stage 3 Objectifying rate in a prediction FAP: Randy why is that [multiplication] going to Reinvented get us a prediction for the number of iPhones in • parametric coefficient a year? How does weeks turn into iPhones? & objectified Randy: Because for every week you have, you produce a certain amount of iPhones, so if you • algebraic equations Assembled multiply it by a certain amount of weeks, the • function tables amount of iPhones will go up. [The reason- & coordinated • rate of change FAP: [For every– make predictions given: Randy: -that might be important is for (investors Activities • rate and start to know) • well-ordered function table ( △ x = 1) Thursday, April 10, 14
stage 3 Objectifying rate in a prediction FAP: Randy why is that [multiplication] going to Reinvented get us a prediction for the number of iPhones in • parametric coefficient a year? How does weeks turn into iPhones? & objectified Randy: Because for every week you have, you produce a certain amount of iPhones, so if you • algebraic equations Assembled multiply it by a certain amount of weeks, the • function tables amount of iPhones will go up. [The reason- & coordinated • rate of change FAP: [For every– make predictions given: Randy: -that might be important is for (investors Activities • rate and start to know) • well-ordered function table ( △ x = 1) Thursday, April 10, 14
stage 3 Objectifying rate in a prediction FAP: Randy why is that [multiplication] going to Reinvented get us a prediction for the number of iPhones in • parametric coefficient a year? How does weeks turn into iPhones? & objectified Randy: Because for every week you have, you produce a certain amount of iPhones, so if you • algebraic equations Assembled multiply it by a certain amount of weeks, the • function tables amount of iPhones will go up. [The reason- & coordinated • rate of change FAP: [For every– make predictions given: Randy: -that might be important is for (investors Activities • rate and start to know) • well-ordered function table ( △ x = 1) Thursday, April 10, 14
stage 3 Objectifying rate in a prediction FAP: Randy why is that [multiplication] going to Reinvented get us a prediction for the number of iPhones in • parametric coefficient a year? How does weeks turn into iPhones? & objectified Randy: Because for every week you have, you produce a certain amount of iPhones , so if you • algebraic equations Assembled multiply it by a certain amount of weeks, the • function tables amount of iPhones will go up. [The reason- & coordinated • rate of change FAP: [For every– make predictions given: Randy: -that might be important is for (investors Activities • rate and start to know) • well-ordered function table ( △ x = 1) Thursday, April 10, 14
stage 3 Objectifying rate in a prediction FAP: Randy why is that [multiplication] going to Reinvented get us a prediction for the number of iPhones in • parametric coefficient a year? How does weeks turn into iPhones? & objectified Randy: Because for every week you have, you produce a certain amount of iPhones , so if you • algebraic equations Assembled multiply it by a certain amount of weeks, the • function tables amount of iPhones will go up. [The reason- & coordinated • rate of change FAP: [For every– make predictions given: Randy: -that might be important is for (investors Activities • rate and start to know) • well-ordered function table ( △ x = 1) Thursday, April 10, 14
stage 3 Objectifying rate in a prediction FAP: Randy why is that [multiplication] going to Reinvented get us a prediction for the number of iPhones in • parametric coefficient a year? How does weeks turn into iPhones? & objectified Randy: Because for every week you have, you produce a certain amount of iPhones , so if you • algebraic equations Assembled multiply it by a certain amount of weeks, the • function tables amount of iPhones will go up. [The reason- & coordinated • rate of change FAP: [For every– make predictions given: Randy: -that might be important is for (investors Activities • rate and start to know) • well-ordered function table ( △ x = 1) Thursday, April 10, 14
stage 3 Objectifying rate in a prediction FAP: Randy why is that [multiplication] going to Reinvented get us a prediction for the number of iPhones in • parametric coefficient a year? How does weeks turn into iPhones? & objectified Randy: Because for every week you have, you produce a certain amount of iPhones , so if you • algebraic equations Assembled multiply it by a certain amount of weeks, the • function tables amount of iPhones will go up. [The reason- & coordinated • rate of change FAP: [For every– make predictions given: Randy: -that might be important is for (investors Activities • rate and start to know) • well-ordered function table ( △ x = 1) Thursday, April 10, 14
