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Participant Viewing Guide Math Module 1 Introduction to Springboard Participant Viewing Guide Math Module 1 Introduction to SpringBoard 1 Table of Contents Overview ......................................................................................... 3 Before Viewing: Consider and Discuss ............................................... 4 During Viewing: Watch and Learn ..................................................... 5 During Viewing: Guided Exploration .................................................. 6 After Viewing: Reflect and Apply ..................................................... 14 Standards for Mathematical Practice ......................................... 15-18 2 Math Module 1: Introduction to SpringBoard Overview This module provides an introduction to the key components of SpringBoard’s Instructional Design. By focusing on essential terms and big ideas, you will gain an understanding of how the instructional elements work together to support student learning. While your own learning style will determine the amount of time you spend working through this self-paced module, you might anticipate an average time of 45-90 minutes. After viewing this module, you will be able to: Describe the foundational elements of the SpringBoard program Identify key features and components of the Teacher and Student Editions Understand SpringBoard’s connections to the Common Core State Standards 3 Math Module 1: Introduction to SpringBoard Consider and Discuss KWL Graphic Organizer K (What Do I Know?) W (What Would I Like to Learn) L (What Did I Learn?) How will you apply what you have learned about SpringBoard to your classroom practice? 4 Math Module 1: Introduction to SpringBoard Watch and Learn Each of the following terms is important to SpringBoard’s Instructional Design. Jot down your initial thoughts about each term. If possible, discuss your ideas with a colleague. After you’ve recorded your first thoughts, watch your grade level video and add additional explanations to your original ideas. Key Term Definition and Significance Coherence Backward Design Embedded Assessment Scaffolding Activities Cognitive Engagement Teaching and Learning Strategies Vocabulary Development SpringBoard Digital Alignment to Standards Rigor 5 Math Module 1: Introduction to SpringBoard Guided Exploration Student Task: THERMOMETER CRICKETS PERFORMANCE TASK In this task, you will organize and analyze data to model the relationship between temperature and the chirping rates of snowy tree crickets. You will develop an equation to describe the relationship, and you will compare your mathematical model to another formula. Data Set: This table shows data about snowy tree crickets. Each data point in the table represents the average number of chirps per minute at a specific temperature. 6 Math Module 1: Introduction to SpringBoard 1. A. Using the data table, create a scatter plot of the temperature and number of chirps per minute for snowy tree crickets. [Note: The online delivery and response format for these types of questions is still being evaluated.] B. Explain the patterns you observe on the graph. 2. A. Estimate the line of best fit for the data points on the graph, and graph this line. B. Write an equation to represent the line. C. Write an interpretation of the slope of your equation (mathematical model) in terms of the context of chirping rates and temperature. 3. Describe how well your mathematical model fits the given observation data on cricket chirps and temperature, using correlation coefficient, R2, and/or plots of residuals. Amos Dolbear developed an equation in 1897 called Dolbear’s law. He arrived at the relationship between number of chirps per minute of a snowy tree cricket and temperature. You can use this law to approximate the temperature, in degrees Fahrenheit, based on the number of chirps heard in one minute. Dolbear's law: where T = temperature (°Fahrenheit) N = number of chirps per minute 4. A. Plot the line that represents Dolbear’s Law on the same graph as your line of best fit. B. What are the differences between this model and the one you developed earlier? (Include a discussion of their slopes and y-intercepts in your answer.) Interpret what these differences mean in the context of chirping rates and temperature. 5. Explain the differences between the results of Dolbear’s formula and what you see in the observation data for determining the temperature depending on the number of times a cricket chirps. Support your conclusion using four data points. Why do you think these differences could occur? 