Strand: OPERATIONS AND ALGEBRAIC THINKING (3.OA)

Represent and solve problems involving multiplication and division within 100 (Standards 3.OA.1–4 and Standard 3.OA.7). They demonstrate understanding of the properties of multiplication and the relationship between multiplication and division (Standards 3.OA.5–6). Students use the four operations to identify and explain patterns in arithmetic (Standards 3.OA.8–9).

Standard 3.OA.5

Apply properties of operations as strategies to multiply and divide. For example: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known (commutative property of multiplication). 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30 (associative property of multiplication). Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56 (distributive property). (Third grade students may, but need not, use formal terms for these properties.)

• Arithmetic Four
In this game for two players, students solve problems involving whole number and integer addition, subtraction, multiplication, and division.
• Grade 3 Math Module 3: Multiplication & Division w/ Units of 0, 1, 6-9, and Multiples of 10
This 25-day module builds directly on students work with multiplication and division in Module 1. Module 3 extends the study of factors from 2, 3, 4, 5, and 10 to include all units from 0 to 10, as well as multiples of 10 within 100. Similar to the organization of Module 1, the introduction of new factors in Module 3 spreads across topics. This allows students to build fluency with facts involving a particular unit before moving on. The factors are sequenced to facilitate systematic instruction with increasingly sophisticated strategies and patterns.
• Grade 3 Unit 2: The Relationship Between Multiplication and Division (Georgia Standards)
In this unit, students will begin to understand the concepts of multiplication and division, learn the basic facts of multiplication and their related division facts, apply properties of operations (commutative, associative, and distributive) as strategies to multiply and divide, understand division as an unknown-factor problem. For example, find 32 8 by finding the number that makes 32 when multiplied by 8. Fluently multiply and divide within 100, using strategies such as the patterns and relationships between multiplication and division, understand multiplication and division as inverse operations, solve problems and explain their processes of solving division problems that can also be represented as unknown factor multiplication problems and represent and interpret data.
• Operations and Algebraic Thinking (3.OA) - Third Grade Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Third Grade Mathematics - Operations and Algebraic Thinking (3.OA)
• Valid Equalities? (Part 2)
This task is a follow-up task to a first grade task "Valid Equalities?" On the surface, both tasks can be completed with sound procedural fluency in addition and multiplication. However, these tasks present the opportunity to delve much more deeply into equivalence and strategic use of mathematical properties.

http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Shannon Olson and see the Mathematics - Elementary website. For general questions about Utah's Core Standards contact the Director - Jennifer Throndsen .

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.