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Alaska Mathematics Standards Teaching and Learning Support Institute September 16-17, Deborah Riddle Math Content Specialist

Goals for Today Revisit the 3 Standards Shifts in math Look at the Mathematical Practices Examine some instructional strategies 3

4 3 Shifts in Mathematics RigorCoherenceFocus

5 2 – 4 topics focused on deeply in each grade Fewer big ideas to be covered Allows more time for students to understand the concepts Strive for understanding not coverage

6 Shift 1: Focus Multiplication Grade 3 New Math Standards Represent and solve problems involving multiplication. –3.OA.1, 3.OA.2, 3.OA.3, 3.OA.4 Understand properties of multiplication and the relationship between multiplication and division. –3.OA.5, 3.OA.6, Multiply and divide up to 100. –3.OA.7 Solve problems involving the four operations and identify and explain patterns in arithmetic. –3.OA.8, 3.OA.9 Use place value understanding and properties of operations to perform multi-digit arithmetic. –3.NBT.3 GLE M3.1.4 Model multiplication as repeated addition and grouping objects; model division as “sharing equally” and grouping objects –[3] E&C-5, [3]E&C-6 Digging Deeper

Coherence 7 systematic or logical connection or consistency ( Merriam-Webster) logical or natural connection or consistency, logical interconnectedness (The Free Dictionary)

Coherence Concepts logically connected form one grade to the next Concepts linked to other major topics within each grade Deeper learning decreases the need for re-teaching topics each year 8

9 Shift 2: Coherence K Grade Level K.OA.1 1.OA.1 2.OA.13.OA.1, 3.OA.2 4.OA.1 5.OA.1 Craig has $20. He buys 6 squirt guns for $2 each. How much money does he have left? 5x7 = 7x5

10 Algebra

Shift 3: Rigor Conceptual understanding Application to real-world situations Fluency with arithmetic 11 With equal intensity

Rigor 12 Conceptual understanding of key concepts. Foster students’ ability to access concepts from a number of perspectives. Math is seen as more than a set of mnemonics or discrete procedures.

NAEP and SBAC 13 Grade 8 Linear Algebra NAEP Grade 8 Linear Algebra SBAC

14 A set of football games is to be organized in a “round- robin” fashion, i.e., every participating team plays a game against every other team once and only once. If 36 games are totally played, how many teams participated? Solution

“When I add 4 times my age 4 years from now to 5 times my age 5 years from now, I get 10 times my current age. How old will I be 5 years from now? ” 15 Solution

Standards for Mathematical Practice 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. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. 16

Resources on the Flash Drive 17

Mathematics Standards 18 Understanding

19 Sidewalk Patterns in Prague A Performance Task

Performance Tasks Demonstrate mastery Organized approach using multiple strategies Fosters self-checking Explanation of mathematical reasoning Utilizes Mathematical Practices 20 lessons-integrating-practice-standards

Create a Performance Task 21

22 Start with an Idea Real-world situations High interest Relevant

Clarify the Task 23 Choose a product Define the purpose and audience Identify Content Standards and Mathematical Practices Create clear expectations and goals

Prepare for Success 24 Prepare questions to assess knowledge to help struggling students Identify prerequisite skills necessary for success

Assess the Task 25 Were the goals met? Did the product reflect mastery? Did the task work as intended?

26 Sample Performance Task Outline com/probability.html

27 Brown University (2013, August 5). New explanation for odd double-layer Martian craters

Resources 28 Illustrative Mathematics Although Alaska did not adopt the Common Core State Standards, there are many Common Core resources that can be helpful to Alaskan teachers.

Contact Information 29 Deborah Riddle Math Content Specialist Link to this presentation in Prezi format

Football Games 30 Go BackBack

Old Enough? 31