Linear Measures, Weight, and Volume
Examples of standards measuressuch as a growth chart, weight scale, or masking tape on the floor to mark off distances in inches or feetshould be displayed and used to build awareness of linear measures (length, width, height). Children should be encouraged during play to describe nonstandard measurements, such as “How many blocks long/high is your castle?” (Charlesworth 2005.)
Activities for linear measurement can include:
- Using any long object (crayon, paper clip, straws, pipe cleaners, string) to measure objects or distances (classroom dimensions, rugs, furniture, height of children, etc.)
- Filling up cups, quart/liter/gallon containers with liquids or sand
- Counting the number of marbles it takes to fill different-sized jars
- Comparing measurements of objects in terms of longer, shorter, wider, narrower, etc.
- Cooking activities
- Using a balance to compare the weights of different objects and combinations of objects
- Pacing off longer distances such as the length of a hallway, sidewalk, or rows in the garden
- Using standard measurement tools such as rulers, yardsticks, or a tape measure
The Twenty-Four Foot Python: A Teachable Moment about Measurement
Ms. Deanna was working her way through Shel Silverstein’s book Light in the Attic (1981, p. 44) with her preschool/kindergarten class when she came to “Snake Problem”:
It’s not that I don’t care for snakes,
But oh what do you do
When a 24-foot python says . . .
I love you.
The poem prompted an animated discussion about how long a twenty-four-foot python would be. Many ideas were suggested, but they could not agree on a single answer. Ms. Deanna decided to follow up, asking what they could do to find out. The children said they wanted to make a twenty-four-foot-long paper python model. It became evident that the focus of the investigation was going to be accuracyexactly twenty-four feet, not an inch shorter or longer! Ms. Deanna produced a ruler, introducing it as a standard unit of measure for one foot. Using the ruler, the children quickly realized the classroom floor tiles all measured exactly one foot square. They spent several hours measuring off distances in the classroom in floor tiles but found that no matter how they measured, there was no twenty-four-foot space in which they could build their model.
Betty, in a flash of insight during a conversation about the problem said, “I know! The hallway is really long. What if we build it in the hallway?” They used masking tape to mark off the beginning and end of twenty-four feet and commenced building the python out of white mural paper, stuffing it with crumpled newspaper. They pored over books and online pictures of pythons to get an idea of how big the head should be in relation to the body. They “amputated” the first head they made when they realized it was too large proportionally and made a smaller one that was “just right.” They painted the python to replicate the coloring patterns they found in their pictures.
The children carried the python to show it to their friends in another classroom, and it lived a long life in their classroom, since Ms. Deanna hung it from the ceiling, where it became a frequent source of reference in other conversations about measurement and snakes.
Stop and Reflect
- How did this project involve children in mathematics and science processes reflected in the standards?
- How might you have documented the work children were doing to encourage ongoing discussion and problem solving?
Temperature
Understanding that temperature is something that can be measured is abstract and difficult for young children other than in general terms such as hot, cold, and warm. The classroom should include different tools for measuring temperature with displays in both analog and digital format, including oral, candy, meat, and refrigerator thermometers and outdoor digital and clock-style thermometers. Children can be encouraged to observe and record temperatures and engage in activities that involve materials that they can heat, melt, or freeze.
Children can also be encouraged to monitor the movement of mercury or dials as temperature changes. For example, many states’ licensing laws prohibit play outdoors when the temperature exceeds 90 degrees Fahrenheit; in applicable climates, if you mark the window thermometer at the 90 degree mark and children can be on the lookout for when the mercury or dial handle reaches that mark to announce “It’s 90!”
Time
Children confuse general use of the word time in the context of nap time, time to go, and so on with actual measurement of time. The various dimensions of timeclock, calendar, and historical timeare also abstract and take time to develop. Charlesworth (2005) describes three kinds of time: personal experience (past, present, future), social activity (routines/order), and cultural (fixed by clocks and calendar measurements).
You can promote basic concepts, such as that:
- Time is relative and cyclical
- Time can be represented as sequence or by duration
- Time always goes forward but we can talk about time that has passed.
