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# Ways to Help Children Communicate and Share Mathematical Ideas (page 3)

By Pearson Allyn Bacon Prentice Hall
Updated on Dec 22, 2010

### Developing Referents for Measurement

When children are ready to use formal tools to measure, such as rulers, they should begin to develop referents for the units they will be using. For example, knowing that a centimeter is about the distance of the width across a child’s little finger at the first crease helps that child to “know” how big or how long a centimeter is. Putting the child’s finger across a centimeter ruler to check to see how close her finger’s width is to a centimeter helps the child to conceptualize the distance more precisely.

Next, you could ask the children to try to draw a line segment 1 centimeter long. They will look at their little fingers and try to replicate the distance on paper. Then take the centimeter ruler and check to see how close the drawn estimate of that length is. Next, ask the children to draw a line segment 5 centimeters long. Follow the same procedure of checking and reflecting on the results. Use many different lengths. Find other similar referents for 10 centimeters and so forth.

After some experience in constructing line segments of different lengths, you can engage the children in estimation activities. Place a few items in front of the children and ask them to estimate how many centimeters long each item is. They can use their fingers to help with this process. Placing their fingers across the length of an item can help them to see the concreteness of the linear distance.

After children have clearly developed a referent for a centimeter, another approach to estimation can be taken. You can ask the children questions such as “Ifound a bug on the sidewalk today. Do you think it was one centimeter long, 50 centimeters long, or one hundred centimeters long?” Such questions get at conceptualization of what a centimeter is. Of course, fun stories can be told when they choose a “silly” answer. After all, silliness occurs when there is a break in what they understand at a logical level. A 100-centimeter-long bug, oh my! What fun stories and art could be constructed about such a creature?

A similar approach could be taken with a milliliter. If children could hold a cubic centimeter (a base-10 unit) in their hands and imagine it filled with water, they would have a referent for how much a milliliter is, because they are the same thing (Figure 4.9). Another referent for milliliter is how much water a scooped-out jelly bean will hold. Using a very small container, say, 10-milliliter capacity, children could estimate how many times they would have to fill the centimeter cube or the jelly bean, and pour it into the container to fill it up. After they estimate how many milliliters will fill it, they should actually fill it up and measure it with a milliliter measure. This small container could be labeled and used as a referent itself.

After more of this type of experimentation, you could ask questions that get at conceptualization of the amount of a milliliter. For example, “Today I washed my hair. Do you think that I used eight milliliters of shampoo, 60 milliliters of shampoo, or five hundred milliliters of shampoo?” Again the logical answer is 8 milliliters, but we could conjure up interesting scenarios about what would happen if we used 500 milliliters of shampoo in our bathtubs. Imaginations can take charge when answering these types of measurement questions.

It is a good practice to apply a child’s understanding of referent to estimation and problem solving. For example, if we have a referent developed for millimeter, centimeter, and meter, we can ask children fun questions such as these:

• I found a bug on my driveway this morning. It was about 8 _______ long! (mm,cm, m)
• If I wanted to measure how tall my pencil is, I would use _______. (cm, m)
• I want to know how much water my aquarium holds. I would measure the water with a _______ measure. (l, ml)

 Confusion often occurs between the use of the terms milliliters and cubic centimeters. A liter is the volume defined as a cube with each side being 10 centimeters. A cube 10 cm by 10 cm by 10 cm would have 1,000 cubic centimeters. Each cubic centimeter is one milliliter. A milliliter is one thousandth of a liter. They are just different ways of saying the same thing.
Volume

For young children, it is recommended that you use only common metric measurements—measurements that are often referred to in their conversations, activities, or their listening or speaking vocabulary. Solid experience with commonly used metric measurements will build a solid foundation for using other, less common increments of metric measurements in later experiences.

It is important to make your own referents based on your own situations and environment. When possible and appropriate, measure out these amounts and construct a “Referent Chart” with the children.