Algebra 1 Common Core Student Edition, Grade 8-9

Common Core Performance Task

Planning a G arden Plot

Each rectangular p lot in a com m unity garden consists of a planting area

su rro u n d e d by a b o rd e r of w ood chips. Kelly a n d R oberto each design a p lot for

th e com m unity garden. They use identical square flower b ed s in th eir plots, b u t

they design different borders, as show n below.

Roberto's Plan

1.5 ft

xft

3ft 3ft

xft

1.5 ft

Kelly's Plan

After som e discussion, Kelly an d Roberto decide to scrap th eir original plans an d
com bine their plots to m ake one larger rectangular plot. They p lan to place the
two x ft-by-x ft sq u are flower beds side by side to m ake a 2x ft-by-x ft flower bed,
centered inside a rectangular border. The area of th e n ew plot will equal th e sum
of th e areas of th e two original plots.

Task D escr i p t i o n

Draw an d label a sketch of th e new flower b e d a n d border. Include expressions for

the length an d w idth of th e new plot. Each expression m u st be a linear polynom ial

with integer coefficients.

Connecting the Task to the Math Practices

As you com plete th e task, y o u ’ll apply several S tandards for M athem atical

Practice.

• You’ll analyze th e polynom ials th a t describe Kelly’s an d Roberto's original
  plots. (MP 6)


• You'll write an expression for the area of each of th e original plots. (MP 2 , 1


• You'll write a n d factor an expression for th e area of th e n ew plot. (MP 7)

| Ch a p t e r 8 Po l y n o m i a l s a n d Fa c t o r i n g 485

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