Operations and Algebraic Thinking

Understand and apply properties of operations and the relationship between addition and subtraction.

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Resource | Resource Type Grade Level | Rating |
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This activity uses Cuisenaire Rods to develop flexibility and fluency with addition facts and to encourage systematic thinking. Several different challenges are posed, all involving making equivalent trains using a given number of rods of different colors. An interactive Flash Cuisenaire applet is provided as an alternative to using real rods. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, and a link to a related activity, Cuisenaire Counting (cataloged separately). | Activity, Interactive Media Grade Level: 1, 2 | |

This document provides descriptions and examples of what each Mathematics Common Core standard means a Grade One 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: 1 | |

This 3-page document (pdf) offers numerous strategies that children can use to perform addition, subtraction, and multiplication mentally. These strategies help develop fact fluency, number sense, operation sense, and use of patterns. | Instructional Strategy Grade Level: K, 1, 2, 3, 4 Resource is part of a PD collection | |

This site features nine Mixing-in-Math fast-paced card games that bring together arithmetic, probability, strategic thinking and logical reasoning. "Capture Cards" and "Ask Me" were designed especially for children just learning to count, compare, and add numbers. Each card game lists the goal, appropriate grade level, number of players and instructions. Players can use regular playing cards or Mixing in Math card decks can be purchased. | Activity, Game Grade Level: K, 1, 2, 3, 4, 5 | |

This open-ended interactive Flash applet helps students develop operation and number sense, facility with number facts, and understanding of equations. Users designate single-digit whole numbers or integers and operations on both sides of an equation and test for balance. Users can enter numbers by using the keyboard or arrow buttons or by dragging number tiles. Each element can be hidden and a seesaw may be toggled on/off. Teachers may use this applet to lead instruction, or students may use it independently to perform specific investigations or explore freely. Supplementary documents include Objectives, containing teaching suggestions, and a student recording sheet. | Activity, Interactive Media Grade Level: 1, 2, 3, 4, 5, 6+ | |

This activity promotes algebraic thinking of equivalency as well as giving children practice in addition and subtraction. Students see weights on each side of a balance, and are asked to find ways they can hang a weight or two weights to balance the bar. An interactive balance allows student to explore the different ways weights can be added to balance or equalize the bars. A more challenging problem,"Getting the Balance" is cataloged separately. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support. | Activity, Interactive Media Grade Level: 1, 2 | |

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 | |

Practice counting, counting by tens, place value, and fact families by entering your answers into the blank boxes; click the big blue and green buttons to check your work. Each of the five levels of Number Grid activities displays a section of a matrix containing a set of of consecutive whole numbers. A move from one number to the next within a row corresponds to a change of one; a move from one number to the next within a column refers to a change of ten. The three levels of Number Triangle activities provide practice with fact families and inverse relationships through flash cards. An addition/subtraction Number Triangle has two addends and a sum; a multiplication/division Number Triangle has two factors and a product. | Problem Set Grade Level: 1, 2, 3, 4, 5 | |

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+ |