TanyaStage1

=Stage 1 Identify Desired Results=
 * ======**Establish Goals:** **(G)**====== ||
 * ** Common Core State Standards **
 * Content Area: ** Math
 * Grade Level: ** Grade 3
 * Domain: ** Operations & Algebraic Thinking
 * Cluster: ** 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 at 5x7.//
 * Standards: **

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 group 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.5. Apply properties of operations as strategies to multiply and divide. //Examples: 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) = 40 + 16 = 56. (Distributive property).//

3.OA.7. Fluently multiply and divide within 100, using strategies such as relationships 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.

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 time a number is always even, and explain why 4 times a number can be decomposed into two equal addends.//


 * Common Core State Standards **
 * Content Area: ** Math
 * Grade Level: ** Grade 3
 * Domain: ** Number & Operations in Base Ten
 * Cluster: ** Use place value understanding and properties of operations to perform multi-digit arithmetic.

3.NBT.3. Multiply one-digit whole numbers by multiplies of 10 in the range 10-90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations.
 * Standards: **


 * Common Core State Standards **
 * Content Area: ** Math
 * Grade Level: ** Grade 3
 * Domain: ** Measurement & Data
 * Cluster: ** Geometric measurement: understand concepts of area and relate area to multiplication and divison


 * Standards:**

3.MD.7. Relate area to the operations of multiplication and division. a. Find the area of a rectangle with whole-number sides lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. b. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. c. Use tiling to show in concrete case that the area of a rectangle with whole-number side lengths //a// and //b + c// is the sum of //a x b// and //a x c.// Use area models to represent the distributive property in mathematical reasoning. d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world world problems. ||

//What understandings are desired?//

 * //Students will understand that:// **(U)** ||
 * =====• multiplication and division are related through predictable patterns and once the pattern is learned it won't vary. =====

• the patterns that are apparent in multiplication and division can be applied to solve more complex multiplication problems.
||

//What essential questions will be considered?//
• How can one model represent multiple multiplication and division problems? • How can the patterns in multiplication and division be applied to solve new or unique problems? ||
 * **Essential Questions:** **(Q)** ||
 * • How do multiplication and division relate to one another?

//What key knowledge and skills will students acquire as a result of this unit?//

 * //Students will know:// **(K)** || //Students will be able to:// **(S)** ||
 * **• Definitions:** multiplication, division, array, fact family, product, quotient, equation, Commutative Property, Associative Property, Distributive Property, variable.


 * • Symbols:** × ∙ ÷ ∕ =

• Tell a story of a multiplication and division fact family, through a piece of writing. • Use the multiplication and division patterns to solve more complex problems. • Compare and contrast the similarities and differences between multiplication and division. • Assume the role of a number between 0-9 and describe your effect on different numbers in terms of multiplication and division. • Realize that there are multiple strategies for solving multiplication and division facts and recognize what strategy works best for you. ||
 * • Procedures:** how to multiply and divide two whole numbers within 100 and how they can apply this process to other problems. || • Model multiplication and division facts using different methods, including arrays and fact families.


 * 2004 ASCD and Grant Wiggins and Jay McTighe**