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Science Math Masters Current Standards: MA.912.G.5.1 Prove and apply the Pythagorean Theorem and its converse. MA.912.G.5.4 Solve real-world problems involving right triangles. Typical Textbook Problem (NGSSS – Current Standards) Dan and Ben start at point A and want to get to point B. Dan walks 1 mile north and 3 miles east to reach point B. Ben takes a shortcut and walks directly from point A to point B. Who travels the greatest distance? By how much? a b c 2 2 12 32 c 2 1 9 c2 10 c 2 10 c 3 miles 2 1 mile B c 10 3.16 miles A Dan travels 4 miles and Ben travels 3.16 miles, so Dan travels approximately 0.84 miles more than Ben. Typical Textbook Problem (NGSSS – Current Standards) Dan and Ben start at point A and want to get to point B. Dan walks 1 mile north and 3 miles east to reach point B. Ben takes a shortcut and walks directly from point A to point B. Who travels the greatest distance? By how much? 3 miles 1 mile B c 10 3.16 miles A What geometric concepts are used in this problem? Where we’re headed with the Common Core…Taco Cart Problem (Modified from Dan Meyers The Taco Cart: http://threeacts.mrmeyer.com/tacocart/) Click picture for video. Who will reach the taco cart first? Write down your guess. What information do you need to answer the question? Taco Cart Problem: Who will reach the taco cart first? Distances Dan Ben Speeds: Walking on the sidewalk: 5 ft./sec. Walking in the sand: 2 ft./sec. Work with your shoulder partner to answer the question. Taco Cart Problem: Who will reach the taco cart first? Click picture for video. How many seconds did Dan beat Ben by? 49.695 seconds Taco Cart Problem: Who will reach the taco cart first? d d rt ; t The work: r Dan Ben Dan travels 325.6 ft. at a rate of 2 ft./sec and 562.6 ft. at a rate of 5 ft./sec. 325.6 ft. 562.6 ft. 2 ft./sec. 5 ft./sec. 162.8 sec. + 112.52 sec. 275.32 sec. 4 minutes and 35.32 seconds Ben travels approximately 650.03 ft. at a rate of 2 ft./sec. (Pythagorean theorem) 650.03 ft. 325.015 sec. 2 ft./sec. 5 minutes and 25.015 seconds Dan’s time: 275.32 seconds = 4 minutes 35.32 seconds (04:35:32) Ben’s time: 325.015 seconds = 5 minutes 25.015 seconds (05:25:02) Therefore, Dan beats Ben by 49.695 seconds. Taco Cart Problem: Where would the taco cart have to be so that both Dan and Ben will reach it at the same time? Click picture for video. Work with your shoulder partner to answer the question. Taco Cart Problem: Where would the taco cart have to be so that both Dan and Ben will reach it at the same time? 310.095 ft. Click picture for video. Taco Cart Problem: Where would the taco cart have to be so that both Dan and Ben will reach it at the same time? The work: d rt ; t 325.6 ft. Dan x ft. 325.62 x 2 d r Dan’s two times Ben’s time 325.6 ft. x ft. 325.62 x 2 ft. 2 ft./sec. 5 ft./sec. 2 ft./sec. 325.6 ft. x ft. 325.62 x 2 ft. 10 2 ft./sec. 5 ft./sec. 2 ft./sec. 1628 + 2 x 5 106015.36 x 2 325.6 0.4 x 106015.36 x 2 106015.36 260.48 x 0.16 x 2 106015.36 x 2 0 0.84 x 2 260.48 x 0 x 0.84 x 260.48 x0 x0 0.84 x 260.48 0 x 310.095 Taco Cart Problem: Where do you think the taco cart problem fits in the Common Core curriculum? The algebraic skills required for this problem are covered by the following Algebra I Common Core State Standard. Group Activity Choose a problem from the hand-out and brainstorm ways to adapt the problem so that it captures the spirit of the Common Core State Standards by adding depth, multiple standards and/or a new level of questioning. Be prepared to share.