Operations and Algebraic Thinking

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

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This is a sample PARCC assessment task based on CCSS grade 3 operations and algebraic thinking standards as well as the measurement and data standards. In this interactive multi-step task students must write a number sentence that can be used to find how many tiles high the mural is at school and then show the value of the Distributive Property in solving a problem. Included are the alignments to the CCSS, a scoring rubric and background on the task itself. | Assessment, Problem Set, Reference Materials Grade Level: 3 | |

This web page links to a series of 6 pages of number puzzles (141 altogether) which develop flexibility and computational fluency. Puzzles provide a target number and several other numbers, each of which must be used exactly once to arrive at the target. Solvers may use any of the four basic operations (addition, subtraction, multiplication, division) and parentheses. Most puzzles are solvable with whole numbers, but a few solutions involve fractions. Each puzzle contains a hint as well as at least one solution. Red asterisks indicate more difficult puzzles. | Activity, Problem Set Grade Level: 3, 4, 5, 6+ | |

In this 14-minute video UK teacher Sally Hill uses patterns to help her students learn the multiples of four and understand how to apply that knowledge to more complex multi-digit problems. Head teacher Kate Frood discusses the school's guiding principles and her own style of leadership. The page includes a link to a pdf document summarizing K-4 Mental Math Strategies [cataloged separately]. | Instructional Strategy, Lesson Plans, Video Grade Level: 3, 4, 5 Resource is part of a PD collection | |

This problem helps children become familiar with the idea of a symbol (in this case a shape) representing a number. Students also have an opportunity to see the multiplication properties of one and zero in a challenging puzzle. By studying the twelve multiplication equations which use eleven different colored shapes, students are to determine each shape's unique number value from a list of 0 to 12. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, support with down loadable handouts and a link to an extension activity, What's It Worth? (cataloged separately). | Activity Grade Level: 4, 5, 6+ | |

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 | |

This number challenge is an opportunity to reinforce mental arithmetic and order of operations while developing systematic work habits. Students are asked to use the numbers 4, 6, 6, and 8 (exactly once each) and the four basic operations to find as many ways as they can to represent the number 24. There are over 60 different ways! The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for support, and a link to a related article, Opening Out. (cataloged separately). | Activity Grade Level: 3, 4, 5 | |

This interactive Flash book of poems by Greg Tang and pictures by Harry Briggs helps children master their times tables through a deeper, more intuitive understanding of multiplication instead of memorization. Students use partial products to multiply larger numbers, first breaking them into smaller, more manageable parts. After reading the poem and examples, learners can test themselves by applying the strategies to a series of 3-5 challenges. | Interactive Media, Problem Set, Illustration, Video Grade Level: 3, 4, 5 | |

This interactive Flash applet contains a progressive range of exercises to sharpen mental math and recall of number facts. Levels include one-digit addition and subtraction within 20, two-digit addition and subtraction within 100, and multiplication up to x5 and x10. The goal is to complete 10 correctly as quickly as possible. An incorrect answer deletes a point, discouraging guessing. At the end of each round the applet reports the time taken and the number of errors. | Activity, Interactive Media Grade Level: 1, 2, 3, 4 | |

Students can use this interactive Java applet to explore multiplication, the distributive property, prime vs composite, square numbers, and more. Users fill in squares and draw rectangles on a 10 x 10 grid with 10 possible colors to use. Use the quick tour to get started. | Activity, Interactive Media Grade Level: 2, 3, 4, 5 | |

This page provides examples of Third Grade Number (Operations and Algebraic Thinking, Number and Operations in Base Ten, and Number Operations-Fractions) activities aligned with the Common Core State Standards. A CCSS standard is stated and the possible activities are listed below and linked. All activities are suitable for use in Math Centers, small group or whole class settings and are designed to elicit a range of responses and provide opportunities for students to communicate their reasoning and mathematical thinking. Instructions for each task are typed in large print and written in child-friendly language to enable students to work on activities independently after a brief introduction to the task. All files listed are in PDF format. | Activity, Game Grade Level: 3 |