Measuring Up:

Personal Benchmarks

Math Teacher Leader Seminar

September 16th & 23rd, 2006

Henry Kepner

Kevin McLeod

DeAnn Huinker

Connie Laughlin

Karen Corlyn

Lee Ann Pruske

Paige Richards


Session Goals

To develop a better understanding of personal benchmarks and familiarity with their use.

To clarify understanding of:

  • measurable attributes;
  • direct and indirect measurement;
  • the role and effects of error in the measurement process.

Personal Benchmarks

Share your personal benchmarks for a meter with the participants at your table.

Now, share your personal benchmarks for an inch.

Focus Question:

Why are these benchmarks useful?

“Benchmarks as Tools for Developing Measurement Sense.”

Jigsaw Reading

Read pages 62- 66 of the article,

  • Enhance Students’ Understanding of Measurement Systems.
  • Teach Measurement Principles.
  • Conclusion

Focus Question:

How can you help your students use personal benchmarks to build understanding of the measurement principles?

State Descriptors

Grade levels where precision of

measurement is specified.

Grade 1 - Measure to 1 inch

Grade 2 - Measure to 1 inch (or centimeter)

Grade 3 - Measure to 1/2 inch (or centimeter)

Grade 4 - Measure to 1/4 inch (or centimeter)

Grade 5 - Measure to 1/8 inch (centimeter or millimeter)

Grade 6 - Measure to 1/16 inch (centimeter or millimeter)

Using non-standard measurement begins in Kindergarten and is continued through 4th grade.

Measuring to the nearest ...

Direct Measurement

Use the ruler on your table to measure the dimensions of quadrilateral ABCDto the nearest unit.

Please have a different person measure each side of the quadrilateral.

Use the sheet to record your answers.

Quadrilateral Direct Measurements

Unit of Measure / Segment

AB

/ Segment

BC

/ Segment

CD

/ Segment

AD

WisconsinDefinitions of

Direct & Indirect Measurement

Direct measurement. A process of obtaining the measurement of some entity by reading a measuring tool, such as a ruler for length, a scale for weight, or a protractor for angle size.

Indirect measurement. A process where the measurement of some entity is not obtained by the direct reading of a measuring tool, or by counting of units superimposed alongside or on that entity. For example if the length and width of a rectangle are multiplied to find the area of that rectangle, then the area is an indirect measurement.

Big Mathematical Ideas

  • There is always error in measurement.
  • The more precise the unit of measure, the smaller the error.
  • A direct measurement is a number and its unit obtained by a single reading of a measurement tool.
  • An indirect measurement is a number and its unit obtained by combining one or more direct measurements.
  • Errors in measurement are compounded in indirect measurement.
  • Personal benchmarks deepen understanding of standard units and make estimation meaningful.

Homework Assignment

  1. Do this measurement of segments with your colleagues using various units.
  1. Take an inventory of measuring tools in your school. Don’t forget time, weight, capacity (volume), temperature, angle measure, etc.

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