Learning Mathematics In Elementary and Middle Schools, 5e Cathcart, Pothier, Vance, and Bezuk ©2011 Pearson Education, Inc. All Rights Reserved Chapter Fifteen Developing Measurement Concepts and Skills

Learning Mathematics In Elementary and Middle Schools, 5e Cathcart, Pothier, Vance, and Bezuk ©2011 Pearson Education, Inc. All Rights Reserved 15-2 Curriculum Focal Points Grade LevelCurriculum Focal Points Related to Measurement Pre-kChildren compare objects based on quantity and length KindergartenChildren compare and order objects based on length or weight Grade 1Children measure objects by laying a unit end to end and then counting the units Grade 2Children understand linear measure and the need for using standard units of measure Grade 3Children understand linear measure and fractional parts of linear units, and develop an understanding of and solve problems involving perimeter Grade 4Children develop an understanding of and solve problems involving area

Learning Mathematics In Elementary and Middle Schools, 5e Cathcart, Pothier, Vance, and Bezuk ©2011 Pearson Education, Inc. All Rights Reserved 15-3 Curriculum Focal Points (cont’d) Grade LevelCurriculum Focal Points Related to Measurement Grade 5Children develop an understanding of and solve problems involving volume and surface area Grade 6Children extend their understanding of and solve problems involving area and volume Grade 7Children develop an understanding of and solve problems involving surface area and volume of three- dimensional shapes Grade 8Children develop an understanding of and solve problems involving distance and angles, to learn properties of particular configurations of lines and about similar triangles to solve a variety of problems, and to explain why the Pythagorean theorem is valid and use the Pythagorean theorem to find distances between points and analyze polygons and polyhedra.

Learning Mathematics In Elementary and Middle Schools, 5e Cathcart, Pothier, Vance, and Bezuk ©2011 Pearson Education, Inc. All Rights Reserved 15-4 What is Measurement? A measureable attribute of an object or event is a characteristic that can be quantified by comparing it to a unit. Process of measurement An appropriate unit is chosen The object or event being measured is compared to the unit The result is a number and a unit Spider is 11 cubes long.

Learning Mathematics In Elementary and Middle Schools, 5e Cathcart, Pothier, Vance, and Bezuk ©2011 Pearson Education, Inc. All Rights Reserved 15-5 Instructional Sequence Meaning of attribute is developed through activities involving perception and direct comparison Children begin to measure, using arbitrary or nonstandard units Children measure and estimate, using standard units

Learning Mathematics In Elementary and Middle Schools, 5e Cathcart, Pothier, Vance, and Bezuk ©2011 Pearson Education, Inc. All Rights Reserved 15-6 Focus of the First Stage: Perception and Direct Comparison Premeasurement – activities at this stage allow children to experience the properties of the attribute and to use sight and touch to compare and order objects with respect to those attributes. Appropriate language Length = “Which is longer?” Capacity = “Which holds more?”

Learning Mathematics In Elementary and Middle Schools, 5e Cathcart, Pothier, Vance, and Bezuk ©2011 Pearson Education, Inc. All Rights Reserved 15-7 Focus of the First Stage: Perception and Direct Comparison Seriation tasks Place the objects in order from smallest to largest.

Learning Mathematics In Elementary and Middle Schools, 5e Cathcart, Pothier, Vance, and Bezuk ©2011 Pearson Education, Inc. All Rights Reserved 15-8 Focus of the Second Stage: Nonstandard Units “How big?” rather than “Which is bigger?” Criterion for selecting an appropriate unit include : Has the same attribute as that to be measured Size of the unit relative to the object to be measured

Learning Mathematics In Elementary and Middle Schools, 5e Cathcart, Pothier, Vance, and Bezuk ©2011 Pearson Education, Inc. All Rights Reserved 15-9 Focus of the Second Stage: Nonstandard Units Measurement of continuous quantities is always approximate Children should be encouraged to estimate their answers before measuring Introduce the idea of subdividing a unit

Learning Mathematics In Elementary and Middle Schools, 5e Cathcart, Pothier, Vance, and Bezuk ©2011 Pearson Education, Inc. All Rights Reserved Focus of the Third Stage: Standard Units Standard units are units that have been agreed on and accepted by a group of people. Two systems of standard units are used in the United States Customary system Metric system Measurement sense includes having knowledge of the units appropriate for a given task and the ability to decide when and how to estimate. asure.html asure.html

Learning Mathematics In Elementary and Middle Schools, 5e Cathcart, Pothier, Vance, and Bezuk ©2011 Pearson Education, Inc. All Rights Reserved Standard Units (cont’d) Strategies used by good estimators include: Referents – using a known quantity such as your own height to estimate another person’s height Adult handspan is about 7 inches. Y Y

Learning Mathematics In Elementary and Middle Schools, 5e Cathcart, Pothier, Vance, and Bezuk ©2011 Pearson Education, Inc. All Rights Reserved Standard Units (cont’d) Strategies used by good estimators include: Chunking – estimating the area of a room by first breaking it into several workable parts Your living room is made up of a square and a half circle. Find the area of the square (s 2 ) then add the area of a circle (pi x r 2 ), then when you have your answer, multiply by ½. Add the 2 answers together and you can carpet your room.

Learning Mathematics In Elementary and Middle Schools, 5e Cathcart, Pothier, Vance, and Bezuk ©2011 Pearson Education, Inc. All Rights Reserved Standard Units (cont’d) Strategies used by good estimators include: Unitizing – estimating the volume of a pitcher by mentally dividing it into smaller, equal parts. About 2 liters or 2 quarts

Learning Mathematics In Elementary and Middle Schools, 5e Cathcart, Pothier, Vance, and Bezuk ©2011 Pearson Education, Inc. All Rights Reserved Common Standard Units of Measure Attribute Being Measured Customary SystemMetric System Length Inch, foot, yard, mileMillimeter, centimeter, meter, kilometer Area Square inch, square foot, square yard, acre Square centimeter, square meter, hectare Volume Cubic inch, cubic foot, cubic yard Cubic centimeter, cubic meter Capacity Fluid ounce, cup, quart, gallon Milliliter, liter Weight Ounce, pound, tonGram, kilogram, metric ton

Learning Mathematics In Elementary and Middle Schools, 5e Cathcart, Pothier, Vance, and Bezuk ©2011 Pearson Education, Inc. All Rights Reserved Common Standard Units of Measure (cont’d) Attribute Being Measured Customary SystemMetric System Temperature Degrees FahrenheitDegrees Celsius Time Second, minute, hour, day, week, month, year Angles Degrees, Radians