1 Alaska Mathematics Standards Teaching and Learning Support

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Alaska Mathematics Standards Teaching and Learning Support Institute September 16 -17, 2013 Deborah Riddle Math Content Specialist deborah. riddle@alaska. gov 907 -465 -3758 2

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

3 Shifts in Mathematics Focus Coherence Rigor 4

Focus 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 5

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

Coherence systematic or logical connection or consistency (Merriam-Webster) logical or natural connection or consistency, logical interconnectedness (The Free Dictionary) 7 http: //www. merriam-webster. com/dictionary/coherence

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

Shift 2: Coherence Grade Level K Represent addition and subtractions with objects. K. OA. 1 1 Solve single step addition and subtraction word problems. 1. OA. 1 2 Estimate and solve multistep addition and subtraction word problems. 2. OA. 1 Craig has $20. He buys 6 squirt guns for $2 each. How much money does he have left? 3 Multiplication (repeated addition) Division (repeated subtraction) 3. OA. 1, 3. OA. 2 4 Recognize multiplication as a comparison (commutative property). 4. OA. 1 5 Use parentheses to construct numerical expressions and evaluate expressions with these symbols. 5. OA. 1 5 x 7 = 7 x 5 9

Algebra 10

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

Rigor 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. 12

NAEP and SBAC Grade 8 Linear Algebra NAEP Linear Algebra SBAC 13 https: //education. alaska. gov/tls/assessment/naep. html

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? 14 Solution http: //www. syvum. com/teasers/

“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 http: //www. syvum. com/teasers/ 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 Understanding 18

Sidewalk Patterns in Prague A Performance Task 19

Performance Tasks Demonstrate mastery Organized approach using multiple strategies Fosters self-checking Explanation of mathematical reasoning Utilizes Mathematical Practices 20 http: //insidemathematics. org/index. php/exemplarylessons-integrating-practice-standards

Create a Performance Task 21

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

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

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

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

Sample Performance Task Outline 26 http: //www. mathplaygrou nd. com/probability. html

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

Resources 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. 28

Contact Information Deborah Riddle Math Content Specialist deborah. riddle@alaska. gov 907 -465 -3758 Link to this presentation in Prezi format http: //prezi. com/tb 5 d 6 bwgkq 7 g/? utm_campaign=share&utm 29

Football Games 30 Go Back

Old Enough? 31