- We measure time by equal intervals of different kinds (e.g., seconds, hours, days, years)
It is also important to develop a “time vocabulary”words like time, age, morning, afternoon, soon, tomorrow, yesterday, early, and late. Concrete tools for measuring time can be very helpful. For example, setting a kitchen timer or using a small sand hourglass while children are engaged in an activity helps them gain a sense of how clock time passes. This is particularly useful for helping impulsive children learn to wait for “just a minute” or “two minutes.” Other things you can do include:
- Counting days until birthdays, holidays, or an anticipated special event
- Talking about what children did over the weekend on Mondays
- Displaying the daily routine in a linear sequence of pictures
- Emphasizing what came before and what comes next in sequenced activities, such as following a recipe
- Gardening activities that offer opportunities to count days and measure growth over time
- “How many things can we do in a minute” games
- Installing a sundial outdoors
Currency
Children find American currency challenging because of centrationthey assume bigger means more and that therefore a nickel should be worth more than a dime or penny. They also have trouble with paper vs. coin. As with the representation of number as quantity in general, it takes time for them to understand the symbolism behind currencythat the nickel represents 5 cents, the dime 10 cents, the dollar 100 cents, and so on.
iStockphoto / Thinsktock
Children do learn about the value of money and its concrete uses (buying things) and can be engaged in using real money judiciously. For example, children in Mr. Dick’s 4-year-old class decided to use the outdoor playhouse to set up a store for selling snacks. They made juice popsicles, secured a “loan” to buy a big box of Goldfish crackers, and determined that each item would cost a penny to buy. They made signs for the store and dictated a note for home, asking parents to send their friends with pennies to spend in the store. They also “hired” children in the 2-year-old class to do jobs for them they didn’t want to do (such as sweeping out the playhouse) for a penny!
While the value placed on work and their product was not realistic in terms of the real world, it definitely showed their understanding of how money is used and critical to the exchange of goods and services. They carefully tracked their revenues over a week and were able to determine when they had enough pennies to pay back their loan. They were also ecstatic to find, at the end of the week, that they had made a profit of $3.34!
Data Analysis and Probability
Through daily experiences, children learn to answer questions of practical value by organizing, interpreting, and representing information with graphs and charts, pictures, and words. Graphing activities should move from concrete to abstract, starting with three-dimensional graphs using beads on a string, stacking rings on dowel rods, or interlocking Unifix cubes to represent each unit of data (Charlesworth, 2005). Two-dimensional charts, wipe-off boards, or lines, paper squares or circles taped on the floor or wall can be used to represent many different kinds of information as children’s understanding grows.
Whitin and Whitin (2003) suggest developmentally appropriate guidelines for using graphs with young children, pointing out that they can:
- Tie to a social context (favorite story, group activities)
- Represent the same data set in multiple ways
- Lead to open-ended discussion questions
- Encourage children to name/title graphs
- Revisit data during/after discussions
- Model/demonstrate throughout process of data collection and creating graphs (p. 39).
Graphs should represent data meaningful to children, such as shoe colors, birthdays, tracking number of children present per day for a week, or preferences. Very simple graphs can be done with children as young as two or three. For example, Ms. Stephanie conducted a unit on babies with her older 2-year-old class, including sampling baby foods. She made a picture graph with the different jar labels across the top and each child put their fingerprint underneath the picture of the food he or she liked the best.
Graphs can be effectively used to represent the cycle of prediction, testing, and results in an investigation of any kind. For example, if you plan to plant seeds, children can predict how many days it will take for them to sprout and compare predictions with observations. Any activity with an either/or outcome, such as sinking/floating can be graphed in terms of predictions/ outcomes. Likewise, any unknown future activity can be graphed by possible outcomes children suggest. Suppose you are reading a new story with a problem to solve. Before getting to the end of the book, children can suggest several possible endings and then you can graph their preferences and compare with the actual ending.
Figure 10.5 Three-Dimensional Graph
Three-dimensional graphs are a good way to begin using graphs with young children, since they involve the use of concrete objects that children can manipulate to represent data. This graph represents animals on land, on sea, and in the air.
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