Before You Begin this Unit… 

Unit at a Glance 
This unit is the first and only Investigations unit in Grade 3 involving multiplication and division. In Grade 2, students explored the idea of repeatedly adding up the number of rectangles in rows and columns of an array and worked on skip counting by 2s, 5s, and 10s. The work that students complete in the beginning of this unit with reallife contexts of groups, concrete and pictorial representations of multiplication are essential for building students’ mathematical understanding and concept of what multiplication and division mean. Students’ fluency of multiplication and division facts are developed during this unit, but may not be fully developed at the end of it. Encourage students to use strategies to help them find the answers to facts they may not know. For example, when finding the product of 8x7, students may know 8x5 = 40 and then add 2 more groups of 8 (16) to get a total of 56. 
Suggested Dates: Estimated Duration: 30 days *Investigation 1: 4 lessons*Investigation 2: 6 lessons *Investigation 3: 9 lessons (Do 3.1A, *3.5A, *3.5B, 3.7A) *Skip 3.5. 3.5A and B will take it's place. *Investigation 4: 7 lessons 

Standards Addressed in the Unit  
Represent and solve problems involving multiplication and division.
3.OA1. 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.
3.OA.2 Interpret wholenumber quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
3.OA.3. 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.^{1}
3.OA.4. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?
Understand properties of multiplication and the relationship between multiplication and division.
3.OA.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.)
3.OA.6. Understand division as an unknownfactor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
Multiply and divide within 100.
3.OA.7. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two onedigit numbers.
Solve problems involving the four operations, and identify and explain patterns in arithmetic. 3.OA.8 3.OA.9
3.OA.8. Solve twostep word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.^{3} 3.OA.9. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. Link to CCSS Unpacking DocumentUpdated Sept. '15 