Unit 1

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

Grade 3
Math

Unit Length and Description:

30 days

The first unit builds upon the foundation of multiplicative thinking with units started in Grade 2. Students will 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.

Standards:

 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 a 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 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. 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. Mathematical Practices 1. Make sense of problems and persevere in solving them.  2. Reason abstractly and quantitatively.  3. Construct viable arguments and critique the reasoning of others.  4. Model with mathematics.  5. Use appropriate tools strategically. 6. Attend to precision 7. Look for and make use of structure.  8. Look for and express regularity in repeated reasoning. Instructional Outcomes ·         3.OA.A.1: o   I can multiply to find the product. o   I can show products using equal groups, arrays, and repeated addition. ·         3.OA.A.2: o   I can find the quotient of whole numbers using equal groups. o   I can tell what the numbers in a division problem mean. o   I can explain what division means. o   I can show division as equal sharing. ·         3.OA.A.3: o   I can multiply to solve word problems. o   I can divide to solve word problems. o   I can decide when to multiply or divide to solve word problems. ·         3.OA.A.4: o   I can find the missing number in a multiplication problem. o   I can find the missing number in a division problem. ·         3.OA.B.5: o   I can use the properties of multiplication and division to solve problems. o   I can explain the commutative property of multiplication. o   I can explain the associative property of multiplication. o   I can explain the distributive property of multiplication. ·         3.OA.B.6: o   I can identify the multiplication problem related to the division problem. o   I can use multiplication to solve division problems. o   I can recognize and explain the relationship between multiplication and division. ·         3.OA.C.7: o   I can memorize all products within 100. o   I can use strategies to solve a multiplication problem. o    I can use strategies to solve a division problem. ·         3.OA.D.8: o   I can construct and equation with a letter standing for the unknown quantity. o   I can solve one-step and two-step word problems involving multiplication and division. ·         3.OA.D.9: o   I can identify patterns. o   I can explain rules for a pattern using properties of operations. o   I can explain relationships between the numbers in a pattern.

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?