3: Q I know all of the Simple and Complex Learning Goals and my understanding goes beyond the grade level target.

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1 Topic Proficiency Scale Domain: Operations and Algebraic Thinking Critical Area: Multiplication & Division within 100 EXPECTED MASTERY: 7 s, 8 s, and 9 s Facts 4.0 I know all of the Simple and Complex Learning Goals and my understanding goes beyond the grade level target. COMPLEX 3.0 I know all of the Simple and Complex Learning Goals. C1: Solve and explain multiplication and division word problems using words, models, equations, and/or strategies within 100 by writing an equation with a symbol for the unknown number to represent the problem (emphasis on 7 s, 8 s, and 9 s facts including previous facts 3 s, 4 s, 6 s, 10 s, 2 s, 5 s, 0 s, 1 s). (3.OA.3) C2: Fluently multiply and divide within 100 using properties and the relationship between multiplication and division (emphasis on 7 s, 8 s, and 9 s facts including previous facts 3 s, 4 s, 6 s, 10 s, 2 s, 5 s, 0 s, 1 s). (3.OA.5, 7) 2.5 I know all of the Simple Learning Goals plus some of the Complex Learning Goals. SIMPLE 2.0 I know all of the Simple Learning Goals. S1: Determine the unknown number in a multiplication and division equation relating three whole numbers. (3.OA.4) Academic Vocabulary: N/A 1.5 Not applicable. 1.0 I know some of the Simple Learning Goals. 0.5 Not applicable. 0.0 No evidence of knowing the Learning Goals.

2 Topic Proficiency Scale Domain: Operations and Algebraic Thinking Critical Area: Multiplication & Division within 100 EXPECTED MASTERY: 7 s, 8 s, and 9 s Facts 3.OA.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 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 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 =? 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.) 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) = = 56. (Distributive property.) 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. 4.0 I know all of the Simple and Complex Learning Goals and my understanding goes beyond the grade level target. COMPLEX 3.0 I know all of the Simple and Complex Learning Goals. Solve and explain multiplication and division word problems using words, models, equations, and/or strategies within 100 by writing an equation with a symbol for the unknown number to represent the problem (emphasis on 7 s, 8 s, and 9 s facts including previous facts 3 s, 4 s, 6 s, 10 s, 2 s, 5 s, 0 s, 1 s). (3.OA.3) Fluently multiply and divide within 100 using properties and the relationship between multiplication and division (emphasis on 7 s, 8 s, and 9 s facts including previous facts 3 s, 4 s, 6 s, 10 s, 2 s, 5 s, 0 s, 1 s). (3.OA.5, 7) 2.5 I know all of the Simple Learning Goals plus some of the Complex Learning Goals. SIMPLE 2.0 I know all of the Simple Learning Goals. Determine the unknown number in a multiplication and division equation relating three whole numbers. (3.OA.4) Academic Vocabulary: 1.5 Not applicable. 1.0 I know some of the Simple Learning Goals. 0.5 Not applicable. 0.0 No evidence of knowing the Learning Goals.

3 Guiding Questions towards Mastery: 1. How would you describe the problem in your own words? 2. What information is given in the problem? 3. What number model could you construct to represent the problem? 4. What equation did you use to solve for the unknown? 5. What strategies or visual model can you use to solve multiplication or division problems using the properties of operation? COMPLEX 3.0 I know all of the Simple and Complex Learning Goals Solve and explain multiplication and division word problems using words, models, equations, and/or strategies within 100 by writing an equation with a symbol for the unknown number to represent the problem (emphasis on 7 s, 8 s, and 9 s facts including previous facts 3 s, 4 s, 6 s, 10 s, 2 s, 5 s, 0 s, 1 s). (3.OA.3) Mastery of Learning Goals: Students will choose the correct operation to solve the problem. Students write a number equation for the unknown before solving. Students will solve and explain multiplication and division word problems with words, pictures, or numbers. (ex. Labeling or telling why you did, what you did, not listing what was done step by step) Many pictures and explanations taken from North Carolina Unpacked Math Standards, and Engage New York,

