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• ### Stephanie Moore

Member
June 6, 2020 at 5:34 pm

I decided to see if I could break down learning about the concept of initial value in linear equations based on the video from Lesson 3-6 using Stacks of Paper. Given 1 pack of paper = 4.95 cm tall and that 5 packs of paper on a table is 130.75 cm tall, find the height of the table.

U.I. The student adds 4.95 five times or multiplies 4.95 by 5 to get that 5 packs of paper is 24.75 cm tall. They then subtract 24.75 from 130.75 to find the height of the table is 106 cm.

C.I. The student makes a table of #packs vs. height from floor by starting with 5 pks plus table is 130.75, 4 pks is 125.8 and on down to 1 pk is 110.95 and 0 pk (just the table) is 106 cm. They think there must be a way to generalize this to any number of packs stacked on a table, but aren’t sure how to do this.

C.C. Student knows they can multiply #packs times hgt/pack and add the table height so they can write total height = #packs(4.95) + table height and then 130.75 = 5(4.95) + 106 which they can connect to y = mx + b once they are shown how.

U.C. Student automatically looks for dependent and independent variables and solves for initial value using y = mx + b whenever they are faced with a situation like this.

C.M When learning another function family, perhaps exponential functions, student postulates that the y-intercept may be the initial value and tests this theory out.

Would appreciate feedback as I’m not sure if I’m mixing too much in and not making it granular enough.