© 2010 Pearson Education, Inc. All rights reserved Concepts of Measurement Chapter 13

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide NCTM Standard: Measurement Recognizing that objects have attributes that are measurable is the first step in the study of measurement. Children in prekindergarten through grade 2 begin by comparing and ordering objects using language such as longer and shorter. Length should be the focus in this grade band, but weight, time, area, and volume should also be explored.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide NCTM Standard: Measurement In grades 3–5, students should learn about area more thoroughly, as well as perimeter, volume, temperature, and angle measure. In these grades, they learn that measurements can be computed using formulas and need not always be taken directly with a measuring tool. Middle-grade students build on these earlier measurement experiences by continuing their study of perimeter, area, and volume and by beginning to explore derived measurements, such as speed. (p. 44)

Slide Copyright © 2010 Pearson Addison-Wesley. All rights reserved Linear Measurement  The English System  Converting Units of Measure  Dimensional Analysis (Unit Analysis)  The Metric System  Distance Properties  Distance Around a Plane Figure  Circumference of a Circle  Arc Length

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide The English System Unit Equivalent in Other Units yard3 feet foot12 inches mile1760 yd or 5280 ft

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Converting Units of Measure Convert 5.25 miles to yards 1 mi = 5280 ft, 1 ft =

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Dimensional Analysis (Unit Analysis) Dimensional Analysis a process to convert from one unit of measurement to another. The process works with unit ratios.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Example 13-1 If a cheetah is clocked at 60 miles per hour, what is its speed in feet per second?

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide PrefixSymbolFactor kilok1000 hectoh100 dekada10 decid0.1 centic0.01 millim0.001 The Metric System

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide UnitSymbol Relationship to Base Unit kilometerkm1000 m hectometerhm100 m dekameterdam10 m metermbase unit decimeterdm0.1 m centimetercm0.01 m millimetermm0.001 m

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Benchmarks for Metric Units

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Converting Metric Units

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Convert each of the following: a.1.4 km = _________ m b.285 mm = _________ m c.0.03 km = ________cm Example 13-3

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Distance Properties 1.The distance between any two points A and B is greater than or equal to 0 (AB  0). 2.The distance between any two points A and B is the same as the distance between B and A (AB = BA). 3.For any three points, A, B, and C, the distance between A and B plus the distance between B and C is greater than or equal to the distance between A and C (AB + BC  AC).

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Triangle Inequality The sum of the lengths of any two sides of a triangle is greater than the length of the third side. AB + BC > AC Can a triangle be made with sides that are 15 cm, 18 cm, and 37 cm? no

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Distance Around a Plane Figure Perimeter the length of a simple closed curve, or the sum of the lengths of the sides of a polygon.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Example 13-4 Find the perimeter of each of the shapes. 9 cm2ℓ + 2w

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Example 13-4 (continued) 4s4s170 mm What is the perimeter of a regular n-gon with side s? ns

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Circumference of a Circle Circle – the set of all points in a plane that are the same distance from a given point, the center. Circumference – the perimeter of a circle. Pi – the ratio between the circumference of a circle and the length of its diameter.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Arc Length

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide a.The circumference of a circle with radius 2 m b.The radius of a circle with circumference 15π m c.The length of a 25° arc of a circle with diameter 10 cm. d.The radius of an arc whose central angle is 87° and whose arc length is 154 cm. 4π m 7.5 m ≈ cm Example 13-5 Find each of the following: