a prekindergarten teacher at Christopher House. She played a game after reading Mouse Count by Ellen Stoll Walsh to bring out the math that was inherent in the story. Games are often best brought out with a good book.

Ms. Johnson used a large jar and “mice” she had created out of three sizes of Styrofoam balls. She first asked each child to estimate how many large mice would fit in the jar and recorded the answers; then the children put the mice in one by one to compare their estimates with the results. She repeated the process with the smaller mice; all along she kept the children thinking actively by discussing what was happening. Using small, medium-sized, and large mice resulted in different questions to the children and different answers from them.

“I could see that it was really important to have concrete materials to do this activity,” Ms. Johnson said. “I also found that it was a good idea to keep asking children questions after placing each mouse in the jar, because it allowed the children to modify their thinking. I could see that the children did begin to understand the idea that larger items take up more space than smaller ones.”

And all along, estimating helped the children think about the reasonableness of their answers.

Tracey Fisher was another participant of the program and tried out a similar activity. With her prekindergarten class at Peirce Elementary, she combined an estimation exercise with a data display to help children order and compare amounts.

For the activity, Ms. Fisher provided a clear jar with a small set of manipulatives inside, in this case bunnies. She put up a chart with three possible amounts, only one of which was correct. Children placed their name card in the column with the amount they think was in the jar. By constraining the number choices, Ms. Fisher helped children focus on reasonable estimates and encourage strategic comparison and logical thinking. If it seemed like more than 4, it had to be either 6 or 10.

“Every time I play the estimation game,” Ms. Fisher commented, “I always realize what a good reinforcement it is for the concepts of highest, middle, and lowest when comparing how many children guessed each number. It is easy for them to see. I also remind them that estimation is not only in math but also is important for scientific purposes.”

With the right questions to the children, both activities can illustrate estimation in purposeful ways.

This video from our Focus on the Lesson series demonstrates an activity for teaching capacity in kindergarten and preschool. Students look at two containers and try to determine which one would hold more liquid.

One of the goals from this lesson is to get young students thinking about precise ways to describe their thinking. Many children use general terms—“it’s big!”— when explaining their ideas about measurement. This activity requires children to use more specific words and concepts to clearly explain their thoughts. While one container might be taller, the other might be wider.

Because it reinforces strong, precise vocabulary, Which Holds More? is a great activity for teaching capacity to English Language Learners.

“The language of capacity is difficult for any child but especially English Language Learners,” explains one of the teachers featured in this video. Students are able to practice using these new words, but the concrete objects in the lesson still allow them to fall back to using gesture to communicate their ideas.

Students compare the size of their hands to objects around the classroom to find ones that are “just right.”

A planning conversation for this lesson is available here.
A reflecting conversation for this lesson is available here.

Students brainstorm ways to sort their shoes. Later, they graphically organize the data from the sets they created.

A child directly compares the lengths of two crayons to determine which one is shorter.

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.