Operations and Algebraic Thinking

Add and subtract within 20.

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Resource | Resource Type Grade Level | Rating |
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This problem provides an opportunity for students to practice counting and to represent and record findings in different ways: "Noah saw 12 legs walk by into the Ark. How many creatures did he see?" Multiple solution possibilities encourage students to be systematic in their strategies. The Teachers' Notes page offers suggestions for implementation, discussion questions, and an idea for extension. | Activity Grade Level: K, 1, 2, 3 | |

In this six lesson unit, students recognize and explore the relationships among pennies, nickels, dimes, and quarters. They estimate and count sets of mixed coins, create equivalent sets, write story problems that involve money, and use coins to make patterns. Within the unit there is a link to US Mint. http://www.usmint.gov/kids/teachers/ | Unit of Instruction Grade Level: Pre-K, K, 1, 2 | |

This Flash applet generates number fact questions for the game of Bingo. Each of the six levels focuses on a different range of number facts (addition, subtraction, and multiplication), which are displayed one at a time in a variety of question formats. The applet is intended for use in a class/group setting with a projector or interactive whiteboard. Downloadable cards for each level are available from the menu page. At any time in a game the "number facts so far" feature will reveal all the questions presented in the current round to facilitate review or verification of a winning board. | Activity, Game, Interactive Media Grade Level: 2, 3, 4, 5 | |

This applet demonstrates operations with whole numbers on a number line. The student selects an operation and the applet represents an example. It helps students understand the commutativity of multiplication, remainders in division, inverse operations, and the relationships between operations. | Activity, Interactive Media Grade Level: K, 1, 2, 3 | |

Teachers and students can use this interactive Java applet to model and carry out arithmetic operations on the number line. Users manipulate the size, position, and direction of color bars to represent addition, subtraction, multiplication and division with whole numbers, integers and fractions. Options include the ability to zoom in and out, change the colors of the bars, and adjust the step size of the bars and number line increments. | Activity, Interactive Media Grade Level: 1, 2, 3, 4, 5, 6+ | |

This interactive applet gives students practice with addition and subtraction of whole numbers and integers. Users drag the given number arrows onto a number line and choose whether to add or subtract them in order to arrive at the given target number. After all arrows are placed in a correct arrangement, a user drags numbers and operations signs to create a number sentence (equation) that represents the arrow sequence. | Activity, Game, Interactive Media Grade Level: 1, 2, 3, 4, 5 | |

This activity helps children become more familiar with horizontal and vertical number lines (0 through 10) and how to use them for addition. It can be used to introduce subtraction as the inverse of addition and the use of an unknown number. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support, printable number lines (pdf), and a link to a related game, Incey Wincey Spider (catalogued separately). | Activity Grade Level: K, 1 | |

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 | |

This article focuses on the role and techniques of effective ("distributed") practice that leads to full and fluent mastery of mental mathematics as well as conceptual growth around properties of arithmetic. It lists the essential mental math skills needed for fluent computation at grades 1, 2, and 3. The article describes a number of strategies for developing mental skills and links to pages with more details on others (some not yet complete). While this article refers to the Think Math! curriculum published by EDC, the methods generalize to any program. The Fact of the Day technique and a related video are cataloged separately. | Activity, Instructional Strategy, Reference Materials, Article Grade Level: 1, 2, 3, 4, 5 Resource is part of a PD collection | |

This pair of videos (8 min and 10 min) and accompanying text illustrate various strategies for providing mental skills practice that is brief, interesting, useful, and effective. They include examples of teachers working with their students in group settings as well as narrative elaboration by Paul Goldenburg. Two related articles (Practice and Fact of the day) are cataloged separately. | Activity, Instructional Strategy, Reference Materials, Article, Video Grade Level: 1, 2, 3, 4, 5, 6+ |