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Educating for Careers 2014 Math Project-Based Learning and the Common Core: Intersection, Union, or Empty Set? March 4, 2014 Kentaro Iwasaki Who’s Here? Raise your hand for all groups that apply to you • Teachers – Career Technical – Mathematics – Other • Pathway Leads • School Administrators • District Administrators • Counselors • Other 2 Who Here Is In a Linked Learning Pathway? Please raise your hand if you are in a Linked Learning Pathway. 3 Components of Linked Learning A comprehensive four-year program of study integrating: • Rigorous academics • Real-world technical skills • Work-based learning • Personalized supports 4 Session Objectives • Explore the Venn of Common Core Math and Project-Based Learning in a Linked Learning context • Explore how Project-Based Learning in a Linked Learning Context enhances students’ understanding of mathematical content and practices from the CCSS-M 6 Agenda 1. What’s Your Venn? 2. ConnectEd’s PBL-based Math Curriculum 3. Focus on One Unit and Project 4. Discuss Links to CCSS-M Standards and Practices 5. Share out 6. What’s Your Venn? 7. Feedback 7 What’s Your Venn? Please draw what your Venn between Math PBL and CCSS-M is and explain why. 8 ConnectEd’s PBL Math Curriculum ConnectEd developed 10 pre-algebra and algebra project-based and problem-based units in order to support engineering pathway students in mathematics. 9 ConnectEd’s PBL Math Curriculum Currently our math curriculum is part of a rigorous randomized controlled trial through a federal i3 (Investing in Innovation) project in 17 districts across California that will impact approximately 6000 students with achievement on 8th grade CST Algebra scores as the measurement. 10 ConnectEd’s PBL Math Curriculum Unit 1: Wind Power Measurement, fraction, and percent skills are applied to build the most efficient wind turbine possible Unit 2: Blueprints and Models Scale, slope, and proportional reasoning are taught through the design of an access ramp and a remodeling plan for a building Unit 3: People Movers Graphs, algebraic expressions, and ratios are used to build and analyze a transportation system Unit 4: Safe Combinations Exponent rules to calculate the number of possible combinations on a constructed combination lock. Writing and solving equations are used to “code” and “decode” solutions ConnectEd’s PBL Math Curriculum Unit 1: Puzzle Cube Solve singlevariable linear equations as students build the pieces of a puzzle cube Unit 2: Air Traffic Control Graph linear equations to chart the progress of multiple planes and direct them to land safely Unit 3: Catapult Game Solve quadratic equations to design and play a game with projectile machines Unit 6: Electrical Resistance Solve rational expressions to calculate the total resistance in circuits Experiential Project from “The Catapult Game” Your group’s task is to use mathematics to determine how far away to place your catapult in order to hit the targets on a castle poster. What mathematical content and practices are involved? Materials: Catapult, Tape Measure, Grid Poster Paper (1”X1” squares), Markers, Laptops or graphing calculators 13 Experiential Project from “The Catapult Game” 14 Experiential Project from “The Catapult Game” y, Height Off Ground x, Distance from Launch Point 15 Where’s the Math? Please discuss in your groups what mathematical content and practices were involved in this project. Be ready to share out. 16 Catapult Game Unit Overview • The main mathematical concept of the Catapult Game unit focuses on connecting various aspects of quadratic functions (factoring, roots, x-intercepts, graphs, quadratic formula, applications). • We work to emphasize the meaning of these math concepts in CONTEXT! 