Topic+Two

= Topic Two: Generate and Analyze Patterns = Pacing (Duration of Unit): 1. Makes 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. 6. Attend to precision.
 * ~ = Desired Results = ||
 * __**Transfer:**__
 * 5. Use appropriate tools strategically.**
 * 7. Look for and make use of structure.**
 * 8. Look for and express regularity in repeated reasoning. ** ||
 * __**Established Goals:**__
 * 4.OA.5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.


 * __Student "I Can" Statements__ **
 * I can create a number or shape pattern that follows a given rule.
 * I can notice different features of a pattern once it is created by a rule.

__**Prerequisite Skills:**__
 * 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// // ´ 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.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. // ||
 * __**Big Ideas:**__
 * Patterns, Relations, and Functions: Relationships can be described and generalizations made for mathematical situations that have numbers or objects that repeat in predictable ways. Fro some relationships, mathematical expressions and equations can be used to describe how members of one set are related to members of a second set.
 * Practices, Processes, and Proficiencies: Mathematics content and practices can be applied to solve problems. || __**Essential Questions : **__
 * How can patterns be used to describe how two quantities are related?
 * How can a relationship between two quantities be shown using a table? ||
 * __**Students will know...**__
 * Some patterns consist of shapes or numbers arranged in a unit that repeats.
 * Some numerical sequences have rules that tell how to generate more numbers in the sequence.
 * Some real-world quantities have a mathematical relationship; the value of one quantity can be found if you know the value of the other quantity.
 * Some real-world quantities have a mathematical relationship; the value of one quantity can be found if the value of the other quantity is known.
 * Patterns can be used to identify some relationships.
 * Some sequences of geometric objects change in predictable ways that can be described using mathematical rules.
 * Some problems can be solved by using objects to act out the information in the problem.
 * Some problems can be solved by reasoning about the conditions in the problem.

__**Vocabulary**__: repeating pattern, || __**Students will be skilled at...**__
 * Identifying and extending repeating geometric or repeating number patterns
 * Identifying and extending whole-number patterns involving addition and subtraction
 * Extending tables of ordered pairs for situations involving multiplication, addition, or subtraction
 * Finding a rule and extending the table, given a table of number pairs
 * Extending patterns of cubes or tiles
 * Using the strategies "Act it Out" and "Use Reasoning" to solve problems ||
 * ~ = Assessment Evidence = ||
 * __**Performance Assessment Task:**__ || Other Evidence: ||
 * ~ = Learning Plan = ||
 * __**Learning Activities:**__

__2-1:__ Some patterns consist of shapes or numbers arranged in a unit that repeats. __2-2:__ Some numerical sequences have rules that tell how to generate more numbers in the sequence. __2-3:__ Some real-world quantities have a mathematical relationship; the value of one quantity can be found if you know the value of the other quantity. __2-4:__ Some real-world quantities have a mathematical relationship; the value of one quantity can be found if the value of the other quantity is known. Patterns can be used to identify some relationships. __2-5:__ Some sequences of geometric objects change in predictable ways that can be described using mathematical rules. __2-6:__ Some problems can be solved by using objects to act out the information in the problem. Some problems can be solved by reasoning about the conditions in the problem. ||
 * R__**esources:**__

__Home-School Connection__

__Problem of the Month__ [|4.OA.5-Growing Staircases] [|4.OA.5-Tri-Triangles] [|4.OA.5-What's Your Angle?]

__Centers:__ __[|4.OA.5-Triangular Numbers]__ ||