Resources and Tools for Elementary Math Specialists and Teachers
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Place Value

How will this collection help to address standards?

The NCTM Number and Operations Standard for Pre-K through Grade 2 states that “It is absolutely essential that students develop a solid understanding of the base-ten numeration system and place-value concepts by the end of grade 2. Students need many instructional experiences to develop their understanding of the system, including how numbers are written.”  Base ten and place value concepts lie at the core of the knowledge students need as they learn first about the operations and properties of whole numbers, and later of other number systems. 

What does research tell us about this topic?

Research indicates that students sometimes have a difficult time understanding our number system.  Some of the difficulties they have can be difficult to diagnose, perhaps because of the structure of our language, or because of the many properties of the number system, and later of the decimal system. 

A research study from Australia provides information about a Base Ten Game that has enabled students to develop a deeper understanding of place value with whole numbers in lower grades, and later with decimals in the upper levels.  The study provides background information about research on the use of “base blocks,” indicating that students do not always connect these materials to other place value representations.  The suggestions from this study and the other resources in this collection may encourage you to vary the assessments, so you can better determine what students really understand.  You may also decide to use the Base Ten Game to aid students in forming the basic concepts underpinning our number system.

Base blocks and other tools and manipulatives

The use of base blocks (often called “units, longs, flats, and blocks,”) to represent place value is a frequent occurrence in our classrooms.  An interactive version of base blocks and a simple interactive abacus are included as useful resources, especially for interactive white boards.  Research suggests that base blocks should be just one of several materials used to represent numbers.  Simple materials, such as paper clips for units, arranged on paper plates for tens, and into boxes for hundreds, might provide an introduction to the basic concepts.  Pictures of objects on which students can circle groups of ten might also be used.  Finding ways to help students make the connection between these objects and the underlying properties of the number system are fundamental to building the necessary understanding.  

Take a few minutes to review these resources and reflect upon the research.  Decide how these resources can help you as you plan activities that help build a deep understanding of place value.

 

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Created:10-11-2012 by Uncle Bob
Last Post:01-01-2013 by bethb
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Created:06-07-2012 by bethb
Last Post:08-23-2012 by bethb

Resource Title/Description

The brief video clips on this webpage illustrate the range of number sense exhibited by students in grades Pre K-2. In interviews, Cena and Jonathan, both age 7, and Rudy, age 9, demonstrate different levels of understanding number and place value concepts. The page includes discussion questions for each set of videos as well as concluding reflection questions.
This paper describes a research project carried out by nine teachers from diverse schools in Australia. The project explored the role of a commonly used teaching activity, referred to in this report as the Base Ten Game, in developing children’s understanding of our number system beginning with whole numbers and extending to decimals. The report includes a description of the game, two case studies, and results and implications for the classroom. An appendix includes strategies for managing the Base Ten Game.
This flexible interactive Java applet helps users develop place value concepts with whole numbers or up to 3 decimal places. Users can use the virtual blocks to freely explore place value grouping rules or to represent a target number provided by the applet. Users may change the default of base 10 to any of the bases 2, 3, 4, or 5.
This interactive Flash applet supports the exploration of place value. A child or teacher can represent numbers (up to 4 digits) by placing beads onto sticks. When carrying out addition and subtraction, an animation demonstrates the process of re-grouping. Users can choose to hide or show values and calculations. This applet lends itself well to an interactive white board.
This page links to an interactive Flash abacus that helps develop and reinforce pupils' understanding of place value. [Click "Start the Activity" to begin.] The abacus has three pegs (representing units, tens and hundreds) onto which users drop beads. The activity has two areas: a "free" (unstructured) area where pupils can represent 3-digit numbers, and a "computer questions" area that presents six challenging tasks to carry out. The page includes notes for teachers and pupils.
The answers to these FAQ from the Teacher2Teacher service at The Math Forum @ Drexel contain many suggestions for providing students with practice on using place value skills. They include ideas contributed by T2T Associates and teacher participants. There are links to Ask Dr. Math resources, children's literature connections, and outside websites with related resources.
This webpage contains instructions for several activities and games designed to develop students' understanding of place value while reinforcing addition and subtraction skills. Downloadable materials and suggestions for variations are included. A second page of additional activities is catalogued separately (More Place Value Activities).
This webpage contains instructions for several activities and games designed to develop students' understanding of place value while reinforcing addition and subtraction skills. Downloadable materials and suggestions for variations are included along with links to online games. This is the second of two pages of similar activities. The first, Place Value Activities, is catalogued separately.
This iOS app includes three games that enhance geometry, spatial sense, and problem solving skills. Patch the Path, an augmented reality game, utilizes the mobile device’s camera and a printable game board to interact with shapes and dimensions. Players must choose the correct shape, rotate it and then place it to continue the path. The Hide and Seek game requires players find where the animals are hiding by identifying shapes based on geometric descriptions. The Feed the Critters game requires players to use their spatial sense and problem solving skills to move the food around obstacles.