Number and Operations in Base Ten

Use place value understanding and properties of operations to add and subtract.

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The authors of this 18-page article discuss their efforts to explore the implications of using rich mathematical tasks and promoting mathematical discourse, as proposed in the NCTM's teaching standards. While team-teaching in a third grade class, they analyzed the relative merits and challenges of presenting children with convergent and divergent tasks. The article includes anecdotes to illustrate the kinds of thinking and communication that children engaged in, and the empowerment they exhibited, as they explored questions about negative numbers and regrouping in subtraction. | Reference Materials, Article Grade Level: 2, 3, 4, 5 Resource is part of a PD collection | |

This 51-page pdf document demonstrates the connections between the CCSS content standards and the mathematical practice standards. It is a compilation of research, standards from several states, instructional strategies, common misconceptions, and examples for each standard at the grade 2 level. It is intended to help teachers understand what each standard means in terms of what students must know and be able to do. Additional flip books are cataloged separately for grades K-1 and 3-5. | Instructional Strategy, Reference Materials Grade Level: 2 | |

This web page provides links to resources aligned to the CCSS that guide and support second grade mathematics teaching and learning. Tasks developed by the Mathematics Assessment Resource Service (MARS), Problems of the Month, (POM home page is cataloged separately) and videos of public lessons and number talks developed by the Noyce Foundation are included. The tasks were designed to measure students’ ability to solve non-routine problems, explain and justify their solutions, and promote high level thinking skills. They include the scoring rubric, student responses, and discussion of student understanding and misconceptions. Resources are listed for specific grade 2 standards and are also organized by progression for an alternate search route. | Assessment, Instructional Strategy, Problem Set, Reference Materials, Video Grade Level: 2 | |

This web site contains information and interactive applets related to our Hindu-Arabic number system. Users learn the history and structure of the system as well as how to count and write numbers. Users can learn and practice various algorithms for whole number computation and explore fractions, decimals and percents in our number system. The site explains various sets of numbers and how they relate to operations. | Activity, Interactive Media, Tutorial, Reference Materials Grade Level: 1, 2, 3, 4, 5 | |

This interactive Java game, similar to Connect Four, helps students develop game strategy and fluency with number facts. Two players each try to connect four game pieces in a row (vertically, horizontally or diagonally) before the opponent does by correctly answering problems. For each game players can choose whole numbers and/or integers as well as the operation(s) – addition, subtraction, multiplication, division. They can also select the difficulty level and the time limit for each problem. | Activity, Game, Interactive Media Grade Level: 1, 2, 3, 4, 5, 6+ | |

This Java applet allows students to practice adding and subtracting whole numbers, decimals, or integers. Students use base blocks in blue to represent positive numbers, and red to represent either negative numbers or subtraction. The applet offers up to three decimal places, 2 to 4 columns, and bases from 2 through 5 and 10. Applet instructions and teaching ideas are available through the links at the top of the page. | Activity, Interactive Media Grade Level: 3, 4, 5, 6+ | |

This web page contains links to a video and several downloadable pdf files documenting the efforts of a third grade class to prove a set of conjectures about even and odd numbers. Included are a 4-minute Blue Stream video segment in which students discuss a classmate's conjecture that the sum of two odd numbers always equals an even number, a document providing background information on the investigation that led to the discussion, a transcript of the video, and the teacher's journal entry reflecting on the discussion and its implications. | Activity, Demonstration, Video Grade Level: 2, 3, 4, 5 Resource is part of a PD collection | |

This interactive Java applet helps students understand place value and regrouping. Base 10 is the default, but users may choose to work in base 2 or 5. A user places (or removes) chips of three colors in three columns to represent numbers of up to three digits. When the number of chips in any column equals the base number, the user can exchange them for a chip in the next column. Similarly a chip of a higher value can be exchanged for the base number of chips of the lower value. The applet can be used to model addition and subtraction with regrouping. | Activity, Interactive Media Grade Level: 1, 2, 3, 4, 5, 6+ | |

This interactive Java applet develops logical reasoning skills and fluency with two-digit addition. The game board consists of a ring of seven overlapping circles, each with 3 regions. Numbers are provided in five regions. The player drags 9 other numbers to the empty regions so that the sum of the numbers within each circle is 99. | Activity, Game, Interactive Media Grade Level: 2, 3, 4, 5 | |

In this Flash game, students may use a variety of activities to practice counting, collecting, exchanging, and making change for coins. Coin representations may show their amounts or not; coins may also be represented by coin tiles on a 10x10 grid, to help visualize their values. The five activities are: count, in which students determine the value of a given set of coins; collect, in which students choose coins to represent a given value; exchange, in which students use the smallest number of coins to represent a given value; change from coins, in which students are given a set of coins and asked how much change would be for a dollar (essentially counting up); and change from value, in which students are given a price owed (from a dollar) and asked to make change. There is a "bank" at the lower left side of the applet in which coins may be exchanged for other coins of the same value. | Activity Grade Level: Pre-K, K, 1, 2, 3, 4, 5 |