1. Grade 3 Common Core Multiplication Represent and solve problems involving multiplication and division. 3.OA.1 Interpret products of whole numbers, e.g., interpret 5 x 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 x 7. Essential Skills and Knowledge Knowledge that multiplication is the process of repeated addition, arrays, and/or equal groups Ability to use concrete objects, pictures, and arrays to represent the product as the total number of objects Knowledge that the product represented by the array is equivalent to the total of equal addends Ability to apply knowledge of repeated addition up to 5 rows and 5 columns and partitioning, which leads to multiplication Knowledge that the example in Standard 30A1 can also represent the total number of objects with 5 items in each of 7 groups (Commutative Property)

2. Grade 3 Common Core Multiplication Represent and solve problems involving multiplication and division. 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. Essential Skills and Knowledge Ability to determine when to use multiplication or division to solve a given word problem situation Ability to solve different types of multiplication and division word problems

3. Grade 3 Common Core Multiplication Represent and solve problems involving multiplication and division. 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 x ? = 48, 5 = ☐ ÷ 3, 6 x 6 = ? Essential Skills and Knowledge Ability to use concrete objects to compose and decompose sets of numbers Ability to use the inverse operation as it applies to given equation Knowledge of fact families Ability to find the unknown in a given multiplication or division equation, where the unknown is represented by a question mark, a box, or a blank line Ability to solve problems that employ different placements for the unknown and product/quotient

4. Grade 3 Common Core Multiplication Understand properties of multiplication and the relationship between multiplication and division. 3.OA.5 Apply properties of operations as strategies to multiply and divide. If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known. (Commutative property of multiplication) 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30. (Associative property of multiplication) Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) which leads to 40 + 16 = 56. (Distributive property) Essential Skills and Knowledge Ability to break apart and manipulate the numbers (decomposing and composing numbers) Knowledge of the properties of multiplication include Zero, Identity, Commutative, Associative and Distributive properties (CCSS, Page 90, Table 3) Knowledge that the properties of division include the Distributive Property, but not Commutative or Associative. Ability to understand and apply the Properties of Operations as opposed to simply naming them Ability to apply of the Properties of Operations as strategies for increased efficiency

5. Grade 3 Common Core Multiplication 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 x 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. Essential Skills and Knowledge Knowledge of multiplication and division strategies and properties to achieve efficient recall of facts Ability to use multiple strategies to enhance understanding Ability to model the various properties using concrete materials

6. Grade 3 Common Core Multiplication Use place value understanding and properties of operation to perform multi-digit arithmetic 3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range of 10-90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations. Essential Skills and Knowledge Ability to apply knowledge of place value (e.g., 9 x 80 is 9 times 8 tens = 72 tens) Ability to apply the Properties of Operations

7. Grade 3 Common Core Multiplication Geometric measurement: understand concepts of area and relate area to multiplication and to addition. 3.MD.7 Relate area to the operations of multiplication and addition. Essential Skills and Knowledge Ability to explain the relationship of multiplication arrays and area

8. Grade 4 Common Core Multiplication Use the four operations with whole numbers to solve problems. 4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Essential Skills and Knowledge Knowledge of and ability to apply understanding of multiplication as repeated addition, as “equal groups of”, and the Commutative Property 4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. Essential Skills and Knowledge Ability to solve various types of problems involving multiplication and division through initial use of concrete materials and pictures, leading to the use of equations as a tool in solutions

9. Grade 4 Common Core Multiplication Gain familiarity with factors and multiples. 4.OA.4 Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range of 1-100 is prime or composite. Essential Skills and Knowledge Knowledge of multiplication as arrays and its connection to area of rectangles to determine factor pairs Knowledge of and ability to apply multiplication facts to determine multiples of one- digit numbers Ability to apply knowledge of basic multiplication facts to determine if products are prime or composite by determining all possible factor combinations for specific products

10. Grade 4 Common Core Multiplication Generalize place value understanding for multi-digit whole numbers. 4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Essential Skills and Knowledge Knowledge of the use of arrays area models for multiplication Knowledge of and ability to apply the Properties of Operations

11. Grade 5Common Core Multiplication Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm. 5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Essential Skills and Knowledge Ability to recognize that the product is not always larger than its factors Ability to recognize that the quotient is not always smaller than the dividend

12. Grade 5Common Core Multiplication Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 5.NF.4 a. Interpret the product (a/b) q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a q ÷ b. For example, use a visual fraction model to show (23) 4 = 83, and create a story context for this equation. Do the same with (23) (45) =815. (In general, (a/b) (c/d) = (ac/bd). b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Essential Skills and Knowledge Knowledge of unit fractions to multiply all fractions. (4.NF.3) Knowledge of using rectangular arrays to find area using rational numbers. (4.NBT.5)

13. Grade 5Common Core Multiplication 5.NF.5 Interpret multiplication as scaling (resizing) by: a.Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. b. Explaining why multiplying a given number by a fraction greater than one results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence