The resources in this professional development collection were assembled to help math specialists and teachers enhance their own understanding of measurement concepts and teaching practices via theory, research, and activities that can be adapted for classroom use. The article “Measuring Length” describes some of the conceptual pitfalls that students may encounter and is a good starting point for educators as they begin to plan their lessons. The articles from the NCTM journal Teaching Children Mathematics are excellent sources of lesson ideas appropriate for helping children develop deep conceptual understanding; two of the articles also connect measurement concepts to children’s literature, and one extends learning to include three simple fractions.
Thinking about Measurement Concepts
Students attempting to measure or make use of measurements are faced with many issues at once – recognizing the attribute, identifying the unit, deciding on the level of precision, and making mental calculations. The Annenberg videos, “What Does It Mean to Measure?” and “Measurement Fundamentals,” and the Victoria instructional guides, “Comparison of Length” and “The Idea of a Unit,” provide teachers with ideas and activities that they can use to help children clarify these concepts.
What Do Students Need?
Students need experiences that lead to an understanding of why measurement is necessary and helpful. They need to work with non-standard units and to create their own measuring instruments, and to discover for themselves the necessity of having standard units and the efficiency of having measuring instruments to count the units. The lesson plan “Lengths of Ladybugs” provides an engaging introduction to these concepts. The resource “Fitting Shapes Together” provides early experience with angle measurement.
This narrative document describes the progression of Geometric Measurement across the K-5 grade band. It is informed both by research on children's cognitive development and by the logical structure of mathematics. The document discusses the most important goals for elementary geometric measurement. Among those are recognizing measurable attributes, comparing, connecting with number, estimating, and differentiating linear measurement from area and volume.
This article focuses on young students encountering the measurement of length. The article cites examples of key concepts in recognizing length as an attribute and in proper and improper ways to measure length. Conservation and additivity of length, standard and non-standard units, iteration, and the zero point are among the topics presented.
This video, the first in a series of twelve, is part of the web-based course for K-8 teachers entitled Learning Math: Measurement offered by the Annenberg Foundation. Participants explore procedures for measuring and learn about standard units in the metric and customary systems, the relationships among units, and the approximate nature of measurement. This first video covers measurable attributes, weight and surface area of irregular objects, estimation, precision and accuracy, the independence of area and perimeter, and the choice of unit.
This 26-minute video, the second in a series of twelve, is part of the web-based course for K-8 teachers entitled Learning Math: Measurement offered by the Annenberg Foundation. Participants explore procedures for measuring and learn about standard units in the metric and customary systems, the relationships among units, and the approximate nature of measurement. In this video participants examine fundamental ideas such as unit iteration, partitioning and precision, ratio, and scale. To access the video from this link click on the VoD icon that is next to the video 2 description.
These 3 activities, part of the Mathematics Developmental Continuum of the State of Victoria, Australia, are intended to introduce young learners to the measurable attribute of length as distinguished from others. Students compare lengths of two or more objects directly or indirectly. Teaching suggestions and progress indicators are included.
These 2 activities, part of the Mathematics Developmental Continuum of the State of Victoria, Australia, are intended to introduce young learners to measuring using an iterated informal unit such as a hand span. Teaching suggestions, materials, and progress indicators are included.
This lesson plan for teachers of kindergarten students involves activities that introduce the concepts of using a non-standard unit to measure length and associating a measurement with a number. After introducing the lesson with a literature connection, students cut out their own measuring cards and use them to compare lengths, and measure distance along a path using a line of ladybug beans and a non-standard tape. Materials, handouts, and suggestions for extensions and parental involvement are included.
The activities in this four-lesson unit enable students to use their knowledge of number, measurement, and geometry to solve interesting problems. Planning and visualizing, estimating and measuring, and testing and revising are components of the ladybug activities. Students design "virtual paths" that enable a ladybug to either hide under a leaf or go through a maze. They develop navigational skills by testing their path and revising it. Two interactive Java applets (Ladybug Mazes and Hiding Ladybug, cataloged separately) support student solutions.
These 4 activities, part of the Mathematics Developmental Continuum of the State of Victoria, Australia, are intended to introduce young learners to types of angles and tessellations through the use of pattern blocks and tangrams. Supporting documents, materials, and teaching strategies are included.
In this 5-lesson unit, students engage in measurement activities involving length, area, volume, time, and weight, using objects, pictures and symbols. Students practice measuring using standard and nonstandard units. Some lessons are introduced using children's literature.
In this article Andrew Tyminski, Monica Weilbacher, Nicole Lenburg and Cindy Brown focus on a sequence of lessons used to develop kindergarten students' conceptual understanding of measuring length. The article presents ideas of how to provide experiences for young students that help them to develop meaningful understanding of length, units, rulers and measurement. It addresses the early childhood teachers' need to support young children's emerging mathematics understanding in a context that conforms to current knowledge about the ways young children learn mathematics. The article is part of the Early Childhood Corner in the journal Teaching Children Mathematics.
In this article from the NCTM journal Teaching Children Mathematics, teachers are encouraged to push instruction beyond procedures. The authors, Leslie C. Dietiker, Funda Gonulates, and John P. Smith III provide information about how to enhance student tasks and offer better opportunities to develop conceptual understanding.
In this article, authors Amy McDuffie and Norma Eve describe how a professional learning team redesigns a lesson aimed at helping second graders understand area by covering physical surfaces with many identical units. The article is from the NCTM journal Teaching Children Mathematics.
This article describes the use of the book “Inchworm and a Half” to stimulate children's investigations in measurement and number. The authors, Patricia Moyer and Elizabeth Mailley, describe a two-day lesson during which children used physical models and visual representations to develop measurement skills and explore equivalent relationships. The article includes a worksheet idea, student solutions, and reflections on their work.