Operations and Algebraic Thinking

Represent and solve problems involving multiplication and division.

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Resource | Resource Type Grade Level | Rating |
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This iOS app helps students to visualize number sentences and create models for addition, subtractions, multiplication, and division. The number line can be adjusted to represent multiples of numbers from one to one hundred. | Interactive Media, Mobile App Grade Level: K, 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 applet reinforces students' knowledge of the properties of rectangles and gives them a game in which to form and test hypotheses. In a 5x5 grid in which a rectangle has been hidden, students try to fix the location with the fewest number of probes (Note: press 'Start' to hide a different rectangle). Ideas for implementation, extension and support are included along with printable sheets and video clips of classroom testing. | Activity, Interactive Media Grade Level: 1, 2, 3 | |

In this series of videos (16 clips, 1-10 min each), math coach Becca Sherman works with a fourth grade class in developing concepts of equal groups, multiplication, division, and the relationships among them. She employs multiple models, including the "Singapore Bar Model," and facilitates student discussion, allowing her to assess students understanding of the language and the math involved. Included are teacher commentary, video transcripts, student work samples, and a video of debriefing among colleague observers. | Instructional Strategy, Video Grade Level: 3, 4, 5 Resource is part of a PD collection | |

This interactive Java applet use arrays and three different computational models (Grouping, Common, or Lattice) to help students visualize and understand the process of multiplication of whole numbers. In each method the user drags sliders to adjust the two factors and then observes the resulting changes in the rectangular array and in the respective algorithm and product. | Activity, Interactive Media Grade Level: 2, 3, 4, 5 Resource is part of a PD collection | |

This interactive Flash applet allows students to explore number properties and to develop systematic search strategies in dealing with divisors and remainders. It could also provide a context for practicing multiplication facts. The user chooses a divisor and the applet arranges counters numbered 1-100 into equal rows of the chosen number. Users can then color code any column, redivide the counters, color another column, and observe the effects. A question generator provides challenges which can be answered with or without the help of the applet. The Teachers' Notes page offers suggestions for implementation, discussion, extension, and support, along with links to related applets. | Activity, Interactive Media Grade Level: 3, 4, 5 | |

This open-ended investigation provides an opportunity for students to develop problem solving skills and explore patterns while applying number skills. Posed in the context of friends sending each other cards, it asks students to find how many cards are sent based on the number of friends, and to look for patterns that emerge in the results. The Teachers' Resources page offers rationale, suggestions for implementation, discussion questions, and ideas for extension and support. Be sure to check out the Solutions page to appreciate the potential range of student thinking. | Activity Grade Level: 3, 4, 5 | |

This is a collection of simple interactive activities to help young children practice early number skills. They use visual representations to develop counting and subitizing skills, number sense, place value concepts, and basic whole number operations (addition, subtraction, doubling). A teacher page summarizes the purpose and functions of each activity. | Activity, Interactive Media Grade Level: Pre-K, K, 1, 2 | |

This 2-lesson unit offers a variety of activities and games to help students master multiplication facts with 6 and 7 as factors. It is intended for students who understand the process of multiplication and have mastered the facts where 0, 1, 2, 3, 4, and 5 are factors. Students make use of the effects and properties of multiplication, write and solve story problems, and develop materials and strategies to assist in becoming fluent with the facts. The unit includes questions for students and teachers, a printable multiplication chart, extension ideas, and link to a Virtual Spinner and an online Times Table applet (both catalogued separately). | Activity, Interactive Media, Lesson Plans, Unit of Instruction, Music Grade Level: 3, 4, 5 |