Current Developments: Sample Mathematics Items and Tasks Being Developed by Smarter Balanced Item and Performance Task Development Theory Of Action and CCSS Item Piloting, Alignment, Bias Review Large Scale Item Writing Content Specifications Initial Item Writing Alignment and Bias Review Large Scale Alignment and Bias Review Item and Test Specifications Cognitive Labs and Prototyping Field Testing and Scaling Item and Performance Task Development • Just started item development for the pilot • If the the pilot is 100% successful than we likely didn’t reach far enough • We are planning for change • Assessments will include Selected Response, Constructed Response and Performance Tasks. • Any of the above items may be “technology enhanced” Smarter Balanced is Building a System, Not a Test Formative, Interim or Summative? Formative, Interim or Summative? Three frogs sit on a log and 18 flies in the air, How many flies should each frog get if each frog gets a fair share? Show your work or explain how you found your answer. Sixteen frogs sit on a log and 139 flies in the air, How many flies should each frog get if each frog gets a fair share? How many flies are still in the air after each frog receives an equal number? Show your work or explain how you found your answer. 4 Assessment Claims for Mathematics Overall Claim (Gr. 3-8) “Students can demonstrate progress toward college and career readiness in mathematics.” Overall Claim (High School) “Students can demonstrate college and career readiness in mathematics.” Concepts and Procedures “Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.” 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.” Communicating Reasoning “Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.” Modeling and Data Analysis “Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.” Assessment Claims for Mathematics Overall Claim (Gr. 3-8) Overall Claim “Students can demonstrate progress toward college and career readiness in mathematics.” “Students can demonstrate college and career readiness (High School) Overall Claim (High in mathematics.” School) Modeling and Data Analysis Mathematics Claim 1 Overall Claim (Gr. 3-8) Concepts and Procedures Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.” Claim 1: Concepts and Procedures Technology Enhanced (Grades 3 – 5) The numbers 0 and 3/5 are shown on the number line. Put a point on the line to represent the number 1. 0 3/5 Claim 1: Concepts and Procedures Technology Enhanced (Grades 5 – 7) 1 2/7 - 5 3/8 = ? Enter a key sequence to perform this operation on the calculator. Assessing Fluency • • The standards require speed and accuracy in calculation. Fluency is called for explicitly in certain standards. Grade Standard K K.OA.5 Add/subtract within 5 1 1.OA.6 2.OA.2 Add/subtract within 10 Add/subtract within 20 (know single‐digit sums from memory) 2.NBT.5 3.OA.7 Add/subtract within 100 MulKply/divide within 100 (know single‐digit products from memory) 4 3.NBT.2 4.NBT.4 Add/subtract within 1000 Add/subtract within 1,000,000 5 5.NBT.5 6 6.NS.2,3 MulK‐digit mulKplicaKon MulK‐digit division 2 3 Required Fluency MulK‐digit decimal operaKons 10 MeeKng DraQ ‐ 05/29/12 Assessing Fluency (Grade 3) Mark each equation True or False. Standards Addressed: ____ 3 x 8 = 10 + 10 + 4 3.OA.7 Mul:ply/divide within 100 ____ 6 x 2 = 15 – 3 2.OA.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one‐digit numbers. ____ 42 ÷ 7 = 24 ÷ 6 1.OA.7 Understand the meaning of the equal sign, and determine if equa:ons involving addi:on and subtrac:on are true or false. Claim 1 – Mathematical Practices Still Matter! How CAT Works (Binet’s Test) 13 Adap:ve Versioning of Items Easier than Level 1 – Item mapped to 5.MD.5a Level 1 (CCSS 6.G.2) Mike is using cubes that measure ½ inch on each side to ﬁll a box that has a height of 5 ½ inches, width of 3 inches, and length of 2 ½ inches. How many ½ inch cubes will Mike need to ﬁll the box? Level 2 (CCSS 6.G.2) Mike is using cubes that measure ¼ inch on each side to ﬁll a box that has a height of 5 ¼ inches, width of 3 inches, and length of 2 ½ inches. How many ¼ inch cubes will Mike need to ﬁll the box? Level 3 (CCSS 6.G.2) Mike is using cubes that measure ¾ inch on each side to ﬁll a box that has a height of 5 ¼ inches, width of 3 ¾ inches, and length of 7 ½ inches. How many ¾ inch cubes will Mike need to ﬁll the box? 14 Mathematics Claim 2 Overall Claim (Gr. 3-8) 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 2: Problem Solving (Grades 9 – 11) The figure below is made up of a square with height, h units, and a right triangle with height, h units, and base length, b units. The area of this figure is 80 square units. Write an equation for the height, h, in terms of b. Show all work necessary to justify your answer. Mathematics Claim 3 Overall Claim (Gr. 3-8) Communicating Reasoning “Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.” Claim 3: Communicating Reasoning Constructed Response (Grades 3 – 5) A tent is 8 feet by 10 feet. A sleeping bag is 3 feet by 6 feet. A camper says that 4 sleeping bags will fit in the tent because 18 + 18 + 18 + 18 = 72. The tent is 80 square feet, so there is enough space. a. Is the camper correct? ______________ b. Explain. Gavin, M. K., Casa, T. M., Chapin, S., Copley, J. V., & Sheﬃeld, L. J. (2008). Project M2: Using Everyday Measures: Measuring with the Meerkats from Project M2: Mentoring Young MathemaOcians series. Claim 3: Communicating Reasoning Constructed Response (Grades 3 – 5) Mathematics Claim 4 Overall Claim (Gr. “Students can analyze 3-8) complex, real-world Modeling and Data scenarios and can construct and use mathematical Analysis models to interpret and solve problems.” Claim 4: Modeling and Data Analysis (Grades 8 – 11) Great white sharks are about 12 to 16 feet long on average. How many great white sharks laid end-to-end would surround the circumference of Earth? The volume of the earth is approximately 10.83 x 1011 km3. 