SBAC-Mathematics November 26, 2013

Outcomes Further understand DOK in the area of Mathematics Understand how the new SBAC assessments will measure student understanding in Math Engage in a Technology Enhanced SBAC Sample Performance Task

DOK Level 1: Recalling and Recognizing Determine the perimeter or area of rectangles given a drawing or labels.

DOK Level 2: Using Procedures Classify plane and three-dimensional figures. Retrieve information from a table or a graph and use it to solve a problem requiring multiple steps.

DOK Level 3: Explaining and Concluding You have a given amount of money. A) Show the different combinations of coins to make that amount of money. B) Show the different combinations of bills and coins to make that amount of money. C) Use the fewest possible number of coins to make that amount of money. Draw conclusions from observations or given data, citing evidence.

DOK Level 4: Making Connections, Extending and Justifying Collect data on the population of your school over the last ten years. Graph the information. What would you predict the school population will be in six years? What trends do you see in the population and what are a few reasons for the trends? Would enrollment figures suggest a need to increase the size of your school facility in the next ten years? Why or why not?

Assessment: What We Know Assessments will begin in California is a governing state in the Smarter Balanced Assessment Consortium ( Assessments will include: Selected Response (computer adaptive) rubric scored Constructed Response rubric scored Extended Response rubric scored Performance Task rubric scored Technology Enhanced

SBAC’s Mathematics Assessment Claims Claim 1: Concepts and Procedures – Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency Claim 2: Problem Solving – Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies Claim 3: Communicating Reasoning – Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others Claim 4: Modeling and Data Analysis – Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems

SBAC Claims and Tasks ClaimTask 1Selected Response (SR) 40% 2Constructed Response or Extended Response (CR or ER) 20% 3Extended Response (ER) 20% 4Performance Task (PT) 20%

Formats and Components of Selected Response Items Traditional Selected Response Item Key and Distractor Analysis Which number is both a factor of 100 and a multiple of 5? A. 4 B. 40 C. 50 D. 500 Which number is both a factor of 100 and a multiple of 5? A. 4 B. 40 C. 50 D. 500 A. 4 B. 40 C. 50 D. 500 OPTIONS: Possible answers the students must select from Which number is both a factor of 100 and a multiple of 5? STEM Statement of the question A.Did not consider criteria of “multiple of 5” B.Did not consider criteria of “factor of 100” C.Correct D.Multiplied 100 and 5 KEY RATIONALE DISTRACTOR

Non-Traditional Selected Response Item Match each shape below to its name. Scoring Rule: Students who properly match the four shapes to their name will receive two points. Students who make two or three correct matches will receive partial credit of one point All other connections will receive a score of 0.

Non-traditional Selected Response

A teacher asked her students to use estimation to decide if the sum of the problem below is closer to 4,000 or 5, , , = One student replied that she thinks the sum is closer to 4,000. She used the estimation shown below to support her reasoning. Is the student’s reasoning correct? In the space below, use numbers and words to explain why or why not. If the student’s reasoning is not correct, explain how she should have estimated. A teacher asked her students to use estimation to decide if the sum of the problem below is closer to 4,000 or 5, , , = One student replied that she thinks the sum is closer to 4,000. She used the estimation shown below to support her reasoning. Is the student’s reasoning correct? In the space below, use numbers and words to explain why or why not. If the student’s reasoning is not correct, explain how she should have estimated. Components of a Constructed Response Item STEM STIMULI

Constructed Response Grade 8 Geometry

Sample MS Extended Response

Google Drive Using Google Docs and Performance Tasks. – From Mahara, select Quadratic Functions – Then “make a copy” of Quadratic Functions into your Google Drive – Begin working on your own copy of Quadratic Functions

Purpose of Performance Tasks (SBAC) Challenge students to apply their knowledge and skills to respond to real-world problems Collections of questions and activities meant to measure capacities such as depth of understanding, research skills, and complex analysis

From SBAC Task Specifications: “An expressed desire on the part of the consortium is that the use of Technology Enhanced items in the assessments will ultimately encourage classroom use of authentic mathematical computing tools as part of classroom instruction.” 18

Performance Tasks We do not have access to the exact tools that the Smarter Balanced Assessment Consortium uses. However, we can use web-based tools to approximate and practice some of the skills that are necessary for high achievement.

Storage Unit/Facility Performance Task Claim #4 How the task addresses the “sufficient evidence” for this claim: Discuss the rigor of this task based on your knowledge of DOK and SBAC Claims. 21

Original Storage Unit Performance Task From Mahara, click on the link under: SBAC Original Storage Facility Performance Task Let’s preview the first part of the task before we engage in the hand’s-on, technology enhanced task.

Reflection What did you notice and how did you feel when completing the task? How can we support our teachers so they can be successful in implementing technology and performance tasks? How can we help our students be successful with these tasks? 23

Performance Tasks should: Integrate knowledge and skills across multiple claims and targets. Reflect a real-world task and/or scenario-based problem. Allow for multiple approaches. 24

Performance tasks should: Represent content that is relevant and meaningful to students. Allow for demonstration of 21 st Century skills such as critically analyzing and synthesizing information presented in a variety of formats. 25

Thank You! Cecilio Dimas 26