Measurement System Basics. What is Measurement? What is Fit? Analog vs. Measurement Environment. Measurement System Types and Characteristics. And what that is is that light, bouncing off a mirror will bounce off at a similar angle.
And by similar I mean congruent. So what we've done is we've created congruent angles there. So again what I did is I'm backed all the way up, I kept the mirror in place or I guess I could stay in place and have someone move the mirror until I could see just very tippy top of whatever I'm trying to measure. The way that we create similar triangles here is assuming I'm standing perfectly straight. So this is a right angle. And assuming that nature did a good job of growing this tree and this is a right angle, then we have an angle angle shortcut so we have 2 similar triangles which I could draw down below.
So that will be your right angle and then this angle would be congruent to the angle formed by light bouncing off that mirror.
So you could use my height which you can measure, you can measure the distance between me and the mirror, you can measure the distance between the mirror and your object, and you could use that proportion to find that missing side, the height of your object.
So that's one way of using similar triangles to measure something tall. The second method uses shadows. So let's say you had the sun up here and at the same time you measured a person's shadow and a shadow of whatever you're trying to measure. So let's say it was a tree. So here is the sun and let's say at some point in time I cast a shadow like that and then the object I'm trying to measure in this case a tree cast a shadow which will be a little bit longer.
Investigate the circumference and area of a circle. Explore several methods for finding the volume of objects, using both standard cubic units and non-standard measures. Explore how volume formulas for solid objects such as spheres, cylinders, and cones are derived and related. Examine the relationships between area and perimeter when one measure is fixed. Determine which shapes maximize area while minimizing perimeter, and vice versa.
Explore the proportional relationship between surface area and volume. Construct open-box containers, and use graphs to approximate the dimensions of the resulting rectangular prism that holds the maximum volume.
Watch this program in the 10th session for K-2 teachers. Explore how the concepts developed in this course can be applied through case studies of K-2 teachers former course participants who have adapted their new knowledge to their classrooms , as well as a set of typical measurement problems for K-2 students.
Watch this program in the 10th session for grade teachers. Explore how the concepts developed in this course can be applied through case studies of grade teachers former course participants who have adapted their new knowledge to their classrooms , as well as a set of typical measurement problems for grade students. Subscribe to our monthly newsletter for announcements, education- related info, and more!
Indirect Measurement and Trigonometry Mathematics K-2 , , Session 2 Fundamentals of Measurement Investigate the difference between a count and a measure, and examine essential ideas such as unit iteration, partitioning, and the compensatory principle. Session 3 The Metric System Learn about the relationships between units in the metric system and how to represent quantities using different units.
Session 4 Angle Measurement Review appropriate notation for angle measurement, and describe angles in terms of the amount of turn. Session 5 Indirect Measurement and Trigonometry Learn how to use the concept of similarity to measure distance indirectly, using methods involving similar triangles, shadows, and transits. Session 6 Area Learn that area is a measure of how much surface is covered. Session 8 Volume Explore several methods for finding the volume of objects, using both standard cubic units and non-standard measures.
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