17 Lesson 1 Overview: Multiplying Binomials and Finding Area Students multiply binomials through an area model and find patterns in perfect square trinomials and difference of squares. –x x –4 x 4x –2 2 2 x 8 Target Dimensions Area in Expanded Form A (10 x )(10 x ) 100 – 20x + x B ( x 15 )( x 15 ) x + 30x + 225 C ( x 2)( x 2) x + 4x + 4 D ( x 5 )( x 5 ) x – 10x +25 E (2 x 1)(2 x 1) 4x + 4x + 1 F ( x 4)( x 4) x + 8x + 16 2 2 2 2 2 2 Total Area: 2 9x + 16x + 371 18 Lesson 2 Overview: Graphs of Equations in Factored Form 2) Graph the three sets of data from Problem 1. Label each graph. y -10 -9 -8 -7 -6 -5 -4 -3 -2 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 0 -2 -1 0 -4 -6 -8 -10 -12 -14 -16 -18 -20 (x+2)(x+4) (x-3)(x+5) x(x-2) x 1 2 3 4 5 6 7 8 9 10 19 Graphs of Equations in Factored Form The x-intercepts or zeroes tell us about the graphs of quadratics in this context The set of x-values that lead to positive areas is bound by the points where the function is equal to zero. We already know that these points are the roots or x-intercepts of the function. They are also called the zeroes of the function. Area of Target Area of Target The regions of the graphs that represent all of the possibilities for real targets. x x Root Root Root Root 20 Lesson 3 Overview: Factoring Factoring using the area model Designer: Bianca Summary: Target Areas Target Area A x 3x 4 (x + 4)(x – 1) B x 1x 6 (x – 3)(x + 2) C x 3 x 10 (x + 5)(x – 2) D x 36 (x + 6)(x – 6) 2 2 2 2 21 Lesson 4.2 Factoring Doesn’t Always Work Consider the trajectory of ammunition launched by Catapult Q: y ( x 2 1 0 x 6 ). Where should you place the catapult in order to shoot ammunition through Target C, which is 25 inches high? 2 5 ( x 1 0 x 6 ) 2 25 x 10 x 6 2 0 x 10 x 19 2 n o t fa c to ra b le 0 x 10 x 19 2 0 6 x 1 0 x (1 9 6 ) 2 6 x 10 x 25 2 6 (x 5) 2 6 x 5 x 5 6 (?, 25) 22 Lesson 4.2 Factoring Doesn’t Always Work This process of completing the square was done to the generic quadratic equation in standard form ( 2 a x b x c 0 ) to create a formula for the solutions: The Quadratic Formula If a x 2 b x c 0 , then x b b 4ac 2 2a Completing the Square Solve the following equations by adding a number to both sides of the equal sign that makes the right side a perfect square. The first one is done for you. 23 Lessons 4.4 Analyze the Catapult Part 2 Determine where to place each catapult in order to hit all of the targets on the castle. The Castle Trajectory Equations x = horizontal distance; y = height of ball Catapult 33 B 28 Q A 25 Inches from the Ground 20 C Ammunition Balls y ( x 2 Supply Balls y ( x 1 3 x 6 ) 9x 6) 2 R y ( x 1 7 x 3 ) y ( x 1 1x 3 ) S y ( x 1 0 x 4 ) y ( x 7 x 4 ) 2 2 2 2 D 13 F 10 E G 6 Target A Must Place Catapult This Distance Away from Castle to Hit the Target (ft.) (Round all answers to the nearest hundredth place) Catapult Q Catapult R Catapult S Ammunition Supplies Ammunition Supplies Ammunition Supplies Impossible; no real solutions 2, 11 1.63, 15.73 3.21, 7.79 4, 6 Impossible; no real solutions 24 Lesson 5 Playing the Catapult Game Virtually Go to http://www.8kindsoffun.com/Catapult/CatapultGUI.html and record your calculations for playing the virtual catapult game below. An example of a quadratic regression applet can be found at http://www.xuru.org/rt/PR.asp Point 1 Data Points for Ammunition Trajectory 𝑥= 𝑦= Point 2 𝑥= 𝑦= Point 3 𝑥= 𝑦= Quadratic Standard Form Calculator Data Points for Ammunition Trajectory Vertex 𝑥= x-intercept 𝑥= 𝑦= 25 Standards of Mathematical Practice What standards of mathematical practice from the CCSS-M did you find in the project? 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. 26 Has Your Venn Changed? Take a look at your Venn from the beginning of the session. Has your Venn changed at all? How so? 27 www.ConnectEdCalifornia.org [email protected] [email protected] 28