Operations and Algebraic Thinking

Understand properties of multiplication and the relationship between multiplication and division.

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Resource | Resource Type Grade Level | Rating |
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This interactive application helps students to learn visually about numbers from their possible arrangements and how those arrangements relate to division, multiplication, and factors. The web applet divides numbers and displays calculation to show the remainder as a number, fraction, or decimal value and allows demonstration of types of numbers such as prime, square, and triangular. The number explorer has automated tests for divisibility, factor pairs, or prime factors. Three different shapes can be used, the original fish swim around and obediently arrange themselves to show number properties. However balls or cards cards can be used instead, these animate faster and are better for displaying numbers. | Activity, Demonstration, Interactive Media, Video Grade Level: 3, 4, 5 | |

This interactive game develops fluency and flexibility with whole number operations. In each round the player is given 4 single-digit whole numbers, presented in the context of a factory. The player uses each number exactly once with the interactive calculator to arrive as close as possible to a given target number. | Activity, Game, Interactive Media Grade Level: 4, 5 | |

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 | |

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 Java applet, based on the familiar game Connect Four, gives students practice in applying order of operations. Two players take turns evaluating expressions involving the four basic operations (addition, subtraction, multiplication and division). If correct, the player places a black or red checker on the board with the goal of connecting four in a row ( horizontally, vertically, or diagonally) before the opponent does. Players choose from four levels of difficulty; they can adjust the timing feature and whether to involve exponents and/or parentheses. | Activity, Game, Interactive Media Grade Level: 3, 4, 5, 6+ | |

This Java tool is used to strengthen student understanding of equality and computation of numerical expressions. The applet also helps students understand that equality is a relationship, not an operation. After entering an expression in both the red and blue pan, the pans will move up and down depending on which expression is greater. When the expressions are equivalent, the pans will balance and the full equation will be entered into the Balanced Equations table. Instructions and exploration directions and questions are included. | Activity, Interactive Media Grade Level: 3, 4, 5 | |

This site provides a detailed instructional plan designed to lead students to explore the number patterns and fractal properties of Pascal's Triangle. Included are links to two interactive activities: "Coloring Multiples" and "Coloring Remainders" each catalogued separately, three guided discussions on" Multiples and Integer Multiplication", "Remainders and Euclidean Division", and "Pascal's Triangle", exploration questions and support material (worksheets). | Activity, Interactive Media, Lesson Plans Grade Level: 3, 4, 5 | |

This mobile app (available for both iOS and Android devices) was developed by the National Council of Teachers of Mathematics with funding from Verizon Foundation. The app is based on the Decimal Maze from the popular lesson "Too Big or Too Small". The goal is to help Okta reach the target (maximum, minimum, or a specific value) by choosing a path from the top of the maze to the bottom — adding, subtracting, multiplying and dividing as the player goes. Seven levels with seven puzzles in each level test the player's skills with operation with powers of ten, negative numbers, fractions, decimals, and exponents. | Game, Interactive Media, Mobile App Grade Level: 3, 4, 5, 6+ |