MEASUREMENT

Activity 1 (Small-Group Activity)
Estimating and Measuring

• penny, nickel, dime, quarter, half dollar, silver dollar, Susan B. Anthony dollar
• ruler (cm with mm marked)
• a postal scale or balance
• calipers
• tape measure (English) or yardstick or meter stick
• Reference Sheet R1

### The Silver Dollar

Several years ago, when the prices of items in vending machines increased, it seemed like a good idea to mint a new silver dollar that was smaller than the silver dollar for use in these machines. The design for a Susan B. Anthony coin was commissioned and it was introduced with much fanfare. As you probably have noticed, however, we don't use the coin much today.

Measure the coins in as many ways as you can think of and offer some reasons for the failure of this coin. Justify your conjecture by using the measurements you made.

If you had been commissioned to design the coin, what would you have done differently?

### What We Measure

When we measure something, we are finding a number to describe something that is present in varying amounts but which we can't just count like we would count twenty dimes. One reason we measure is so that we can compare two items. It is difficult to tell how much two similar hams should cost just by lifting them. If I pay a fair price, the value or cost of a ham is tied to its weight. Cost, weight, length, and temperature are attributes that we measure. Dollars, pounds, centimeters, and degrees are units used to tell how much of the attribute an object has.

Make a list of attributes we commonly measure, and tell what unit or units are used to measure each attribute.

### A World of Units

Sometimes many units are invented to measure the same attribute. For example, the weight of a pill is in milligrams, and the weight of a serving of spaghetti is in ounces. The weight of a person in America is in pounds. In England it used to be in stones and in France it is in kilograms. The weight of quarried stone is in tons.

Make a list of units in both the English and the metric system that are used in measuring the attribute of length. For each, tell what type of attribute you might measure with that unit. List at least ten different units.

### "I am a Ruler"

Most of us don't carry around measuring tools. When a volleyball player wants to check the height of the net, she or he stands in the center of the court and raises their arm. Although it will vary from player to player, a spiker will know where the top of net should touch her or his arm (and will complain if the net is too high).

Use a ruler and tape measure to find objects in your classroom that you could use to approximate a millimeter, centimeter, decimeter, meter, inch, foot, and yard. Using the objects, estimate the width of a sheet of paper, the length of a car key, the length of the hall and the height of the desk. Check by using an appropriate measuring tool.

### Another Brick in the Wall

Estimate the height of your school. Base your estimate on the measured height of a brick in the wall, the height of a window, or the height of one story. Explain in writing how you arrived at your estimate.

Estimate first and then measure the large objects listed in the table on the Reference Sheet. Remember to record the unit of measure in the table. Use the two tape measures to measure each object. Remember not to pull the tape out too far; this may damage the tool.

### Tools for all Seasons

The two tape measures have the same units but one has more subdivisions for each unit. List situations in which each measurement would be appropriate. When would it be appropriate to use only an estimate?

### The Estimator

In what occupations is estimation an important part of the job? Give examples of how estimation would be used in each. List any estimations you made today with respect to time, money, distance, temperature, and velocity.