Utah Core Standards
UT.3.OA. OPERATIONS AND ALGEBRAIC THINKING (3.OA)
Represent and solve problems involving multiplication and division within 100. Demonstrate understanding of the properties of multiplication and the relationship between multiplication and division. Use the four operations to identify and explain patterns in arithmetic.
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.)
3.OA.7. Fluently multiply and divide.
3.OA.7.a. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations. (For example, knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8.)
UT.3.NBT. NUMBER AND OPERATIONS IN BASE TEN (3.NBT)
Use place value understanding and properties of operations to perform multi-digit arithmetic. A range of algorithms may be used.
3.NBT.2. Fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.