Measurement

1. Measurement EDN 322

2. Why teach measurement? Provides many applications to everyday life Can be used to help learn other topics in mathematics Can be related to other areas of the school curriculum Involves students in active learning Can be approached through problem solving Brainstorm list of ways you used numbers in the past few days. (How long it took to drive to school, how many calories are in a piece of chocolate cake, how far it is to the nearest store, or how many cups of coffee you drank?) All of these are examples of measurement. Measurement is the topic from the elementary curriculum that we use the most in our daily lives. Measurement has been designated as one of the ten standards in the NCTM Principles and Standards because of its power to help students see the usefulness of mathematics in everyday life. Measurement can be used in learning other topics in mathematics. It is apparent that children need many of the other math topics to help them with measuring. For example, they may count the number of grams it takes to balance an object on a scale, multiply to find a volume, divide to change minutes to hours, subtract to see how close an estimate was, or add to find the perimeter of a rectangle. To report the number of units, children may use whole numbers, common fractions, decimals, and negative numbers. Can help teach about numbers and operations. Many of the numeration models we use have a measurement base. Ex: the number line is based on length. One model for multiplication is the area of a rectangle. You will also find that there is a strong connection between measurement and music, art, science, social studies, and language arts. It is one of the easiest areas of the math curriculum to integrate with other disciplines. You will find this integrative aspect of measurement to be true of the activities we do this week. Many other areas of the curriculum are naturally covered through a study of measurement. It would be inappropriate and difficult to parcel these other areas out of the measurement activity. In fact, NCTM recommends that measurement be a continuing part of the math program, rather than being presented in a few isolated lessons. You will find many ways to include measurement activities as you teach many mathematical ideas and other subject areas. The final reason measurement is an important part of the mathematics curriculum is because it is an effective way to involve students in problem-solving experiences at every level. Measurement activities just lend themselves to rich problem solving. Brainstorm list of ways you used numbers in the past few days. (How long it took to drive to school, how many calories are in a piece of chocolate cake, how far it is to the nearest store, or how many cups of coffee you drank?) All of these are examples of measurement. Measurement is the topic from the elementary curriculum that we use the most in our daily lives. Measurement has been designated as one of the ten standards in the NCTM Principles and Standards because of its power to help students see the usefulness of mathematics in everyday life. Measurement can be used in learning other topics in mathematics. It is apparent that children need many of the other math topics to help them with measuring. For example, they may count the number of grams it takes to balance an object on a scale, multiply to find a volume, divide to change minutes to hours, subtract to see how close an estimate was, or add to find the perimeter of a rectangle. To report the number of units, children may use whole numbers, common fractions, decimals, and negative numbers. Can help teach about numbers and operations. Many of the numeration models we use have a measurement base. Ex: the number line is based on length. One model for multiplication is the area of a rectangle. You will also find that there is a strong connection between measurement and music, art, science, social studies, and language arts. It is one of the easiest areas of the math curriculum to integrate with other disciplines. You will find this integrative aspect of measurement to be true of the activities we do this week. Many other areas of the curriculum are naturally covered through a study of measurement. It would be inappropriate and difficult to parcel these other areas out of the measurement activity. In fact, NCTM recommends that measurement be a continuing part of the math program, rather than being presented in a few isolated lessons. You will find many ways to include measurement activities as you teach many mathematical ideas and other subject areas. The final reason measurement is an important part of the mathematics curriculum is because it is an effective way to involve students in problem-solving experiences at every level. Measurement activities just lend themselves to rich problem solving.

3. Teaching Measurement Children must measure frequently and often. Children must develop estimation skills with measurement. Children should encounter activity-oriented measurement situations by doing and experimenting rather than by passively observing.

4. Measurement Attributes Length Perimeter Area Capacity Volume Weight Time Temperature Money Measurement is a process by which a number is assigned to an attribute of an object or event. Length � Linear concept answers question �How long?� � How wide?� �How high?� Area � a measure of surface that concerns two dimensions. Capacity � Attribute that addresses the question, �How much does a container hold?� Capacity often pertains to pourable substances � water and other liquids, sand, flour, etc. Volume � 3-dimensional concept concerning filling space with cubic units. Weight � How heavy? How light? Time � unlike other measurement concepts, is not applied to physical objects; rather it is a concept that people apply to events; concerns duration Temperature � How warm? How cool? Attribute that indicates the presence or absence of heat. Measurement is a process by which a number is assigned to an attribute of an object or event. Length � Linear concept answers question �How long?� � How wide?� �How high?� Area � a measure of surface that concerns two dimensions. Capacity � Attribute that addresses the question, �How much does a container hold?� Capacity often pertains to pourable substances � water and other liquids, sand, flour, etc. Volume � 3-dimensional concept concerning filling space with cubic units. Weight � How heavy? How light? Time � unlike other measurement concepts, is not applied to physical objects; rather it is a concept that people apply to events; concerns duration Temperature � How warm? How cool? Attribute that indicates the presence or absence of heat.

