Measurement

Measurement is one of the strands that lends itself to students being able to connect aspects of their own life to mathematics. While students may have experience with measurement, it is important for them to understand the attributes of measurement along with the units and proccesses that are woven in to their comprehension. According to PSSM, students should be able to understand how objects are measured, be able to convert units within those measurements, and apply this knowledge to using appropriate techniques and procedures to use tools for measuring in meaningful ways. The following interactives use these principles, with the help of technology, to support students understanding of how measurement relates to the world around them.


 * Measurement Evaluation #1 **

 **//An interactive lesson in measuring area and perimeter //** || **Measurement ** Area and Perimeter Measurement || * || //Rationale //: Students are given the array method of measuring area and perimeter first and must count squares in order to determine these measurements. Students are then introduced to the formulas for solving area and perimeter and are given several problems to practice their chosen strategy. Students are then required to apply this knowledge to solve the fence and fertilizer problem. Then students create tables for both perimeter and area of rectangles and squares to discover the relationship between counting squares and the actual formula. ||
 *  **//[|Area-Rancher ‘Rithmetic 3] //**
 * **Which standard? **
 * [|understand measurable attributes] of objects and the units, systems, and processes of measurement;
 * [|apply appropriate techniques], tools, and formulas to determine measurements. || * || //<span style="font-family: 'Times New Roman','serif';">Rationale //<span style="font-family: 'Times New Roman','serif';">: In this interactive, students are given measurements of various rectangles and use the formula to find the area and perimeter of the rectangles. Detailed examples and formulas for solving simple area and perimeter of given shapes are explained, modeled and available for practice. Students help ranchers calculate the amount of barbed wire needed to keep cattle on their property, calculate the amount of fertilizer ranchers need by solving area of their land and answer questions about perimeter and area with given shapes/information. ||
 * **<span style="color: green; font-family: 'Times New Roman','serif';">What mathematical content is being learned (or intended to be learned)? **
 * **<span style="color: green; font-family: 'Times New Roman','serif';">Is the focus on instrumental or relational understanding? **

<span style="font-family: 'Times New Roman','serif'; line-height: normal; margin: 0in 0in 0pt;">Instrumental understanding <span style="font-family: 'Times New Roman','serif'; line-height: normal; margin: 0in 0in 10pt;">Relational understanding || <span style="color: white; font-family: 'Times New Roman','serif'; line-height: normal; margin: 0in 0in 0pt;">* || //<span style="font-family: 'Times New Roman','serif';">Rationale //<span style="font-family: 'Times New Roman','serif';">: There is a mixture between instrumental understanding and relational understanding. Students are given two methods of solving area problems and practice each of these methods. Students then apply this knowledge in real-world contexts to build a fence and spread fertilizer. Students also use an organized table to discover the relationships between side lengths and the formulas. ||
 * **<span style="color: green; font-family: 'Times New Roman','serif';">What role does technology play? ** || <span style="color: white; font-family: 'Times New Roman','serif'; line-height: normal; margin: 0in 0in 0pt;">* || //<span style="font-family: 'Times New Roman','serif';">Response //<span style="font-family: 'Times New Roman','serif';">: Technology serves as an informational tool to help students discover the relationships and applications of perimeter and area. Although formulas are given, students must apply them in real world contexts and identify which formula is appropriate to use and why. Students must think about the ideas presented to them critically and collaborate at the end of the activity to communicate how rectangular and square measurements can help them derive each formula. ||
 * **<span style="color: green; font-family: 'Times New Roman','serif';">What instructional function(s) does the resource serve? **

<span style="font-family: 'Times New Roman','serif'; line-height: normal; margin: 0in 0in 0pt;">Practice <span style="font-family: 'Times New Roman','serif'; line-height: normal; margin: 0in 0in 0pt;">Direct Instruction · <span style="color: black; font-family: 'Times New Roman','serif';">Learning through exploration  || <span style="color: white; font-family: 'Times New Roman','serif'; line-height: normal; margin: 0in 0in 0pt;">* || //<span style="font-family: 'Times New Roman','serif';">Rationale //<span style="font-family: 'Times New Roman','serif';">: This lesson is designed to help students develop formulas and procedures for determining the perimeter and area of rectangles and squares. Through direct instruction, students are introduced to counting squares and the formulas for each measurement. Students then practice calculating the perimeter and area of common objects as well as helping a rancher solve applied problems. Through exploration, students learn and discover the relationship between the counting method and the formulas and realize how people apply measurement skills in everyday situations. ||
 * **<span style="color: green; font-family: 'Times New Roman','serif';">What kinds of representations of the mathematics are used? **

