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All About Multiplication 4: Balance Beam Discoveries
3, 4
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Professional Commentary

Students explore the balance beam model of multiplication and write the corresponding number sentences. They also play The Product Game using an online applet. A link to the applet, discussion questions, suggestions for assessment, and questions for teacher reflection are included. (author/sw)

Common Core State Standards for Mathematics
Grade 3
Operations and Algebraic Thinking
Represent and solve problems involving multiplication and division.
Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
Understand properties of multiplication and the relationship between multiplication and division.
Apply properties of operations as strategies to multiply and divide. 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.)
Grade 4
Operations and Algebraic Thinking
Gain familiarity with factors and multiples.
Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.
Ohio Mathematics Academic Content Standards (2001)
Number, Number Sense and Operations Standard
Grade Level Indicators (Grade 3)
Model, represent and explain multiplication; e.g., repeated addition, skip counting, rectangular arrays and area model. For example: a. Use conventional mathematical symbols to write equations for word problems involving multiplication. b. Understand that, unlike addition and subtraction, the factors in multiplication and division may have different units; e.g., 3 boxes of 5 cookies each.
Principles and Standards for School Mathematics
Number and Operations Standard
Understand meanings of operations and how they relate to one another
Expectations (3–5)
understand various meanings of multiplication and division;