5. Stages for teaching measurement Identify the attribute by comparing and ordering objects Choose a unit Nonstandard units Standard units of measurement Compare the object to the unit Find the number of units Report the number of units Measurement is a process by which a number is assigned to an attribute (like length) of an object or event. The attributes covered in the elementary curriculum are length, perimeter, area, capacity, weight, volume, time, temperature and money. Even though each of these attributes is different, there are some overall commonalities in how to help children learn about measuring them. The following stages are useful in helping children learn to measure If a new attribute is being introduced, one recommended approach is to cycle through the outline several times. If you had a large box to measure, you would first have to decide which attribute of the box you were interested in and then select a unit that possesses that same attribute. If you wanted to know how long the box was, possible choices for the unit would include your hand span, a paper clip, or the centimeter. Depending on the unit chosen, the length of a given box might be 3 spans, 20 paper clips or 62 cm. If you wanted to know how heavy the box was, you would use a balance scale to compare it with a unit of mass such as a book or the pound. To measure how much the box holds, you could find how many smaller boxes of a particular size would fit into it, or measure its l, w, and h in centimeters and compute the volume in cubic centimeters. Children should first directly compare pairs of items. Children can use real objects, physically manipulating objects or placing them side by side. A second stage for measurement activities is ordering or seriating. Here children work with 3 or more objects and arrange them along a continuum � perhaps from shortest to longest. Children must work with ordering in direct ways � lining up classmates to see who is tallest, or placing their hands in cold, very warm and cool water to order the samples of water by temperature. Children can next work with nonstandard units of measurement as small, equal-sized units. For example, they might use scoops and measure the capacities of larger bowls in �scoop units.� Work with nonstandard units helps children grasp the idea that measurement involves telling how much of an appropriate unit are needed to match the object being measured. BENCHMARKS � upper grades corner of a paper can be a reference for a 90 degree angle. 4. After many experiences with comparing, ordering and using nonstandard units, children are ready for work with standard units of measurement. In this stage they work with units familiar to many people: centimeters, feet, hours, and liters. Measurement is a process by which a number is assigned to an attribute (like length) of an object or event. The attributes covered in the elementary curriculum are length, perimeter, area, capacity, weight, volume, time, temperature and money. Even though each of these attributes is different, there are some overall commonalities in how to help children learn about measuring them. The following stages are useful in helping children learn to measure If a new attribute is being introduced, one recommended approach is to cycle through the outline several times. If you had a large box to measure, you would first have to decide which attribute of the box you were interested in and then select a unit that possesses that same attribute. If you wanted to know how long the box was, possible choices for the unit would include your hand span, a paper clip, or the centimeter. Depending on the unit chosen, the length of a given box might be 3 spans, 20 paper clips or 62 cm. If you wanted to know how heavy the box was, you would use a balance scale to compare it with a unit of mass such as a book or the pound. To measure how much the box holds, you could find how many smaller boxes of a particular size would fit into it, or measure its l, w, and h in centimeters and compute the volume in cubic centimeters. Children should first directly compare pairs of items. Children can use real objects, physically manipulating objects or placing them side by side. A second stage for measurement activities is ordering or seriating. Here children work with 3 or more objects and arrange them along a continuum � perhaps from shortest to longest. Children must work with ordering in direct ways � lining up classmates to see who is tallest, or placing their hands in cold, very warm and cool water to order the samples of water by temperature. Children can next work with nonstandard units of measurement as small, equal-sized units. For example, they might use scoops and measure the capacities of larger bowls in �scoop units.� Work with nonstandard units helps children grasp the idea that measurement involves telling how much of an appropriate unit are needed to match the object being measured. BENCHMARKS � upper grades corner of a paper can be a reference for a 90 degree angle. 4. After many experiences with comparing, ordering and using nonstandard units, children are ready for work with standard units of measurement. In this stage they work with units familiar to many people: centimeters, feet, hours, and liters.

