Integrating Mathematical Practices K-12 Gila County Teacher Institute Gail Gorry & Deb Leverance June 1, 2012

Agenda Background of Common Core Explore the Mathematical Practices Discover Level of Knowledge Develop a Mathematical Practice Integrated Lesson

Where Are You Now? How comfortable do you feel implementing the 2010 Arizona Mathematics Standards? How knowledgeable are you about the components and how to access them?

___The CCSS are a national curriculum. ___ The CCSS represent a modest change from current practice. ___ The CCSS will transform schools. True or False?

Background Information The Partnership for Assessment of Readiness for College and Careers (PARCC) Arizona: Is a PARCC Governing State Will be Pilot State for Assessment Development Starts Computer/Performance based testing in 2014/2015 Follows the 2008 Math Standards format

6 45 States + DC Have Adopted the Common Core Math Standards

Video Watch the David Coleman video. Listen for the 3 main focuses of the Mathematics Common Core. Discuss. Link: g-the-common-core-to-life.html g-the-common-core-to-life.html

Standards of 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.

Activity Jigsaw with your table one of the Standards of Mathematical Practice. Share your thoughts about what this practice means with your table group. Record key ideas on easel paper. Post your paper. Gallery walk.

Mathematical Practices Take Home How are the mathematical practices reflected in your daily instruction? Move into integrated grade level groups. Compare and contrast the grade level mathematical practices. Share findings.

Grade Level Documents Find a person who shares your grade level. Locate the mathematical practices from the standards documents. Any changes from your earlier discussion? K = p.21 1 st = p.212 nd = p.20 3 rd = p.27 4 th = p.33 5 th = p.37 6 th = p.44 7 th = p.30 8 th = p.31 9 th -12 th = p.122

Depth and Rigor Hess’ Cognitive Rigor Matrix describes the type of thinking involved, not whether it will be completed correctly applies Webb’s Depth of Knowledge to Bloom’s Cognitive Process Dimensions identifies cognitive levels of student activities and test questions Involves multiple levels (sometimes) in one activity

13 Karin K. Hess, Ed.D., Senior Associate National Center for Assessment, Dove, NH

14 Karin K. Hess, Ed.D., Senior Associate National Center for Assessment, Dove, NH

Identify the DOK Level Analyze the following chart entitled, “The Speed of Indy 500 Cars per Lap” and be ready to share your conclusions. Retrieve information from a table or graph.

Identify the DOK Level Gather information about the speed of vehicles in your neighborhood. Analyze and evaluate the information in a presentation of your choice to the class. Compare and contrast the data from 1985 to 2010 from the following table.

Your team will be assigned a verb from Bloom’s Revised Taxonomy. Design activities that will fill the matrix (Levels 1-4) for your assigned verb. Make a chart and be ready to share with the entire group. Design activities to fill the matrix 17

Cognitive Demand (Expectations for Student Performance ) Skill/ConceptRecall Strategic Thinking Extended Thinking Use Extend Memorize Perform Procedures Demonstrate Understanding Conjecture, Generalize Prove Solve non- routine/ make connections Acquire

Cognitive Demand Sorting Activity A Memorize Facts, Definitions, Formulas E Solve Non-Routine Problems, Make Connections B Perform Procedures C Demonstrate Understanding of Mathematical Ideas D Conjecture, Analyze, Generalize, Prove

SEC Math Expectations for Students

Mathematical Practices Watch the video. Note times during the lesson where mathematical practices were being implemented. Watch teacher and student behaviors.

Video Here’s the link to the videos: p=yes&pid=921# p=yes&pid=921# hexominoes – 5 th gr geometry p=yes&pid=879# p=yes&pid=879# 2 nd gr marshmallows

Video Here’s the link to the video: ml?pop=yes&pid=921# ml?pop=yes&pid=921# rods and rafts – surface area ?pid=925http:// ?pid=925 bungee jumping

Teacher/Student Insights Note mathematical practices. Discuss teacher/student actions and words. What DOK levels were illustrated? How do these activities compare to the learning activities in your classroom?

Activity Choose a math standard. Develop a lesson imbedding mathematical practices. Write the specific guiding questions. Share your common core math lesson outline.

StandardMathematical Practices Explanations and Examples Students are expected to: 5.NF.2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g. by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result: 2/5 + ½ = 3/7, by observing that 3/7 < ½. Connections: 5.NF.2 5.MP.1. Make sense of problems and persevere in solving them. 5.MP.2. Reason abstractly and quantitatively. 5.MP.3. Construct viable arguments and critique the reasoning of others. 5.MP.4. Model with mathematics. 5.MP.5. Use appropriate tools strategically. 5.MP.6. Attend to precision. 5.MP.7. Look for and make use of structure. 5.MP.8. Look for and express regularity in repeated reasoning. Examples: Jerry was making two different kinds of cookies. One recipe needed ¾ cup of sugar and the other needed 2/3 cup of sugar. How much sugar did he need to make both recipes? Mental estimation A student may say that Jerry needs more than one cup of sugar but less than 2 cups of sugar. An explanation may compare both fractions to ½ and state that both fractions are larger than ½ so the total must be more than 1. in addition, both fractions are slightly less than 1 so the sum cannot be more than 2. Area model ¾ cup of sugar 2/3 cup of sugar ¾ = 9/12 2/3 = 8/12 ¾ + 2/3 = 17/12 = 12/12 + 5/ 12 =1 5/12 continued next page Number and Operations - Fractions (NF) Use equivalent fractions as a strategy to add and subtract fractions.

Math Standard 7 NS 3 Solve real-world and mathematical problems involving the four operations with rational numbers, (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)

Session Review Discover level of knowledge Investigate the format of the 2010 Math Standards Explore and use the Mathematical Practices Develop a “math practices” focused lesson

Closing Remarks Questions Evaluation Now the work begins State Resources - County Resources –Coaching –County Curriculum Specialist –Teacher Resource Library –Professional Development workshops Differentiated Instruction STEM Education and Training Intel Math Training Common Core

Gila County Education Service Agency Globe –1400 E Ash St. – Payson –112 W. Cedar Ln. –