Number and Operations in Base Ten

Generalize place value understanding for multi-digit whole numbers.

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This interactive Flash applet helps students explore place value and develop number sense within whole numbers, integers and decimals. It allows a child or teacher to select an interval in the given number line and show that interval divided into ten equal parts but on a larger scale, which can then be repeated. Users may choose the size of the interval between markers on the first number line and the starting number of that line, as well as whether to hide or show individual number lines and the numbers on them. This applet lends itself well for use on an interactive white board. A pdf guide to this collection of teaching applets is cataloged separately. | Activity, Interactive Media Grade Level: 1, 2, 3, 4, 5 | |

This collection of 6 games develops place value, operation sense and fluency, estimation, and strategic thinking. It is played on paper with a 6- or 9-sided die (printable pdf game sheets included). Players choose a game grid with empty cells representing the digits of a computation (addition, subtraction, multiplication, or division). They take turns rolling a die and placing the resulting number in a cell on their own grids. The goal is to create a sum/difference/product/quotient that is closest to a target number. Variations include using a decimal point and scoring options. Teachers' Notes include suggestions for introducing the game, discussion questions, support suggestions, and a link to a more challenging extension (Countdown, cataloged separately). | Activity, Game Grade Level: 2, 3, 4, 5, 6+ | |

This webpage offers a variety of games which develop strategic thinking, analytical skills, and basic number skills. Three pdfs provide instructions and materials for sets of games played on reusable boards, on consumable sheets, and with number cards. The only other materials required are counters/chips, dice, and pens/pencils. The site also includes instructions for games that require only counters or paper and pencil. A short article describes the rationale for using such games in the classroom and offers suggestions for organizing and managing games and for maximizing their benefits. | Activity, Game, Instructional Strategy, Instructor Guide/Manual Grade Level: 1, 2, 3, 4, 5 | |

This document provides descriptions and examples of what each Mathematics Common Core standard means a Grade Four student will know, understand and be able to do. This "unpacking" of the standards provides instructional guidelines and was developed to assist North Carolina educators teach the Mathematics Common Core (Standard Course of Study). | Reference Materials Grade Level: 4 | |

The authors of this website have identified 8 common misconceptions that lead to errors in mathematics (and promise to add more as time permits). Topics include: Rounding Numbers, Multiplication can Increase or Decrease a Number, Multiplying Decimals, Decimals and their Equivalent Fractions, Dividing Whole Numbers by Fractions, Adding with Negative Numbers, Calculations with Negative Numbers, and Calculations with Hundreds and Thousands. Each misconception is described in a pdf document which explains how the misconception arises, the rationale for the correct concept, and exercises aimed at reinforcing the correction. | Problem Set, Tutorial Grade Level: 4, 5, 6+ | |

This interactive Flash applet can be used to explore and predict the effect of multiplying and dividing by 10 and 100. Teachers or students click and drag number cards into places in either of the two middle rows. The cards in the first row move when the multiply or divide buttons are clicked, while cards in the second row stay in place for comparison. The information button (i) allows users to mouse over features to learn about their use. This applet lends itself well to use on an interactive white board. A pdf guide to this collection of teaching applets is cataloged separately. | Activity, Interactive Media Grade Level: 4, 5, 6+ | |

This lesson helps students develop conceptual understanding of 2-digit multiplication. Students decompose 2-digit numbers, model area representations using the distributive property and partial product arrays, and carry out paper-and-pencil calculations from the arrays. Included are student activity sheets, a link to a supporting online applet, and extension suggestions. | Activity, Lesson Plans Grade Level: 3, 4, 5 Resource is part of a PD collection | |

This professional development video from Minnesota Department of Education presents an algebra training session in action. Viewers watch Dr. Terry Wyberg, a methods professor at the University of Minnesota; discuss strategies to help teachers to elicit mathematical understanding with their students with an example of multiplying by 10. He poses the question: “Why when you multiply by 10 do you just add a zero?” Through the use of base 10 blocks, he shows his audience how to develop relational reasoning or algebraic thinking to do the arithmetic. | Reference Materials, Article, Video Grade Level: 3, 4, 5 | |

This simple game with 5 variations develops place value understanding and strategic thinking. It is played on paper with a 6- or 9-sided die (printable pdf game sheet included). Two players take turns rolling a die and placing the resulting number in one of their four cells, representing the places of a 4-digit number. In the basic version the player who creates the larger number wins. Variations include aiming for the smaller number or a predetermined target number, using a decimal point, placing numbers in an opponent's cells, and several scoring options. Teachers' Notes include suggestions for introducing the game, support suggestions, and a link to a more challenging extension (Dicey Operations, cataloged separately). | Activity, Game Grade Level: 2, 3, 4, 5 | |

This engaging web site contains information and interactive applets related to various number systems: Egyptian, Babylonian, Chinese, Greek, Roman, Mayan, and Arabic. Users learn the history and structure of each system as well as how to count and write numbers. The site also allows users to explore finger systems, calculating machines, other number bases, and "interesting numbers." A series of pages on data and graphs includes information and activities on gathering, analyzing, graphing and sorting data. (Because the section on the Arabic number system is so extensive, it is cataloged separately as a related resource.) | Activity, Interactive Media, Tutorial, Reference Materials Grade Level: 1, 2, 3, 4, 5 |