 Unit 1

Properties of Multiplication and Division and Solving Problems with Units 2-5 and 10

Math

Unit Length and Description:

Unit 1 builds upon the foundation of multiplicative thinking with units. Students concentrate on the meaning of multiplication and division and begin developing fluency for learning products involving factors of 2, 3, 4, 5, and 10. They solve one and two-step word problems.

Louisiana Student Standards for Mathematics (LSSM)

 Major Cluster Standards Represent and solve problems involving multiplication and division. 3.OA.A.1 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.A.2 Interpret whole-number 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 context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. 3.OA.A.3 Use multiplication and division within 100 to solve word problems 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. 3.OA.A.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.B.5 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.) 3.OA.B.6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. Multiply and Divide within 100 3.OA.C.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 one-digit numbers. Solve problems involving the four operations, and identify and explain patterns in arithmetic. 3.OA.D.8 Solve two-step 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.OA.D.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.

Enduring Understandings:

·         I can show how to multiply and divide in different ways.

·         Mental pictures help me remember facts and ideas.

·         Knowing and understanding multiplication helps me understand division.

·         I can solve problems by using multiplication and division.

Essential Questions:

·         How can I solve multiplication and division problems in different ways?

·         How do mental models help me remember?

·         How can multiplication and division help me solve problems?

·         How can working a problem help me better understand the answer?