Mathematics The mathematics resources can be found at the following site:

COMMON CORE STATE STANDARDS- MATHEMATICS (CCSS-M)

Mathematics Outcomes Review the CCSS-M Standards, instructional strategies, and assessments Learn how CCSS-M games can be integrated into after school. Understand how to use questioning strategies to increase students critical thinking.

Mathematics Agenda Welcome Mathematics Standards Number Talks Assessment Mathematics Games Next Steps

CCSS-M OVERVIEW

Standards for Mathematical Practices 1. Make sense of problems and persevere in solving them …start by explaining to themselves the meaning of a problem and looking for entry points to its solution 2. Reason abstractly and quantitatively …make sense of quantities and their relationships to problem situations 3. Construct viable arguments and critique the reasoning of others …understand and use stated assumptions, definitions, and previously established results in constructing arguments 4. Model with mathematics …can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace

Standards for Mathematical Practice 5. Use appropriate tools strategically …consider the available tools when solving a mathematical problem 6. Attend to precision …communicate precisely using clear definitions and calculate accurately and efficiently 7. Look for and make use of structure …look closely to discern a pattern or structure 8. Look for and express regularity in repeated reasoning …notice if calculations are repeated, and look for both general methods and for shortcuts

Standards for Mathematical Practice Take a moment to examine the first three words of each of the 8 mathematical practices…what do you notice? Mathematically Proficient Students…

California Comparison Common Core State Standards for CA DOMAINS California Standards Grades K-7 STRANDS K-5 Counting and Cardinality (K only) Operations and Algebraic Thinking Number and Operations in Base 10 Number and Operations-Fractions Measurement and Data Geometry 6-8 Ratio and Proportional Relationships (grade 6-7) The Number System Expressions and Equations Functions (Grade 8) Geometry Statistics and probability Number Sense Algebra and Functions Measurement and Geometry Statistics, Data Analysis and Probability Mathematical Reasoning

CCSS Domains and Conceptual Categories K HS Counting & Cardinality Number and Operations in Base Ten Ratios and Proportional Relationships Number & Quantity Number and Operations – Fractions The Number System Operations and Algebraic Thinking Expressions and EquationsAlgebra Functions Geometry Measurement and DataStatistics and Probability Statistics & Probability Findwell, Bradford & Foughty, Zachary. “”Preparing to Implement the Common Core State Standards for Mathematics. Indiana Department of Education and Ohio Department of Education. March 30, 2011

Instructional Practice Number Talk

A planned daily routine for whole ‐ class instruction Number Sense (e ffi ciency, accuracy & flexibility) Generalized Arithmetic-conceptual understanding Reasoning and Problem Solving Mental Mathematics 10 minutes per day Preview-­Review-­Conceptual Understanding

Today’s Number Talk 90-16

Assessment: What We Know Assessments will begin in California is a governing state in the SMARTER Balanced Assessment Consortium. Assessments will include: – Computer Adaptive Assessments (interim & summative) – Selected Response – Performance Assessments (interim & summative) Technology Enhanced Constructed Response Performance Task Extended Performance Event

Traditional Selected Response CST Example A company has 6 big trucks. Each truck has 18 wheels. How many wheels is this in all? A 24 B 96 C 108 D California Standards Test Released Test Question pg. 14, #34

Non-Traditional Selected Response

Non-Traditional Selected Response Rubric

Performance Tas k

Performance Task (Continued)

Performance Task Rubric

The main point in mathematics teaching is to develop the tactics of problem solving. George Polya Expert Tasks

Common Core-Mathematics Implementation What have been your successes with CCSS-M implementation? What have been your concerns with CCSS-M implementation? 22

DEPTH OF KNOWLEDGE (DOK) AND QUESTIONING

Name the capital of California.

Name the capitals of three other states.

Compare and contrast two state capitals from your list.

Evaluate the location of Sacramento as your state capital.

Theorize possible impacts of moving your state capital to San Francisco.

Metacognition What was going on inside your brain as you were trying to answer each of these questions? What was the difference in your thinking as the questions progressed?

Level 1: Recalling and Recognizing Level 2: Using Procedures/Basic Application Level 3: Explaining and Concluding/ Strategic Thinking and Reasoning Level 4: Making Connections, Extending and Justifying/Creating Depth of Knowledge (DOK) Region 5 Afterschool Providers

Same Verb— Three Different DOK Levels DOK 1- Describe three characteristics of metamorphic rocks. (Requires simple recall) DOK 2- Describe the difference between metamorphic and igneous rocks. (Requires cognitive processing to determine the differences in the two rock types) DOK 3- Describe a model that you might use to represent the relationships that exist within the rock cycle. (Requires deep understanding of rock cycle and a determination of how best to represent it)

TOM TORLAKSON State Superintendent of Public Instruction Common Core Big Ideas Depth of Knowledge (DOKs) 32 MathematicsELA/Literacy DOK3DOK4DOK3DOK4 Former Assessments <2% 0% 20% 2% New SBAC Assessments 49% 21% 43% 25% Yuan & Le (2012); Herman & Linn (2013) from Linda Darling-Hammond, Assembly Hearing, % 68%

QUESTIONING STRATEGIES

Let’s Learn About Questions

Support for Asking Questions to Increase Critical Thinking Why do you think… What would happen if… How does _______ affect _________ ? How come… How is it possible that… What do you think ________ means? What do you think ________ represents? Does _______ give you any ideas?

MORE GAMES FROM THE RESOURCE AREA FOR TEACHERS (RAFT) Practice Questioning Standards for Mathematical Practice

Resource Area for Teachers (RAFT) Mathematics Kits Add It Up – 2-4 players – Grades K-4 – =272 =272

Add It Up

Resource Area for Teachers (RAFT) Mathematics Kits Flip Over Fractions 2 players Grades sid=583 sid=583

Flip Over Fractions

Resource Area for Teachers (RAFT) Mathematics Kits Leftover Quilt Patches – 2 players – Grades 2-6 – =670 =670

Leftover Quilt Patches

Resource Area for Teachers (RAFT) Mathematics Kits Place Your Number Value – 2-4 players – Grades 1-8 – =576 =576

Place Your Number Value

Resource Area for Teachers (RAFT) Mathematics Kits Tic Tac Trouble – 2 players – Grades 1-3 – =669 =669

Tic Tac Trouble

Let’s Play the Games

Discussion Questions How can these games support student learning? How can these games be integrated into your after school programs? What support do you need to implement these games?

To find more Idea Sheets

Next Steps What are your next steps regarding CCSS-M implementation for after school?

Questions

Goal Prepare ALL students for college and career success! 52

Mathematics Outcomes Review the CCSS-M Standards, instructional strategies, and assessments Learn how CCSS-M games can be integrated into after school. Use more questioning strategies to increase students critical thinking.

Evaluations 54 Rhonda Beasley Kirsten Sarginger Sandi Yellenberg Please complete Sign-in sheet Evaluation