<span style="font-family: 'Times New Roman','serif'; line-height: normal;">symbolic <span style="font-family: 'Times New Roman','serif'; line-height: normal;">graphical <span style="font-family: 'Times New Roman','serif'; line-height: normal;">visual/spatial <span style="font-family: 'Times New Roman','serif'; line-height: normal;">concrete or real world objects <span style="font-family: 'Times New Roman','serif'; line-height: normal;">dynamic || <span style="color: white; font-family: 'Times New Roman','serif'; line-height: normal; margin: 0in 0in 0pt;">* || //<span style="font-family: 'Times New Roman','serif';">Rationale //<span style="font-family: 'Times New Roman','serif';">: The interactive uses a variety of ways to represent math. Symbolically, students enter numerical terms after making appropriate calculations. The concept of area is displayed in an array model with inner boxes being colored in to determine how many squares “fit” in the designated shape. Students also use graph paper to create their own array models and determine area and perimeter. Throughout the interactive students are given visuals of the objects they are measuring and pictorial representations of fertilizer and fencing are used. Students complete variety of dynamic movements from drag and drop to “sliding” to the next problem. ||

<span style="display: block; line-height: normal; margin: 0in 0in 0pt; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 44.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;"> **//<span style="font-family: 'Times New Roman','serif'; font-size: 16pt;">An interactive lesson in measuring length, mass, and volume //** || **<span style="color: green; font-family: 'Times New Roman','serif';">Measurement ** <span style="font-family: 'Times New Roman','serif'; line-height: normal; margin: 0in 0in 10pt;">Process of Measurement || <span style="color: white; font-family: 'Times New Roman','serif'; line-height: normal; margin: 0in 0in 0pt;">* || //<span style="font-family: 'Times New Roman','serif';">Rationale //<span style="font-family: 'Times New Roman','serif';">: Students are given a menu board that allows them to choose which measurement process they will encounter. Once they are within those parameters, a brief explanation of the topic is discussed and then the user must measure different real world objects using the appropriate tool and unit. Students must also choose appropriate units when determining length, mass, or volume. ||
 * <span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 130%;">Measurement Evaluation #2 **
 * <span style="display: block; line-height: normal; margin: 0in 0in 0pt; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 44.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;"> **//<span style="font-family: 'Times New Roman','serif'; font-size: 24pt;">[|Measurements] //**
 * **<span style="color: green; font-family: 'Times New Roman','serif';">Which standard? **
 * <span style="font-family: 'Times New Roman','serif'; line-height: normal; margin: 0in 0in 10pt; tabstops: list .5in;">[|understand measurable attributes] of objects and the units, systems, and processes of measurement;
 * <span style="font-family: 'Times New Roman','serif'; line-height: normal; margin: 0in 0in 10pt; tabstops: list .5in;">[|apply appropriate techniques], tools, and formulas to determine measurements. || <span style="color: white; font-family: 'Times New Roman','serif'; line-height: normal; margin: 0in 0in 0pt;">* || //<span style="font-family: 'Times New Roman','serif';">Rationale //<span style="font-family: 'Times New Roman','serif';">: In this interactive tool, students are engaged by the problem that Jack the Builder doesn’t know how to measure things appropriately or which units to use when he is building things. Students must devise ways of measuring length, mass, and volume in metric units in order to help Jack. Students go through a series of practice selections for each concept and must identify appropriate units at each phase. Students use rulers, metric sticks, graduated cylinders and other tools to determine appropriate measures. ||
 * **<span style="color: green; font-family: 'Times New Roman','serif';">What mathematical content is being learned (or intended to be learned)? **
 * **<span style="color: green; font-family: 'Times New Roman','serif';">Is the focus on instrumental or relational understanding? **

