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 Flash game develops students' computational fluency and flexibility. It can be played alone or with others. Players choose 6 face-down number cards, and the applet provides a target number. Number cards include one each of 25, 50, 75, and 100, and multiple copies of 1 to 10. The goal is to use the selected numbers and the four basic operations (addition, subtraction, multiplication, division) to arrive at the target. Players can ask the applet to Show a Solution, although others may be possible. Several rule and scoring variations are suggested. A full screen option facilitates use on an interactive board. (This game is not self-checking.) | Activity, Game, Interactive Media Grade Level: 3, 4, 5 | |

This interactive 100 grid has a variety of open-ended uses. Users can "make" as many counters as they choose from among three different kinds, and then drag them onto the grid, allowing any number to be covered by up to 3 different markers at one time. An Ideas page offers possible tasks and games suited to the applet. | Activity, Interactive Media Grade Level: K, 1, 2, 3, 4, 5 | |

With this flexible Flash applet students can explore a wide range of concepts, including addition and subtraction, factors and multiples, fractions, ratios, and combinations. Users place, move and rotate virtual Cuisenaire Rods on a grid which can be enlarged, reduced, moved or printed. It contains a link to page of challenges which can take advantage of this tool. | Activity, Interactive Media Grade Level: 1, 2, 3, 4, 5 | |

This Java applet shows the distributive property in action. Toggle to change the height and width of a rectangle, the side lengths of which represent two factors; click on any interior edge of the rectangle's unit squares to create a new re-grouping. An expression appears at the bottom displaying the numeric representation of the new groups, illustrating the distributive property. | Interactive Media Grade Level: 3, 4, 5 | |

This Flash applet allows the user to explore the concept of a function using an input-output machine with two operations and options to set and hide or reveal all operations and numbers. A notepad is available for recording inputs and outputs, and a loop function takes the current output as the next input. | Activity, Interactive Media Grade Level: 3, 4, 5, 6+ | |

This narrative document describes the progression of Counting and Cardinality and Operations and Algebraic Thinking across the K-5 grade band. It is informed both by research on children's cognitive development and by the logical structure of mathematics. The document discusses the most important goals for elementary students that of understanding and using numbers. The focus is on the basic operations—the kinds of quantitative relationships they model and consequently the kinds of problems they can be used to solve as well as their mathematical properties and relationships. | Reference Materials, Article Grade Level: K, 1, 2, 3, 4, 5 | |

This lesson plan provides the teacher with an activity for introducing the game Krypto, which helps to develop number sense, computational skill, and an understanding of the order of operations. Players are given five number cards. They combine them, using the standard arithmetic operations, to create a target number. As students investigate the game, they develop strategies for finding solutions efficiently. The plan includes learning objectives, materials needed, questions to ask students, assessment options, extensions, teacher self-reflection questions, and a link to the online version, Primary Krypto, (catalogued separately). | Activity, Game, Lesson Plans Grade Level: 3, 4, 5, 6+ | |

This flash applet provides students with an activity to become more familiar with factors and multiples. The challenge is to arrange the four number cards (1, 2, 3 and 21) on a square of the grid to make as many different diagonal, vertical or horizontal lines as possible. The number card can be placed on a square of the grid if the square is the same number, a multiple of that number and or a factor of that number. Users have the ability to change the difficulty level. The Teachers' Notes page offers rationale, suggestions for implementation, key discussion questions, ideas for extension and support. | Activity, Interactive Media Grade Level: 3, 4, 5 | |

This interactive applet allows a student to visually explore the concept of factors by creating different rectangular arrays for a number. The user constructs the array by clicking and dragging on a grid. The length and width of the array are factors of the number. A student can elect an option of a randomly selected number or the student selects his own number between 2 and 50. Exploration questions are included to promote student discovery of mathematical concepts with factors. | Activity, Interactive Media Grade Level: 3, 4, 5 Resource is part of a PD collection | |

This interactive Java applet helps students explore the relationship between area and multiplication. First, users are asked to input all factor pairs of a given number. Then, selecting each of those factor pairs, the user draws the respective rectangular array by clicking and dragging across a grid. Options include the use of the commutative property (e.g., user must enter both 2x4 and 4x2 for factors of 8 and represent them with different arrays), entering a number of the user's own choice, and an optional scoring feature allowing the user to keep track of the number correct. | Interactive Media Grade Level: 2, 3, 4 |