6. Concepts Related to Units A measurement must include both a number and the unit Two measurements may be easily compared if the same unit is used. One unit may be more appropriate than another to measure an object. This is one of the most difficult points to make to children. You may remember your teacher stressing to you the importance of including the unit when we measure. One reason this may be so difficult for students is because students are used to being presented with a worksheet of measuring tasks that require the same unit. The unit seems obvious in this situation. In the early grades, we need to make sure that students are measuring the same object with many different nonstandard units. Research indicates that when students use a variety of units to measure, they are more likely to see the necessity of reporting the unit. If children are in the habit of only relying on the number, they may use only this number to compare two objects. For example, if one pencil is 6 paper clips long and another is 2 strips long, some will say that the one that measures 6 is longer. They have not reached the stage where they can coordinate the number with the unit. The size of the unit selected depends on the size of the object and on the degree of accuracy desired. One activity that I have used with students requires them to use body parts to measure various objects. They might use the width of their finger, their hand span, of the length of their arm. We would certainly get a more accurate answer if we measured the length of this paper using finger widths rather than hand spans. This is one of the most difficult points to make to children. You may remember your teacher stressing to you the importance of including the unit when we measure. One reason this may be so difficult for students is because students are used to being presented with a worksheet of measuring tasks that require the same unit. The unit seems obvious in this situation. In the early grades, we need to make sure that students are measuring the same object with many different nonstandard units. Research indicates that when students use a variety of units to measure, they are more likely to see the necessity of reporting the unit. If children are in the habit of only relying on the number, they may use only this number to compare two objects. For example, if one pencil is 6 paper clips long and another is 2 strips long, some will say that the one that measures 6 is longer. They have not reached the stage where they can coordinate the number with the unit. The size of the unit selected depends on the size of the object and on the degree of accuracy desired. One activity that I have used with students requires them to use body parts to measure various objects. They might use the width of their finger, their hand span, of the length of their arm. We would certainly get a more accurate answer if we measured the length of this paper using finger widths rather than hand spans.

7. Concepts Related to Units There is an inverse relationship between the number of units and the size of the unit. A smaller unit will give a more exact measurement. Standard units are needed to communicate effectively. When measuring the same object with three different units, children soon realize that the larger the unit, the fewer are required. A smaller unit will give a more exact measurement. First, children need to realize that all measurements are approximate. Through much measurement practice, students will come to realize that the smaller the unit, the closer our measurement will be to the �actual� attribute. When students are transitioning between using nonstandard and standard units, we want them to recognize the importance of using standard units. Stories and activities that demonstrate the difficulty in communicating sizes then there is no standard are one way to present the necessity of using standard units. One book that I have enjoyed using with students is How Big is a Foot? by ____ Myller. (share a little bit of the book) When measuring the same object with three different units, children soon realize that the larger the unit, the fewer are required. A smaller unit will give a more exact measurement. First, children need to realize that all measurements are approximate. Through much measurement practice, students will come to realize that the smaller the unit, the closer our measurement will be to the �actual� attribute. When students are transitioning between using nonstandard and standard units, we want them to recognize the importance of using standard units. Stories and activities that demonstrate the difficulty in communicating sizes then there is no standard are one way to present the necessity of using standard units. One book that I have enjoyed using with students is How Big is a Foot? by ____ Myller. (share a little bit of the book)