<span style="font-family: 'Times New Roman','serif'; line-height: normal; margin: 0in 0in 0pt;">Instrumental understanding <span style="font-family: 'Times New Roman','serif'; line-height: normal; margin: 0in 0in 10pt;">Relational understanding || <span style="color: white; font-family: 'Times New Roman','serif'; line-height: normal; margin: 0in 0in 0pt;">* || //<span style="font-family: 'Times New Roman','serif';">Rationale //<span style="font-family: 'Times New Roman','serif';">: This applet focuses mostly on the instrumental understanding of how to measure different objects that students encounter within the interactive. Students are given instructions and procedures for developing their measurements, and also must spell metric units correctly (in the British form, i.e. centimetres). Students receive a lot of exposure in measuring different things that they regularly see in the real world. Students can connect how measurement is used to “help” Jack. ||
 * **<span style="color: green; font-family: 'Times New Roman','serif';">What role does technology play? ** || <span style="color: white; font-family: 'Times New Roman','serif'; line-height: normal; margin: 0in 0in 0pt;">* || //<span style="font-family: 'Times New Roman','serif';">Response //<span style="font-family: 'Times New Roman','serif';">: This technology gives students access to the varying tools they need to measure with along with the units they will need to measure them. Students will have to have prior knowledge of these concepts before completing this activity. Using the virtual measurement tools, students can measure many things in a quick amount of time without having to gather all the necessary materials to actually measure them. This simplification gives students more time to focus on measurement procedures and correctly identifying units of measure. ||
 * **<span style="color: green; font-family: 'Times New Roman','serif';">What instructional function(s) does the resource serve? **

<span style="font-family: 'Times New Roman','serif'; line-height: normal; margin: 0in 0in 0pt;">Practice · <span style="color: black; font-family: 'Times New Roman','serif';">learning through exploration  || <span style="color: white; font-family: 'Times New Roman','serif'; line-height: normal; margin: 0in 0in 0pt;">* || //<span style="font-family: 'Times New Roman','serif';">Rationale //<span style="font-family: 'Times New Roman','serif';">: Students are given no explicit direction in measuring or in using the tools necessary to measure, so students must use prior knowledge in order to practice the concepts within this interactive. Through exploration, students begin to connect that liquids are measured in graduated cylinders in liters and represent volume, solids are measured in scales using grams and represent mass, and that distances are measured in meters and constitute lengths of objects. ||
 * **<span style="color: green; font-family: 'Times New Roman','serif';">What kinds of representations of the mathematics are used? **

<span style="font-family: 'Times New Roman','serif'; line-height: normal;">symbolic <span style="font-family: 'Times New Roman','serif'; line-height: normal;">concrete or real world objects <span style="font-family: 'Times New Roman','serif'; line-height: normal;">dynamic || <span style="color: white; font-family: 'Times New Roman','serif'; line-height: normal; margin: 0in 0in 0pt;">* || //<span style="font-family: 'Times New Roman','serif';">Rationale //<span style="font-family: 'Times New Roman','serif';">: students represent math symbolically in this applet by typing numeric values that represent mass, length or volume. The interactive requires students to write each measurement using correct units, so students need to be able to convert units within the metric system. Each pathway uses real world objects to measure, such as pencils, parcels, and jugs of water. It is dynamic in the sense that these objects move throughout the investigation and a “Well Done!” spins out whenever the correct answer is displayed. ||

<span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 130%;">Measurement Annotated Links:


 * ** Screen Shot ** ||  ** Name and Description **  ||
 * [[image:Star_Gazing.png width="325" height="216" align="center" link="http://pbskids.org/cyberchase/games/anglemeasurement/anglemeasurement.html"]] || <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: normal; margin: 0in 0in 0pt;">In Cyberchase’s [|Star Gazing], students use a virtual protractor to measure the planets in the night sky. A key element to the game is being able to estimate angle measurements and use that thinking to identify where to point the virtual telescope. Once a student completes a level, they are given a star map based on their measurements of each imaginary planet. The goal of the game is to create a cyber-scrapbook of all the planets’ measurements within the game. Each level becomes more difficult and students must adjust their estimations quickly. If students don’t measure all of the planets within a level, the sun rises and the student does not get the star map for that level and must try the game again. Although this game focuses mostly on the instrumental understanding of using protractors and measuring angles, students do connect how making these measurements are used in the real world. ||
 * [[image:Metric_conversion.png width="353" height="243" align="center" link="http://www.learner.org/interactives/metric/index.html"]] || <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: normal; margin: 0in 0in 10pt;">In [|Interactivate Metric Conversions], students are introduced to a series of metric units and must identify, measure, and convert metric units from one unit to another within the metric system. For instance, students practice basic length conversions, including converting meters to centimeters, millimeters, and kilometers, and then back to the original unit again using real world objects. For mass conversions, students will learn to convert grams to milligrams, and kilograms back to grams. For volume conversions, students will practice converting kiloliters to liters and liters to milliliters. Students will begin to understand relationships among units and convert from one unit to another within the same system. Students will also make decisions about units and scales that are appropriate for problem solving using measurement at the end of the interactive. There is also a multiple choice quiz that can be emailed to instructors for assessment. ||