5 km ≈ 3.1 miles. A Sample High School Performance Task: “What is the Cost of Speeding?” Sample Task Stimulus Stimulus/Information Source for Task Massachusetts (http://www.sudbury.ma.us/services/individual_faq.asp?id=69) The initial 10MPH over the speed limit is assessed a $50 fine. In other words, there is a flat fee for the first 10MPH. Each MPH above the initial 10MPH is then calculated at $10 per MPH thereafter. In addition to the fines established relative to the speed traveled, there is a $50 assessment applied to the fine schedule which goes to a Head Injury Fund established by the state. Example: 46MPH in a 30MPH zone = 16MPH over the speed limit Fine = $50 Head Injury Fund assessment + $50 (first 10MPH over the speed limit) + $60 (next 6MPH) = $160 Sample Task Stimulus (cont.) How the Classroom-Based Portion Supports Accessibility to the Task • • • Teacher clarifies some of the everyday and mathematical language in the task (e.g., Head Injury Fund Assessment, mph) Teacher presents different ways that “speed zones” are marked (e.g., by showing visuals of the signs used to indicate allowable speeds and discussing what they mean) and relate this to the information presented in the stimuli Teacher demonstrates a simpler version of a speeding ticket cost function to ensure even understanding of the variables that students will encounter Student Products • Develop graphical and tabular representations of speeding costs in MA • Determine which representation is most effective and explain why • Compare the MA method of assigning tickets to the NY method • Develop a “more fair” system for assigning tickets in NY based on given constraints Contextually Linked Item The function f(x) = 5(x – 65) + 120 is used to calculate a speeding ticket for a driver going x mph in a 65 mph speed zone. Explain what the difference (x – 65) means in the context of this problem. Contextually Linked Item The function f(x) = 5(x – 65) + 120 is used to calculate a speeding ticket for a driver going x mph in a 65 mph speed zone. If the “5” in the function is changed to “4” and the “120” is changed to “180,” for what values of x would ticket costs be greater than before the change? Contextually Linked Item Ticket Cost 800 700 600 500 400 300 200 100 0 MPH Over Limit The graph shows the relationship between the number of miles over the speed limit a person is traveling and the cost of a speeding ticket. Explain how the graph supports or refutes the statement below: “As driving speeds become more reckless, the penalties are more severe.” English Language Arts Items Assessment Claims for ELA Overall Claim (Gr. 3-8) “Students can demonstrate progress toward college and career readiness in English language/Arts.” Overall Claim (High School) “Students can demonstrate college and career readiness in English language/Arts.” Reading “Students can read closely and analytically to comprehend a range of increasingly complex literary and informational texts” Writing Speaking/Listening Research “Students can produce effective and well-grounded writing for a range of purposes and audiences.” “Students can employ effective speaking and listening skills for a range of purposes and audiences” “Students can engage in research/inquiry to investigate topics, and to analyze, integrate, and present information. Assessment Claims for ELA Overall Claim (Gr. 3-8) Overall Claim “Students can demonstrate progress toward college and career readiness in English language/Arts.” “Students can demonstrate college and career readiness (High School) Overall Claim (High in English language/Arts.” School) Modeling and Data Analysis ELA Claim 1 Overall Claim (Gr. 3-8) Reading “Students can read closely and analytically to comprehend a range of increasingly complex literary and informational texts” Claim 1: Reading -- Using Supporting Evidence (Grade 4) SKmulus Text… Rightly Unfair Janie frowned as Chandra left the room. “What’s wrong, Janie?” Ms. Simpson asked. “Every day at 3:00 Chandra’s mother picks her up from school,” Janie explained. “Even though she gets to go home when class is over, I have to wait until 3:20 just like everyone else before I’m allowed to leave.” Ms. Simpson smiled at Janie. “Have you talked with Chandra about it?” “No,” Janie admitted. “But she should have to wait like everyone else, no matter what.” “I think it would be best if you told her how you feel,” Ms. Simpson said. “Then maybe you’d think differently about the situation.” Janie