Cattaraugus Allegany BOCES Math Science Technology DeptCattaraugus Allegany BOCESOlean, New York, US,

June 24, 2008

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This document contains information needed to complete the Intermediate Level Measurement Math Kit.

This wiki version can be edited or built up with other materials on the same topic by members of the Curriki community. The entire Intermediate Level Measurement collection is also available as downloadable PDFs.

- Mathematics > General

- Grade 3
- Grade 4
- Grade 5
- Grade 6
- Grade 7
- Grade 8

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This resource was reviewed using the Curriki Review rubric and received an overall Curriki Review System rating of 3, as of -0001-11-30.

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This resource received a 3* rating because it is part of Intermediate Level Measurement Math Kit, which received a rating of 3-Exemplary in the Curriki Review System and which you can see here: http://www.curriki.org/xwiki/bin/view/Coll_cabocesmst/IntermediateLevelMeasurementMathKit

**Unit Overview**

This unit provides students with the opportunity to measure various objects and use their data to determine area, volume, radius, diameter, and density. They will use Math rulers, protractors, and Vernier Calipers to make their measurements rounding to four different scales. They will measure the radius and diameter of a cylinder and use Pi to calculate the area of various cylindrical objects. Students will measure the circumference and determine the surface area

of a sphere and using the thickness of the wall of a hollow sphere, determine the volume inside the sphere as well. The mathematical skills emphasized in Intermediate Level Measurement are measuring, collecting data, and calculating for volume, area, and density.

**Scheduling**

This unit may take from a day if you choose to use only one of the measurement activities to the entire year to complete depending upon the goals of the teacher and the interests of the students.

**Materials to be obtained
locally, in addition to other materials required by the individual Learning
Experiences:**

Please make one student activity book for each student.

water

chart paper

felt tip markers

calculator

8.5 x 11 white paper

**About the Format**

Each learning experience is numbered and titled. Under each title is the objective for the learning experience.

Each learning experience page has two parts. The first part lists materials, preparations, basic skill processes, an evaluation strategy, and vocabulary. The evaluation strategy is for the teacher to use when judging the student’s understanding of the learning experience.

The second part begins with a “Focus Question” which is typed in italicized print. The purpose of the “Focus Question” is to guide the teacher’s instruction toward the main idea of the learning experience. The “Focus Question” is not to be answered by the students. The learning experience includes directions for students, illustrations, and discussion questions. These discussion questions can be used as a basis for class interaction.

**Background
Information**

A prism is a three-dimensional figure that has two (2) congruent and parallel faces called bases, which are polygons. The shape of bases is used to identify the type of prism. The space occupied by a prism is its volume. Volume is measured in cubic units. The circumference of a circle is about 3x as large as its diameter. The exact factor is ? (Pi). We write this as C = ? x d.

**Perimeter**

Perimeter is the linear distance around an object or figure. Also it is the boundary of a closed plane figure.

**Area**

Area is the surface included within a set of lines; specifically: the number of square units (e.g., square inches, square centimeters) a figure contains. The square units used to measure area are often based on multiplying units of length and width.

**Volume**

Volume is the amount of space occupied by a three-dimensional object as measured in cubic units (e.g., cubic inches, cubic centimeters, liters). The cubic units used to measure volume are often based on multiplying units of length, width, and height.

**Vernier Calipers**

The Vernier calipers are used to make accurate measurements of both “outside” and “inside” dimensions of objects by using both fixed scales and a Vernier scale on a sliding piece. The Vernier Calipers consist of a “ruler” with fixed scale(s) etched on it and a fixed “jaw” at one end. The other part is a slider with a “jaw” and a viewing window (with Vernier scale). The Vernier scale (Pierre Vernier 1580-1637) allows an accurate reading to be made to one tenth of the smallest division of a fixed ruler. As an example, if you have a scale in centimeters with ten divisions per centimeter (i.e. millimeters), then by using a Vernier scale you can make an accurate measurement to 1/10th of a millimeter.

Hold the Vernier calipers in your right hand with the
“window” on the slider facing you and the side of the adjusting guide under
your thumb. To make an outside measurement, hold the object to be measured in
your left hand, open the “jaws” of the Vernier Calipers until they are a bit
wider than the object to be measured. This is done by moving the adjusting
guide with your thumb. **Note: When the jaws
are opened, a thin metal guide is extended from the end of the Vernier Calipers.
This can cause injury! Use caution!**

Next place the object to be measured between the jaws and
slide the jaw until it firmly clamps the object. You can hold the Vernier
Calipers firmly and then carefully remove the object from between the jaws to
make your reading. Look at the position of the Vernier scale in relation to the
fixed scale as seen in the window of the slide. The measurement will be the
total of that part of the fixed scale to the left of the Vernier scale ** plus**
that number of divisions of the Vernier scale that are to the left of the
position where the two scales most nearly line up. This number is expressed as
a decimal. See example below.

1) Take a "zero reading". In theory, the Vernier Calipers should be perfectly calibrated. In reality, they usually are not. With the jaws totally closed, measure how far apart the first lines on the top and the bottom scale are. You will have to add or subtract this from the measurement you get at the end.

(2) Place the jaws around the thing that you want to measure and close them tightly. The distance between the jaws is the distance that you are trying to find.

(3) Read the measurement. Now measure the distance between the first lines on the top and bottom scale again. Add or subtract out what you got in step (1) and you will find out how far the bottom scale moved when you spread it open around the object. This distance is the width of the object.

Notice that the value for the upper scale is determined by where the 0 on the lower scale lines up with the upper scale and the number on the lower scale is determined by finding which mark on the lower scale best lines up with ANY mark on the upper scale.

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