Unit 3

Multiplication and Division with Units of 0, 1, 6–9, and Multiples of 10

Grade 3

Math

Description: Students learn the remaining multiplication and division facts in as they continue to develop their understanding of multiplication and division strategies within 100 and use those strategies to solve one- and two-step word problems. The “2, 3, 4, 5 and 10 facts” unit (Unit 1) and the “0, 1, 6, 7, 8, 9 and multiples of 10 facts” unit (Unit 3) both provide important, sustained time for work in understanding the structure of rectangular arrays to prepare students for area in Unit 4.

Louisiana Student Standards for Mathematics (LSSM)

Instructional Outcomes

 Major Cluster Standards Represent and solve problems involving multiplication and division. 3.OA.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.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.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. (Students need not use formal terms for these properties.) 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 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.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.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.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. Use place value understanding and properties of operations to perform multi-digit arithmetic. A range of algorithms may be used. 3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

Enduring Understandings:

·         I can show how to multiply 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.

·         I can learn more from working the problem than looking at the answer.

·         Unfamiliar multiplication problems may be solved by using known multiplication facts and properties, e.g., 8 x 7 = (8 x 2) + (8 x 5)

Essential Questions:

·         Why is multiplication necessary?

·         How can I show how to solve a multiplication problem in different ways?

·         Why 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?

·         What operation can we use to solve the problem and why?

·         How is multiplication related to division and other operations?