Measurement and Data Archives | Page 8 of 11

There are any number of wonderful books that give children very concrete images to show how big creatures are and to make comparisons to their own size. Steve Jenkins’ Actual Size and Prehistoric Actual Size have been favorite choices in our past learning labs on measurement.

Last year Laura Miller reported how she and and her preschoolers from Prieto Academy explored linear measurement after studying polar animals. They wondered, “Are we taller or shorter than an Emperor Penguin?” They used the book Penguins! by Anne Schreiber to find out that the average height of an emperor penguin was about 44 inches tall.

They used measuring tape and large butcher paper to mark this height and, with the help of an overhead projector and a toy penguin, they created a shadow of a penguin. Students worked together to make the penguin shadow match the mark they made on the butcher paper. Children compared the height of the shadow to the mark on the butcher paper. Comments such as “We have to make it bigger,” “Not that big!” and “Move it over!” were made until the height of the shadow and the mark on the butcher paper were the same. The class traced the shadow of the penguin and then they were ready to compare their heights to that of the penguin. Comparison statements that the children used included, “I am the same size as the penguin,” and “I am a little bit taller.”

After this experience with direct comparison, Ms. Miller asked the students, “How else can we measure this penguin?” The first response from a student in the morning class was, “Books!” Discussion arose surrounding how they could use books to measure. There were a number of questions to consider:

Should they lay the books flat or stand them up?
Would they fall down?
Are all books the same size?

Ms. Miller shares the conversation that ensued:

One student, Laura, suggested we could lay the books flat so they would balance better than if we stood them up. After realizing that not all books are the same size and it would take a lot of books to complete the task, Jonathan suggested we use blocks! “We can use blocks; they’re the same!” Jonathan said in reference to blocks being the same size. Children shared their ideas of what they thought would be the best blocks to use. It was decided that triangles would be too tricky and rectangular ones would work best. After stacking the blocks and counting how many long rectangle blocks (8) and how many square rectangle blocks (16) would equal the size of a penguin, one of our reading buddies pointed out that the number was doubled because it takes two square rectangles to make a long rectangle.

At one learning lab, participants observed a fun project tradition. As has been true for years, the authors of this year’s Idea Book were in the room for its unveiling and discussion. The Idea Book allows program participants to submit write-ups and photos of activities they used to make their math lessons more engaging and to put their own spin on the research lessons discussed in the learning labs. They are organized according to the major content strands and printed in a spiraled book so that even though the program is over, these Big Ideas remain accessible and inspiring for years to come.

Since a recent session addressed important ideas of geometry, the discussion of data analysis didn’t get much attention—in the workshop, that is. However, the Idea Book includes a variety of great ways to make surveys and analyzing data meaningful, engaging activities.

Heather Duncan did a particularly striking job of explaining how she and her kindergartners at South Shore Elementary have made collecting data from surveys and discussing them a regular part of their classroom life.

Heather prefaced her description of their process by pointing out how important it is to take time to really explore the ideas and emphasize the children’s work and thinking. She typically does a process that stretches from three to five days and always ends up with a product everyone can see.

Day One, they collected results of a survey, usually related to a topic they were already studying. For example, while studying the human body, Ms. Duncan had them compare each student’s height to a cut-out of an average kindergartener hung up in the class.
Day Two, they synthesized the results. “We used the chart,” she wrote, “to count and determine totals for each designation (taller, shorter, same size) and whether any groups have more/less or the same amount as any others. We also compare totals from the a.m. class with the p.m. class and discuss any similarities or differences in results.”
Day Three, they further discussed the results and talked about the best way to show them on a graph. In this case, they decided on a bar graph.
Day Four, they used the resulting graphs to make some conclusions. She wrote, “Which group had more or the most? Which had less, the least, or the fewest? What do we know about the question or our class as the result of our survey?”

They turned the results into a poster, a bulletin board display, or part of a “trivia book” at the end of the school year. Ms. Duncan comments, “[The activity] has since become practice, because we have found it to be a very rich experience. It’s been invaluable using math in context to study things we care about and to answer questions generated from our own interests.”

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.

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

The New York Times examines one of the creative math projects developed by the Early Math Collaborative. The article follows a teacher taking part in our in-person math coaching. She is trying out the lesson Just Right for Me, in which students search the classroom for objects that are the same size as their hands. This gives students the opportunity to practice measurement in a way that is hands-on and personally relevant to them.

As part of the coaching process, the lesson is recorded on video and reviewed with a coach afterwards. The teacher and coach discuss what went well in the lesson, as well as what could be improved for next time.

Just Right for Me is part of our Focus on the Lesson video series, which presents several creative math projects for preschool and kindergarten classes, as well as teachers’ thoughts about the benefits and difficulties of implementing these lessons.

A child seriates cups by their capacity.