4 Fluently multiply and divide within 100 using properties and the relationship between multiplication and division (emphasis on 7 s, 8 s, and 9 s facts including previous facts 3 s, 4 s, 6 s, 10 s, 2 s, 5 s, 0 s, 1 s). (3.OA. 5 & 7) Students will demonstrate the relationship between multiplication and division (ex. 8 x 5 = 40 so 40 8 = 5) Strategies students may use to attain fluency include: Multiplication by zeros and ones Doubles (2s facts), Doubling twice (4s), Doubling three times (8s) Tens facts (relating to place value, 5 x 10 is 5 tens or 50) Multiples of ten (3 x 50 = 3 x 5 x 10 or 3 x 10 x 5) Five facts (half of tens) Skip counting (counting groups of and knowing how many groups have been counted) Square numbers (ex: 3 x 3) Nines (10 groups less one group, e.g., 9 x 3 is 10 groups of 3 minus one group of 3) Decomposing into known facts (6 x 7 is 6 x 6 plus one more group of 6) Turn-around facts (Commutative Property) Fact families (Ex:6x4=24;24 6=4;24 4=6;4x6=24) Missing factors Students should have exposure to multiplication and division problems presented in both vertical and horizontal forms. Write a multiplication expression to represent this array. Students are introduced to the distributive property of multiplication over addition as a strategy for using products they know to solve products they don t know. Students would be using mental math to determine a product. Here are ways that students could use the distributive property to determine the product of 7 x 6. Again, students should use the distributive property, but can refer to this in informal language such as breaking numbers apart. Another example if the distributive property helps students determine the products and factors of problems by breaking numbers apart. For example, for the problem 7 x 8 =?, students can decompose the 7 into a 5 and 2, and reach the answer by multiplying 5 x 8 = 40 and 2 x 8 =16 and adding the two products ( = 56). Student 1 Student 2 7 x 6 7 x 6 7 x 5 = 35 7 x 3 = 21 7 x 1= 7 7 x 3 = = = 42 ***** Another example if the distributive property helps students determine the products and factors of problems by breaking numbers apart. For example, for the problem 7 x 8 =?, students can decompose the 7 into a 5 and 2, and reach the answer by multiplying 5 x 8 = 40 and 2 x 8 =16 and adding the two products ( = 56)

5 As third graders explore and develop conceptual understanding of multiplication and division, they recognize the structure of multiplication by noticing patterns and making generalizations about multiplication and division applying a variety of properties. These properties are not taught in isolation, but rather should be developed and discussed as a part of carefully related student experiences. Note that instruction does not stop to teach the properties. Incorporate opportunities for students to use the properties to develop strategies and patterns to simplify what is happening when they multiply two numbers. (The Common Core Mathematics Companion by the National Council of Teachers of Mathematics) Mathematical Practices: 1. Make sense of problems and persevere in solving them 4. Model with mathematics 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning District Resources: My Math Lsn. 8.2 (pg 435), Lsn. 8.3 (pg 441), Lsn 8.4 (pg 449), Lsn. 8.5 (pg 455), Lsn 8.6 (pg 461), Lsn. 9.1 (pg 501) and Lsn. 9.2 (pg 507) Exemplar: Mr. Doyle shares 1 roll of bulletin board paper equally with 8 teachers. The total length of the roll is 72 meters. How much bulletin board paper does each teacher get? 72 8 = n 8 teachers are dividing 72 meters of paper. I can multiply up to find the quotient. 8 x 3 = 24 8 x 3 = 24 8 x 3 = I figured 8 teachers, each getting 3 meters of paper = 24 meters. I kept doing this and added the products until I reached 72 meters. I had to do it 3 times so I added 3 meters of paper 3 times or multiplied 3 x 3 meters and got 9 meters of paper. Each teacher will get 9 meters of paper. It is important for students to understand what is actually happening when they use a strategy. While representing the multiply up strategy to find a quotient may be challenging, it cements understanding. Gabriella solves 90 x 3 by thinking about 9 x 3 x 10. Explain her strategy. 90 x 3 = 9 x 3 x 10 = 9 x 3 x 10 = 27 x 10 = 270 Gabriella breaks the 90 x 3 into 9 x 3 x 10. This makes the problem easier to solve. Instead of thinking of the problem as 90 x 3, she can solve by thinking of an easier fact, 9 x 3 and then 27 x 10. Describing procedural steps does not constitute an explanation. An explanation uses words, pictures, and/or numbers and tells how they solved the problem. (ex. Labeling or tell why you did what you did, not listing what was done step by step) Many pictures and explanations taken from North Carolina Unpacked Math Standards, and Engage New York,