7 Math Module 1: Introduction to SpringBoard Sample Assessment Task: PARCC Algebra 1/Math II Mini-Golf Prices November 2013 A local mini-golf course charges $5 per person to play a round of golf, and the course sells 120 round of golf per week. The manager of the course studied the effect of raising the price to increase revenue and found the following data. The table shows the price, number of rounds of gold, and weekly revenue for different numbers of $0.25 increases in price. Number of $0.25 0 1 2 3 4 price increases, Price of a round $5.00 $5.25 $5.7 $6.00 $6.2 of golf, ( ) 5 5 Number of 120 117 114 111 108 rounds of golf sold, ( ) Weekly revenue, $600 $614. $62 $638. $64 ( ) 25 7 25 8 Part A Based on the data, write a linear function to model the price of one round of golf, ( ), in terms of , the number of $0.25 increases. Based on the data, write a linear function to model the number of rounds of golf sold in a week, ( ), in terms of , the number of $0.25 increases. Part B Based on the data, write a quadratic function for the weekly revenue in a week, ( ), in terms of , the number of $0.25 increases. Use your quadratic function to determine the weekly revenue in a week when tickets cost $6.25. Part C The maximum possible weekly revenue is what percent greater than the weekly revenue with no price increases? Justify your answer graphically or algebraically. 8 Math Module 1: Introduction to SpringBoard 2009 AP® Calculus AB Free-Response Question Calculus AB Section II, Part A Time—45 minutes Number of problems—3 A graphing calculator is required from some problems or parts of problems. 1. Caren rides her bicycle along a straight road from home to school, starting at home at time = 0 minutes and arriving at school at time = 12 minutes. During the time interval 0 12 minutes, her velocity ( ), in miles per minute, is modeled by the piecewise-linear function whose graph is shown above. ≤ ≤ a. Find the acceleration of Caren’s bicycle at time = 7.5 minutes. Indicate units of measure. b. Using correct units explain the meaning of | ( )| in terms of Caren’s trip. Find the value 12 | | of ( ) . 0 12 ∫ 0 c. Shortly∫ after leaving home, Caren realizes she left her calculus homework at home, and she returns to get it. At what time does she turn around to go back home? Give a reason for your answer. d. Larry also rides his bicycle along a straight read from home to school in 12 minutes. His velocity is modeled by the function given by ( ) = sin , where ( ) is in miles per minute for 0 12 minutes. Who lives closer to school: Caren or Larry? Show your work that leads to your answer. 15 �12 � ≤ ≤ 9 Math Module 1: Introduction to SpringBoard As you examine one unit from your grade level, consider and respond to the following. Unit Planning Guide Articulate the Story of the Unit Notes: What is the “story” or “big picture” of the unit? Planning the Unit/Unit Overview: Read the opening paragraphs and essential questions to understand the concepts and skills developed in this unit. Table of Contents: Skim/scan to understand how the concepts and skills develop over the course of a unit. Academic Vocabulary/Math Terms: Read to identify additional skills and concepts. AP/College Readiness: Read to provide additional big-picture focus. Become comfortable enough that you can describe the big ideas and organization of the unit to colleagues, students, and parents. Explore the Embedded Assessments Notes: What key skills/knowledge will students need to learn? Planning the Unit: Read through the unpacked skills/knowledge for the EAs as a preview. Embedded Assessments: Read through each embedded assessment and scoring guide to answer these two questions: o What do students need to know? o What do students need to know how to do? Use your colleagues and the SB Online Community to gain clarity. 10 Math Module 1: Introduction to SpringBoard Unit Planning Guide (Page 2) Plan for Unpacking the Embedded Notes: Assessment with Students How will you ensure that students understand the expectations of the EA? . Process: Consider what method of unpacking will make the process and information meaningful to students. Formative Assessment: Determine how students will self-assess their initial understanding of the skills/knowledge. Progress: Consider what system is in place for students to be able to track their growth as they practice the skills/knowledge in the activities. Connect to the Standards for Mathematical Notes: Practice (SMPs) Where will students apply the SMPs in the EAs and the activities? Which EAs and activities provide teachable moments that will help students internalize the SMPs? Select an SMP and scan the EAs for specific instances where students have the opportunity to demonstrate that SMP. Examine activities to further clarify your understanding: o Look for the bold text within an item calling out the SMPs. o Look for chunks of an activity that develop students’ ability to demonstrate SMPs. o Read the associated TE steps and consider how you will support
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