Topic+Four

= Topic Four: Meanings of Multiplication = Pacing (Duration of Unit):
 * ~ = Desired Results = ||
 * **Transfer:**

Standards for Mathematical Practices 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||
 * 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.**
 * **Established Goals:**
 * 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 drawings and equations with a symbol for the unknown number to represent the problem.

Examples:
 * 3.OA.5** Apply properties of operations as strategies to multiply and divide.
 * If 6 X 4 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.)

**Student I Can Statements:**
 * I can determine when to multiply in word problems.
 * I can represent multiplication word problems using drawings, and equations with unknowns in all positions.
 * I can explain the commutative, associative, and distributive property of multiplication.
 * I can apply the commutative, associative, and distributive properties to decompose, regroup, and/or reorder factors to make it easier to multiply two or more factors.


 * Prerequisite Standards:**
 * 2.OA.3** Determine whether a group of objects (up to 20) has an add or even numbers of members, e.g., by pairing objects or counting them by 2s,


 * 2.OA.4** Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. ||
 * **Big Ideas:**

There are multiple interpretations of addition, subtraction, multiplication, and division of rational numbers, and each operation is related to other operations.
 * Operation Meanings and Relationships**

For a given set of numbers there are relationships that are always true, called properties, and these are the rules that govern arithmetic and algebra.
 * Properties**

Mathematics content and practices can be applied to solve problems. || **Essential Questions:**
 * Practices, Processes, and Proficiencies**
 * What are the different meanings of multiplication?
 * How are addition and multiplication related?
 * How are properties of operations helpful for computing numbers?
 * How can different strategies be helpful when solving a problem? ||
 * **Students will know...**
 * Repeated addition involves joining equal groups and is one way to think about multiplication.
 * An array involves equal groups and is one way to think about multiplication.
 * Some real-world problems involving joining or separating equal groups or comparison can be solved using multiplication.
 * Two numbers can be multiplied in any order and the product remains the same.
 * Mathematical explanations can be given using words, pictures, numbers, or symbols. A good explanation should be correct, simple, complete and easy to understand.

multiplication factors product array Commutative (Order) Property of Multiplication || **Students will be skilled at...**
 * Vocabulary:**
 * writing multiplication number sentences for given equal group situations, using the X symbol.
 * writing multiplication sentences for arrays and using arrays to find products.
 * applying the Commutative Property of Multiplication to solve multiplication number sentences.
 * writing math stories for given multiplication facts.
 * explaining to reflect their math understanding by using objects, words, pictures, numbers, and technology. ||
 * ~ = Assessment Evidence = ||
 * **Performance Assessment:**

These tasks are adapted from authentic Smarter Balance/PARCC Sample Tasks. || **Other Evidence:** ||
 * __Tasks Adapted from Smarter Balance and/or PARCC Assessment Sample Tasks__ **
 * ~ = Learning Plan = ||
 * **Learning Activities:**


 * 4-1** Repeated addition involves joining equal groups and is one way to think about multiplication.


 * 4-2** An array involves equal groups and is one way to think about multiplication.


 * 4-3** Two numbers can be multiplied in any order and the product remains the same


 * 4-4** Some real-world problems involving joining or separating equal groups or comparison can be solved using multiplication.


 * 4-5** Mathematical explanations can be given using words, pictures, numbers, or symbols. A good explanation should be correct, simple, complete and easy to understand. ||
 * **Resources:**


 * Home School Connection**

[|The Product Game] [|Illuminations Concentration]
 * Centers:**

[|Thinking Blocks Multiplication] [|Learn Zillion Video: Problem Solving]
 * Student Video:**

media type="custom" key="23513032" ||
 * Teacher Video:**