The second part of our exploration expanded upon the mathematical concepts and thinking introduced in the children’s first experience with measurement (“How Tall Am I?” - December 19, 2014), while integrating a variety of meaningful literacy experiences. The children worked with a partner throughout the process, setting the stage for collaboration and problem solving.
The children had expressed an interest in animals since our field trip to the zoo in November, building zoos with unit blocks, looking at non-fiction books about zoo animals, and using reference photos to draw zebras, giraffes, and rhinos.
To connect the children’s interest in animals with our initial exploration of measurement, we shared two books that illustrate the actual size of animals with the children during Story Time: Actual Size by Jenkins and More Life-Size Zoo by adapted by Earhart. The children were fascinated to see a full-size lion’s head and to learn that an anteater’s tongue can be two feet long! They were also eager to share their experiences with animals at the zoo, the aquarium, and during vacations with their families; which lead to more questions about animals and their size.
In response to children’s comments and questions, we asked the children if they would like to measure the size of animals, just as we had measured their heights. Their response was an enthusiastic “yes”! We then asked the children to think of something they were wondering about related to the size of an animal - in essence, to pose a research question. Their questions were intriguing, and reflected both their curiosity and their prior knowledge:
“How long is a zebra’s tail?”
“How long is a rhino’s horn?”
“How big is a tiger’s tummy?”
“How long is an elephant’s trunk?”
“How long is a spider’s leg?”
“How long is a crab’s claw?”
“How big is a whale?”
“How long is a rhino’s horn?”
“How big is a tiger’s tummy?”
“How long is an elephant’s trunk?”
“How long is a spider’s leg?”
“How long is a crab’s claw?”
“How big is a whale?”
Measurement is a complex concept that involves many aspects of mathematical thinking and reasoning. It can be used to measure different attributes in a variety of contexts, such as the length of a bed, the height of a window, the volume of a container, the distance to a destination, the weight of luggage, or the time until an appointment. The children’s use of “how long” in their questions indicates that they want to measure the attribute of length (height). This interest reflects their experience measuring their own heights.
Two questions, however, refer to different attributes. The child who asked “How big is a tiger’s tummy?” used his hand to visually form a circle, indicating that he wanted to measure circumference, but he did not yet have that word as part of his vocabulary. The child how asked “How big is a whale?” initially wanted to know how heavy a whale is (weight). When we explained that we could find the answer to that question but that it would be difficult to “show” the weight of a whale, he decided to measure its length. Both children understood the concept of “length” and knew that they wanted to measure a different attribute, so they used the more general term “big” when posing their question.
Two questions, however, refer to different attributes. The child who asked “How big is a tiger’s tummy?” used his hand to visually form a circle, indicating that he wanted to measure circumference, but he did not yet have that word as part of his vocabulary. The child how asked “How big is a whale?” initially wanted to know how heavy a whale is (weight). When we explained that we could find the answer to that question but that it would be difficult to “show” the weight of a whale, he decided to measure its length. Both children understood the concept of “length” and knew that they wanted to measure a different attribute, so they used the more general term “big” when posing their question.
Since the books and websites we shared with the children gave answers to their questions in feet and inches, the children used rulers and tape measures to determine the length of the object they were measuring. In their previous experience, the children used paper cut to the size of rectangle unit blocks (non-standard measurement) to represent their height. For this experience, they used paper strips cut into one-foot lengths (standard measurement). While the children may not yet fully understand the meaning of these standard units, they knew that they needed to tape together srtips of paper that were “nine rulers long” or that reached the number 25 on the tape measure to represent the appropriate length.
When the children used unit blocks to measure their heights, they shifted from direct comparison (standing side by side in front of a mirror) to indirect comparison (looking at the lengths of paper unit blocks mounted side by side on the wall). In this experience, the measuring experience became more complex and abstract as they used standard rather than non-standard measuring tools.
As adults, we are conditioned to think in terms of feet and inches and can visualize the length that six inches or six feet represent. These are “foreign” terms to young children and they will need many experiences over a period of years to fully understand their meaning. The children understood, however, that they all needed to use the same measuring tools to make a fair comparison.