8. NCTM Understand measurable attributes of objects and the units, systems, and processes of measurement Apply appropriate techniques, tools, and formulas to determine measurements The first goal that NCTM delineates is to � In the early grades, children should begin to develop an understanding of attributes by looking at, touching, or directly comparing objects. They can determine who has more by looking at the size of piles of objects or identify which of two objects is heavier by picking them up. They can compare shoes, placing them side by side, to check which is longer. Adults should help young children recognize attributes through their conversations. "That is a deep hole." "Let's put the toys in the large box." "That is a long piece of rope." In school, students continue to learn about attributes as they describe objects, compare them, and order them by different attributes. Seeing order relationships, such as that the soccer ball is bigger than the baseball but smaller than the beach ball, is important in developing measurement concepts. Although a conceptual foundation for measuring many different attributes should be developed during the early years, linear measurements are the main emphasis. Measurement experiences should include direct comparisons as well as the use of nonstandard and standard units. For example, teachers might ask young students to find objects in the room that are about as long as their foot or to measure the length of a table with connecting cubes. Later they can supply standard measurement tools, such as rulers, to measure classroom plants and use those measurements to chart the plants' growth. If students initially explore measurement with a variety of units, nonstandard as well as standard, they will develop an understanding of the nature of units. For example, if some students measure the width of a door using pencils and others use large paper clips, the number of paper clips will be different from the number of pencils. Students in grades 3�5 should measure the attributes of a variety of physical objects and extend their work to measuring more complex attributes, including area, volume, and angle. They will learn that length measurements in particular contexts are given specific names, such as perimeter, width, height, circumference, and distance. The second goal� In grades 3�5, an expanded number of tools and range of measurement techniques should be available to students. When using conventional tools such as rulers and tape measures for measuring length, students will need instruction to learn to use these tools properly. For example, they will need to recognize and understand the markings on a ruler, including where the "0," or beginning point, is located. When standard measurement tools are difficult to use in a particular situation, they must learn to adapt their tools or invent techniques that will work. The first goal that NCTM delineates is to � In the early grades, children should begin to develop an understanding of attributes by looking at, touching, or directly comparing objects. They can determine who has more by looking at the size of piles of objects or identify which of two objects is heavier by picking them up. They can compare shoes, placing them side by side, to check which is longer. Adults should help young children recognize attributes through their conversations. "That is a deep hole." "Let's put the toys in the large box." "That is a long piece of rope." In school, students continue to learn about attributes as they describe objects, compare them, and order them by different attributes. Seeing order relationships, such as that the soccer ball is bigger than the baseball but smaller than the beach ball, is important in developing measurement concepts. Although a conceptual foundation for measuring many different attributes should be developed during the early years, linear measurements are the main emphasis. Measurement experiences should include direct comparisons as well as the use of nonstandard and standard units. For example, teachers might ask young students to find objects in the room that are about as long as their foot or to measure the length of a table with connecting cubes. Later they can supply standard measurement tools, such as rulers, to measure classroom plants and use those measurements to chart the plants' growth. If students initially explore measurement with a variety of units, nonstandard as well as standard, they will develop an understanding of the nature of units. For example, if some students measure the width of a door using pencils and others use large paper clips, the number of paper clips will be different from the number of pencils. Students in grades 3�5 should measure the attributes of a variety of physical objects and extend their work to measuring more complex attributes, including area, volume, and angle. They will learn that length measurements in particular contexts are given specific names, such as perimeter, width, height, circumference, and distance. The second goal� In grades 3�5, an expanded number of tools and range of measurement techniques should be available to students. When using conventional tools such as rulers and tape measures for measuring length, students will need instruction to learn to use these tools properly. For example, they will need to recognize and understand the markings on a ruler, including where the "0," or beginning point, is located. When standard measurement tools are difficult to use in a particular situation, they must learn to adapt their tools or invent techniques that will work.

9. NC SCOS Kindergarten 2.01 Compare attributes of two objects using appropriate vocabulary (color, weight, height, width, length, texture). 2.02 Recognize concepts of calendar time using appropriate vocabulary (days of the week, months of the year, seasons).

10. 2.01 For given objects: a) Select an attribute (length, capacity, mass) to measure (use non-standard units). b) Develop strategies to estimate size. c) Compare, using appropriate language, with respect to the attribute selected. 2.02 Develop an understanding of the concept of time. a) Tell time at the hour and half-hour. b) Solve problems involving applications of time (clock and calendar). NC SCOSFirst Grade

11. 2.01 Estimate and measure using appropriate units. a) Length (meters, centimeters, feet, inches, yards). b) Temperature (Fahrenheit). 2.02 Tell time at the five-minute intervals. NC SCOSSecond Grade

12. 2.01 Solve problems using measurement concepts and procedures involving: a) Elapsed time. b) Equivalent measures within the same measurement system. 2.02 Estimate and measure using appropriate units. a) Capacity (cups, pints, quarts, gallons, liters). b) Length (miles, kilometers) c) Mass (ounces, pounds, grams, kilograms). d) Temperature (Fahrenheit, Celsius). NC SCOSThird Grade

13. 2.01 Develop strategies to determine the area of rectangles and the perimeter of plane figures. 2.02 Solve problems involving perimeter of plane figures and areas of rectangles. NC SCOSFourth Grade

14. 2.01 Estimate the measure of an object in one system given the measure of that object in another system. 2.02 Identify, estimate, and measure the angles of plane figures using appropriate tools. NC SCOSFifth Grade