Activity 1 (Small-Group Activity)
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.
The Silver DollarStudents 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 MeasureSample attributes/units follow:
World of Unitsmm—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,
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 WallStudents 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).
A Head for MeasurementThe 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 SeasonsThe 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 EstimatorAnswers will vary. All jobs include some form of estimation.
Closing DiscussionDid 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