Historically, “...Factorization was first considered by ancient Greek mathematicians in the case of integers. In mathematics, factorization or factoring consists of writing a number or another math object as a product of
several factors, usually smaller or simpler objects of the same kind. For example, 3 × 5 is a factorization of
the integer 15, and the factorization of the polynomial x2 – 4 is (x – 2)(x + 2)”. A student once asked,
“When Will I Ever Use This In Real Life? Let’s explore a real world possibility task below. A teacher assigned the following task below for students to work in groups and apply their factoring skills he taught them in class.

TASK: Factoring and the length vs width dilemma!!: The groundskeeper at the local community Zoo would like to build a new enclosure around the large reptile house located in the North West Corner of the Zoo. The area of the shape represented algebraically is 42k2 – 30k ft2; however, he needs help to figure out the blueprint measurements for the perimeter of the enclosure algebraically. Shown below is a map of the Zoo.

Group D completed the task and made the following claims below.

1) The shape of the large reptile house is a rectangle

2) They used prime factorization and the sum of common factors to identify the GCF as 5k

3) The factored form of 42k2 – 30k ft is (5k ft)(7k – 5 ft)

4) The length can be represented by (7k – 5ft) and the width can be represented by (5k ft)

5) The perimeter of the reptile house algebraically can be represented by 24k – 10 feet

6) They concluded that their blueprint response made sense and wanted to share their results with the zookeeper

Create a written response that express and demonstrates your point of view about Group Ds’ work and include the following in your written response. (Hint: R. A.C. E)

 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