Measuring Up:Measurement Error

Math Teacher Leader WorkshopOctober 3rd & 4th, 2006

Henry KepnerKevin McLeodDeAnn HuinkerConnie LaughlinKaren CorlynLee Ann PruskePaige Richards

Developed by the Milwaukee Mathematics Partnership (MMP) 1with support by the National Science Foundation under Grant No. 0314898.

Session Goals

To clarify understanding of:

Direct and indirect measurement;

Measurement of area (both direct and indirect); and

The role and effects of error in the measurement process, particularly indirect measurement.

Developed by the Milwaukee Mathematics Partnership (MMP) 2with support by the National Science Foundation under Grant No. 0314898.

How accurate do you have to be?

Developed by the Milwaukee Mathematics Partnership (MMP) 3with support by the National Science Foundation under Grant No. 0314898.

Curriculum Focal Points and Connections for Grade 4

Measurement: Developing an understanding of area and determining the areas of two-dimensional shapes

Students recognize area as an attribute of two-dimensional regions. They learn that they can quantify area by finding the total number of same-sized units of area that cover the shape without gaps or overlaps. They understand that a square that is 1 unit on a side is the standard unit for measuring area. They select appropriate units, strategies (e.g., decomposing shapes), and tools for solving problems that involve estimating or measuring area. Students connect area measure to the area model that they have used to represent multiplication, and they use this connection to justify the formula for the area of a rectangle.

Developed by the Milwaukee Mathematics Partnership (MMP) 4with support by the National Science Foundation under Grant No. 0314898.

Wisconsin Definitions 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.

Developed by the Milwaukee Mathematics Partnership (MMP) 5with support by the National Science Foundation under Grant No. 0314898.

Developed by the Milwaukee Mathematics Partnership (MMP) 6with support by the National Science Foundation under Grant No. 0314898.

B

D

C

A

Quadrilateral Direct Measurements

Unit Segment AB

Segment BC

Segment CD

Segment AD

1 inch 5 6 5 6

21 inch 5 6 2

1 5 6 21

21 inch 10 ( 2

1 in.) 13 ( 21 in.) 10 ( 2

1 in.) 13 ( 21 in.)

41 inch 4 4

3 6 42 4 4

3 6 42

41 inch 19 ( 4

1 in.) 26 ( 41 in.) 19 ( 4

1 in.) 26 ( 41 in.)

81 inch 4 8

6 6 83 4 8

6 6 83

81 inch 38 ( 8

1 in.) 51 ( 81 in.) 38 ( 8

1 in.) 51 ( 81 in.)

161 inch 416

13 6165 416

13 6165

161 inch 77 (16

1 in.) 101 (161 in.) 77 (16

1 in.) 101 (161 in.)

Developed by the Milwaukee Mathematics Partnership (MMP) 7with support by the National Science Foundation under Grant No. 0314898.

What do the various measurements allow you to say about the perimeter of

rectangle ABCD?

Developed by the Milwaukee Mathematics Partnership (MMP) 8with support by the National Science Foundation under Grant No. 0314898.

Measurement of Rectangle ABCD

1 inch ¼ inch

Length of AB(range)

Length of AB(tolerance)

Length of BC(range)

Length of BC(tolerance)

Developed by the Milwaukee Mathematics Partnership (MMP) 9with support by the National Science Foundation under Grant No. 0314898.

The Meaning of “Area”

Jigsaw Reading ActivityFrom NCTM “Learning and Teaching Measurement.”

Group A: p. 10-14 Area Measurement

Group B: p. 122-126 Students’ thinking

Group C: p. 126-129 & 135-136 The Units

Jigsaw Reading Focus Questions

What are some student misconceptions about area measurement?

What instructional activities could you use to help overcome these misconceptions?

Developed by the Milwaukee Mathematics Partnership (MMP) 10with support by the National Science Foundation under Grant No. 0314898.

Making Connections to Navigations Through Measurement

K-2 p. 57 Cover Up ( gr. 1-2)

3-5 p. 53 Big Cover Up (gr. 3-4)

3-5 p. 58 Stuck on Stickers (gr. 3-4)

6-8 p. 32 Seeing is Believing (gr. 6-8)

Making Connections to Navigations Through Geometry

6-8 p. 73 Minimizing Perimeter (gr. 6-8)

Developed by the Milwaukee Mathematics Partnership (MMP) 11with support by the National Science Foundation under Grant No. 0314898.

Big Ideas of Measurement

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.

The degree of accuracy in measurement depends upon the problem context and the intended use of the information obtained.

Personal benchmarks deepen understanding of standard units and make estimation meaningful.

Developed by the Milwaukee Mathematics Partnership (MMP) 12with support by the National Science Foundation under Grant No. 0314898.

Don’t forget . . .

Homework Assignment

1. Do this measurement of segments with your colleagues using various units.

2. Take an inventory of measuring tools in your school. Don’t forget time, weight, capacity (volume), temperature, angle measure, etc.

Developed by the Milwaukee Mathematics Partnership (MMP) 13with support by the National Science Foundation under Grant No. 0314898.

Wisconsin State DescriptorsGrade 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.

Developed by the Milwaukee Mathematics Partnership (MMP) 14with support by the National Science Foundation under Grant No. 0314898.