## Common Core State Standards for Mathematics

Grade(s) 3 resources related to the following standard:
Operations and Algebraic Thinking
Understand properties of multiplication and the relationship between multiplication and division.
5. Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)

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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
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
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
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
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
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