Modeling with mathematics – “How can I help farmer Bob?” TASK: Farmer Bob is planting a garden this spring. He wants to plant squash, pumpkins, corn, beans, and potatoes. He wants to start by placing the potato patch on the south end corner of the farmland. The area of the potato patch is represented algebraically as 2k2 + 13k – 24 (feet2), however, he needs help to figure out the length, width and the perimeter measurements algebraically. A blueprint of the Farmland and its produce is displayed below to determine a correct plan for his field layout in feet (units). Use the blueprint and your knowledge of factoring polynomials and finding perimeter to make all determinations.
Samantha used the “Factor by Grouping Method” to complete the task and made the following claims below.
1) She claimed the factored form of 2k2 + 13k – 24 (feet2), is (k + 6)(2k – 3)
2) She recommended that the length of the potato patch should be (k + 6) and the width should be (2k – 3)
3) She found the perimeter of the potato patch by adding all the sides, but forgot to include it in her claim. Find the perimeter for her algebraically.
4) If k = 7, what is a VALUE that can be used to determine the TRUE dimensions of the perimeter of the potato patch. (hint: units must be included)
Create a WRITTEN response that express and demonstrates your point of view of Samanthas’ work and include the following in your written response supported by mathematical evidence.

 Write a claim. Statements written in sentences that expresses your point of view about the claim(s) made in the scenario given above. Provide evidence/justification and supported reasoning using
any method of your choice

 Write a counterclaim. Write a sentence that contradicts the claim made and clearly states your
position.

 Explain the counterclaim you are making. The more “real” you make the opposing position, the
more “right” you will seem when you disprove it using clear sentences and mathematical language.

 State a clear conclusion. A concluding statement that summarizes your point of view/claim

Extra Credit Challenge: (only if you complete 1,2,3,4 and still have time)Farmer Bob realized he forgot to include a zucchini field into his field layout. He plans to use half the length and half the width of the potato patch in order to plant the zucchini. Write a polynomial expression that represents the AREA of the new zucchini field.