stage 3 Objectifying rate in a prediction FAP: Randy why is that [multiplication] going to Reinvented get us a prediction for the number of iPhones in • parametric coefficient a year? How does weeks turn into iPhones? & objectified Randy: Because for every week you have, you produce a certain amount of iPhones , so if you • algebraic equations Assembled multiply it by a certain amount of weeks, the • function tables amount of iPhones will go up. [The reason- & coordinated • rate of change FAP: [For every– make predictions given: Randy: -that might be important is for (investors Activities • rate and start to know) • well-ordered function table ( △ x = 1) Thursday, April 10, 14
stage 3 Objectifying rate in a prediction FAP: Randy why is that [multiplication] going to Reinvented get us a prediction for the number of iPhones in • parametric coefficient a year? How does weeks turn into iPhones? & objectified Randy: Because for every week you have, you produce a certain amount of iPhones, so if you • algebraic equations Assembled multiply it by a certain amount of weeks, the • function tables amount of iPhones will go up. [The reason- & coordinated • rate of change FAP: [For every– make predictions given: Randy: -that might be important is for (investors Activities • rate and start to know) • well-ordered function table ( △ x = 1) Thursday, April 10, 14
Up and down in the cascade stage 3 Reinvented • parametric coefficient & objectified • algebraic equations Assembled • function tables & coordinated • rate of change make predictions given: Activities • rate and start • well-ordered function table ( △ x = 1) Thursday, April 10, 14
Up and down in the cascade stage 3 Reinvented • parametric coefficient & objectified • algebraic equations Assembled • function tables & coordinated • rate of change make predictions given: Activities • rate and start • well-ordered function table ( △ x = 1) Thursday, April 10, 14
Up and down in the cascade stage 3 Reinvented • parametric coefficient & objectified • algebraic equations Assembled • function tables & coordinated • rate of change make predictions given: Activities • rate and start • well-ordered function table ( △ x = 1) Thursday, April 10, 14
Up and down in the cascade stage 3 Reinvented • parametric coefficient & objectified • algebraic equations Assembled • function tables & coordinated • rate of change make predictions given: Activities • rate and start • well-ordered function table ( △ x = 1) Thursday, April 10, 14
Up and down in the cascade stage 3 Reinvented • parametric coefficient & objectified • algebraic equations Assembled • function tables & coordinated • rate of change make predictions given: Activities • rate and start • well-ordered function table ( △ x = 1) Thursday, April 10, 14
stage 4 Thursday, April 10, 14
stage 4 Thursday, April 10, 14
stage 4 Reinvented • unit rate strategy • algebraic ratio & objectified Thursday, April 10, 14
stage 4 Reinvented • unit rate strategy • algebraic ratio & objectified • ratio table Assembled • “find one” strategy • fraction as quotient & coordinated • rate of change • function tables Thursday, April 10, 14
stage 4 Reinvented • unit rate strategy • algebraic ratio & objectified • ratio table Assembled • “find one” strategy • fraction as quotient & coordinated • rate of change • function tables make predictions given: Activities • one value in proportional situation • two data points with △ x ≠ 1 Thursday, April 10, 14
stage 4 Thursday, April 10, 14
stage 4 make predictions given one value in proportional situation Thursday, April 10, 14
stage 4 make predictions given one value in proportional situation Ms. Magro runs 6 miles every day. On average, she can run six miles in 54 minutes. At this rate, how long would it take Ms. Magro to run an 11-mile race? ! ! Thursday, April 10, 14
stage 4 make predictions given one value in proportional situation Ms. Magro runs 6 miles every day. On average, she can run six miles in 54 minutes. At this rate, how long would it take Ms. Magro to run an 11-mile race? ! ! Thursday, April 10, 14
stage 4 make predictions given one value in proportional situation Ms. Magro runs 6 miles every day. On average, she can run six miles in 54 minutes. At this rate, how long would it take Ms. Magro to run an 11-mile race? ! ! Thursday, April 10, 14
stage 4 make predictions given one value in proportional situation Ms. Magro runs 6 miles every day. On average, she can run six miles in 54 minutes. At this rate, how long would it take Ms. Magro to run an 11-mile race? ! ! Thursday, April 10, 14
stage 4 make predictions given one value in proportional situation Ms. Magro runs 6 miles every day. On average, she can run six miles in 54 minutes. At this rate, how long would it take Ms. Magro to run an 11-mile race? ! ! Thursday, April 10, 14
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