In this experience, the strips of paper cut to a one-foot length helped the children use a ruler in a meaningful way. They often referred to a measurement as “five rulers long” because “one foot” does not yet have meaning for them. In a similar way, they were able to find the numeral “three-five” on the measuring tape and recognized that the measurement was longer than if it had been “three-one”, even though they may not know that the numeral is called thirty-five and that it is a quantity comprised of three tens and five ones. They also recognized that the 35-inch length was almost “three rulers long”.
As adults, we are conditioned to think in terms of feet and inches and can visualize the length that six inches or six feet represent. These are “foreign” terms to young children and they will need many experiences over a period of years to fully understand their meaning. The children understood, however, that they all needed to use the same measuring tools to make a fair comparison.
In this experience, the strips of paper cut to a one-foot length helped the children use a ruler in a meaningful way. They often referred to a measurement as “five rulers long” because “one foot” does not yet have meaning for them. In a similar way, they were able to find the numeral “three-five” on the measuring tape and recognized that the measurement was longer than if it had been “three-one”, even though they may not know that the numeral is called thirty-five and that it is a quantity comprised of three tens and five ones. They also recognized that the 35-inch length was almost “three rulers long”.
The children worked in pairs to create their measurements, and then wrote signs to label the measurements before displaying them in the classroom. Measuring with a peer, rather than with a teacher, encouraged both collaboration and problem solving. The children discovered that it worked best when one child held the two paper strips while the other child taped them together, and they often took turns taking each role. When a measurement was given in inches, the children found the numeral on the tape measure (often after much discussion) and then measured and then cut the one-foot paper strips to the correct length.
The children continued to practice one-to-one correspondence (pointing to each object in order as they count and knowing that the last counting number tells “how many”) to determine when their measurement was accurate. This process was much easier for the children measuring a seven-foot elephant trunk than for the children measuring a 16-foot long beluga whale!
Most children are able to accurately count up to 10 concrete items by the end of the Junior Kindergarten year, but their accuracy often decreases when counting a larger number of objects or when counting symbols. Like all mathematical skills and concepts, children need many meaningful counting experiences over a long period of time to fully understand and apply this concept.
Most children are able to accurately count up to 10 concrete items by the end of the Junior Kindergarten year, but their accuracy often decreases when counting a larger number of objects or when counting symbols. Like all mathematical skills and concepts, children need many meaningful counting experiences over a long period of time to fully understand and apply this concept.
Then the children wrote signs to label their measurements, copying both their research question and its answer. The children focused intently as they copied the letters, often naming each letter as they wrote, and sometimes asking their partner to help form a difficult letter. Meaningful writing experiences nurture both children’s interest in and understanding of symbolic communication. It is a powerful experience for a young children to transfer their spoken words into written words that can be read by their teachers and families! A photo of the animal on each sign supported the children’s growing ability to make meaning from written language as they looked at their friends’ measurements.
We displayed the measurements in the classroom from longest to shortest to foster the children’s ability to make thoughtful comparisons.
The children eagerly awaited each new addition to our measurement display, and they made many observations as they compared the measurements:
“The rhino’s horn is longer than the zebra’s tail.”
“The stone crab’s claw is the same length as the Huntsman spider’s leg.”
“An elephant’s trunk is almost the same as a tiger’s tummy.”
“The beluga whale is the longest!”
“The stone crab’s claw is the same length as the Huntsman spider’s leg.”
“An elephant’s trunk is almost the same as a tiger’s tummy.”
“The beluga whale is the longest!”
As the measurements were displayed, the children were immediately interested in comparing the lengths. The ability to compare sets of objects and use language to describe their relationship (longer, shorter, the same, more, less) is an essential mathematical concept.
Young children use this type of comparison to determine who has more cars or Legos, and what they need to do to make the situation “fair”. These experiences help numbers (quantity) become meaningful to children and build the number relationships that are the foundation for understanding the concepts of addition and subtraction.
As we looked for a “common thread” in the children’s research questions, we noticed that many of the animals they chose to measure and draw lived in the African savanna. This observation provided the starting point for the next steps in our exploration...