MEASUREMENT

Activity 1 (Small-Group Activity)
Estimating and Measuring

Students will conjecture about possible solutions to problems using data collected by measuring length, weight, etc. Students estimate and measure small and large objects. Use with the Student Copy and the Reference Copy.

• To estimate, make, and use measurements to collect data, describe and compare phenomena, and apply to real-world problems.
• To select appropriate units and tools to measure to the degree of precision required in a particular situation.
• To distinguish among attributes that we measure and among units used to measure those attributes.
• To look at the role of estimation and precision in measurement.

### The Silver Dollar

Students should measure diameter, thickness, circumference, weight, and coin value. A discussion might also look at tensile strength, or ease of bending a coin. The similarity of the quarter and the Susan B. caused inconvenience and mistakes in choosing the correct coin as people made change.

### What We Measure

Sample attributes/units follow:

Attribute Units
weight g, mg, kg, lb, oz, ton
distance m, km, dm, mm, cm, in, yd, mile
time hours, minutes, hours, years
temperature degrees Fahrenheit or Celsius
volume cc, in3, ft3, cup, pint, gallon, liter
value dollars, cents, pesos, francs, marks
area in2, cm2, yd2, or acres
sobriety blood alchohol level
speed or velocity mph or fps

### World of Units

mm—thickness of a dime,
cm—width of a book or stamp,
dm—width of a desk,
m—height of the room,
km—distance to Indianapolis,
furlongs—horse race,
inch—length of a sheet of paper,
foot—width of a room,
yard—length of fabric,
mile—distance to Paris,
light years—distance to stars.

### "I am a Ruler"

Answers will vary depending on the objects and units chosen. Note that finger length, arm length, etc. should be accepted as "objects."

### Another Brick in the Wall

Students will need to go outside and measure the height of one part of the school to arrive at the estimate. Their written estimates should show how the height of the school is based on their measurements (e.g., 10 bricks are 24" high, the school is 200 bricks high [20 groups of 10], so its height is about 20 x 2' or 40 feet).

The point is that different units of measurement can be useful in different situations, depending on how large the object being measured is and how much precision is needed.

### Tools for all Seasons

The point of the two tape measures is the issue of precision. A greater number of marks used to subdivide a unit makes it possible to refine a measurement. Although a more precise answer can be obtained by using an instrument with more subdivisions, students should realize that an exact answer is impossible. Answers will vary. It is better to come up with a good estimate when a measurement is not necessary or appropriate. Examples are how much food to serve for dinner, how long it will take to drive to school, and how many miles you can drive before you must fill up the family car with gasoline. If I am paying for fabric, I expect the material to be measured, probably to the nearest inch. If I am laying carpet or putting up drapes, rounding to the nearest inch may cause the carpet to buckle or leave a gaping hole.

### The Estimator

Answers will vary. All jobs include some form of estimation.

### Closing Discussion

Did your estimates improve as you got more experience? Hopefully, students will find that their estimates get better as they go along. Collection of data often includes measurement. How does decision-making require the use of data and hence measurement in determining who plays center on the basketball team? Some considerations might be player height, player arm span, number of shots taken and percentage made from within a given distance of the basket, jumping ability, and rebounding average.

Area 10 Mathematics and Technology Professional Development Center
Permission is granted to duplicate these materials for classroom use.

Last updated on 1/30/1999