SECONDARY MATH I // MODULE 8

CONNECTING ALGEBRA & GEOMETRY – 8.1

Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org

5.1 Go the Distance

A Develop Understanding Task

TheperformancesofthePodunkHighSchooldrillteamareverypopularduringhalf-timeattheschool’sfootballandbasketballgames.WhenthePodunkHighSchooldrillteamchoreographsthedancemovesthattheywilldoonthefootballfield,theylayouttheirpositionsonagridliketheonebelow:

Inoneoftheirdances,theyplantomakepatternsholdinglong,wideribbonsthatwillspanfromonedancerinthemiddletosixotherdancers.The dashed lines represent the ribbon measured in yards. The question the dancers have is how long to make the ribbons. Gabriela (G)

is standing in the center and some dancers think that the ribbon from Gabriela (G) to Courtney

(C) will be shorter than the one from Gabriela (G) to Brittney (B).

1. To help them figure this out, find out howlongeachribbonneedstobe. Explain orshow how you found the length of each ribbon in yards.

CCBY

https://flic.kr/p/rFBHk

2. What is the total amount of ribbon the drill team will need for this formation?

This task has been adapted to meet the NC standards.Page 1

SECONDARY MATH I // MODULE 8

CONNECTING ALGEBRA & GEOMETRY – 8.1

Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org

Debbie (D) suggests that perhaps their formation would look better to the crowd if they held their

ribbons as shown in the diagram below. Notice, most of the girls have moved slightly.

3. How long will theribbonsneed to bebetweenDebbie (D)andCourtney(C)inthenewformation?Explainyouranswer.

Gabrielanoticesthatthecalculationssheismakingforthelengthoftheribbonsremindsherofmathclass.Shesaystothegroup,“Hey,Iwonderifthereisaprocessthatwecoulduselikewhatwehavebeendoingtofindthedistancebetweenanytwopointsonthegrid.”Shedecidestothinkaboutitlikethis: “I’m going to start with two points and draw the line between them that represents the distance that I’m looking for. Since these two points could be anywhere, I named them A (x1, y1)

and B (x2, y2). Hmmmmm. . . . when I figured the length of the ribbons, what did I do next?”

4. How much total ribbon is needed for the outside edge of this inthenewformation?Explainyouranswer.

(x2,y2)

(x1,y1)

B

A

5. Thinkbackontheprocessyouusedtofindthelengthoftheribbonandwritedownyourstepshere,intermsof(x1,y1)and(x2,y2).

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SECONDARY MATH I // MODULE 8

CONNECTING ALGEBRA & GEOMETRY – 8.1

Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org

6. Usetheprocessyoucameupwithin#6tofindthedistancebetweentwopointslocatedfarenoughawayfromeachotherthatusingyourformulafrom#5ismoreefficientthangraphingandcounting.Forexamplefindthedistancebetween(-11,25)and(23,-16)

7.The dancers have come up with one more formation, and they need to know how much

ribbon they will need for the Perimeter of their new shape. Show and explain the total

amount of ribbon they will need.

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