kept frowning and sat in her seat until the bell rang at 3:20 and she left the room. The next day, she sat next to Chandra at lunch. “So why do you get to leave early every day while the rest of us have to wait?” Janie asked immediately. “What?” Chandra asked. “At 3:00” Janie explained. “Your mom picks you up every day.” “Oh!” Chandra exclaimed. “My mom gets me early so I can go with her to read to the kids at the library. Every day from 3:15 until 5:15, kids visit the library for story time. We read for a half hour to each age group, three-year-olds, four-year-olds, five-year-olds, and six-year-olds. The kids love it. I love it, too.” “Oh, I didn’t know that,” Janie said. “It’s great to be able to read to the younger kids,” Chandra continued. “It makes me feel so good to do that for them. I’ll admit, though, it’s not easy finding interesting stories for them every day. The three-year-olds get bored very easily.” “Well, I have a few great stories at home that I read when I was that age,” Janie said. “Do you want me to give them to you to read to the kids? I’m sure they would find them interesting. I could bring them to you tomorrow during lunch.” “That would be great!” Chandra replied. “I guess it is fair that you get to leave early,” Janie said. “I never realized that you had such a good reason.” Item Stem: Read the sentences below. Select a sentence from the passage that best supports each statement. Drag and drop the sentence into the box below. How Janie changes in the story Janie is jealous in the beginning of the story. Janie is helpful by the end of the story. Scoring Key: (Note: No text is highlighted in the passage when presented to students; highlighting is for scoring rules only. Any sentence in the passage can be selected and dragged into a response block.) 2-Point Response: Student selects any of the first three highlighted sentences for Block 1 and either of the last two highlighted sentences for Block 2 1-Point Response: Student selects only one correct sentence – either for Block 1 or for Block 2 0-Points: Student does not select a correct sentence for Block 1 and for Block 2 ELA Claim 2 Overall Claim (Gr. 3-8) Writing “Students can produce effective and well-grounded writing for a range of purposes and audiences.” Claim 2: Writing – Composing Full Texts (Grade 6) Claim 2: Writing – Composing Full Texts (Grade 6) Task Title: GeneKcally Modiﬁed Food (105 total minutes): Part 1 (35 minutes): UlKmately tasked with wriKng an argumentaKve essay on geneKcally modiﬁed food, students will ﬁrst view a brief video explaining gene:c modiﬁca:on and some of the ways it relates to food producKon. Students will then read a text arguing for the producKon of geneKcally modiﬁed food, and view a second video in which several experts present evidence against the producKon of geneKcally modiﬁed food. Students will take notes on both of these sources. They will then respond to three constructed‐response items focused on research skills. All work will be completed independently. Claim 2: Writing – Composing Full Texts (Grade 6) Part 2 (70 minutes): Students will work individually to compose a full‐length argumenta:ve essay either supporKng or opposing the producKon of geneKcally modiﬁed food, referring to their notes as needed. Students will be allowed access to the sources they read/viewed during Part 1. Pre‐wriKng, draQing, revising, and ediKng will be involved. Scorable Products: Student responses to the research quesKons and the essay will be scored. Claim 2: Writing – Composing Full Texts (Grade 6) Part 1 Ques>ons for Students to Respond to: 1. Explain why most people have strong feelings about geneKcally modiﬁed food. Use details from the sources to support your answer. 2. Which piece of informaKon from the arKcle you read could be used as the strongest, most convincing supporKng evidence for the producKon of geneKcally modiﬁed food? Use details from the arKcle to explain your answer. 3. Which piece of informaKon from the second video you viewed could be used as the strongest, most convincing supporKng evidence against the producKon of geneKcally modiﬁed food? Use details from the video to explain your answer. Claim 2: Writing – Composing Full Texts (Grade 6) Part 2 Ques>on for Students to Respond to: Your science class is creaKng a website on recent scienKﬁc discoveries. Your assignment is to write an argumentaKve essay about geneKcally modiﬁed food for the website. In the essay, you should brieﬂy explain what geneKcally modiﬁed food is and argue either for or against its producKon, including speciﬁc details and evidence from the sources you read/viewed during part 1. The audience for your essay will be your teacher and classmates, as well as parents and friends who visit the website where your essay will be published. ELA Claim 3 Overall Claim (Gr. 3-8) “Students can employ effective speaking and Speaking/Listening listening skills for a range of purposes and audiences” ELA Claim 4 Overall Claim (Gr. 3-8) Research “Students can engage in research/inquiry to investigate topics, and to analyze, integrate, and present information. Keep in Touch Smarter Balanced can be found online at: www.smarterbalanced.org

© Copyright 2020