# NC Math 1 MVP 7.4: The x Factor

- Author:
- Douglas Bynum, Tim Brzezinski

- Topic:
- Algebra, Area, Quadratic Equations

*Optima’s Quilts*is accepting orders for rectangular blocks, their business is growing by leaps and bounds. Many customers want rectangular blocks that are bigger than the standard square block on one side.

## Task 7.4 Question 1

**Sometimes they want one side of the block to be the standard length, x, with the other side of the block 2 inches bigger.**

## Draw your illustration: Click the buttons to add each element (blue, green, and yellow represent positive terms)

## Task 7.4 Question 1a

Sometimes they want one side of the block to be the standard length, 𝑥, with the other side of the block 2 inches bigger.
Write two different expressions for the area of the block.
*Use the ^ key to enter an exponent, if needed, when typing your expression.*

## Task 7.4 Question 2

**Sometimes they want blocks with one side that is the standard length, x, and one side that is 2 inches less than the standard size.**

## Draw your illustration: Click the buttons to add each element (blue, green, and yellow represent positive terms)

## Task 7.4 Question 2a

Sometimes they want blocks with one side that is the standard length, 𝑥, and one side that is 2 inches less than the standard size**.**
Write two different expressions for the area of the block. Use your diagram and verify algebraically that the two expression are equivalent.
*Use the ^ key to enter an exponent, if needed, when typing your expression.*

**There are many other size blocks requested, with the side lengths all based on the standard length, . Construct each of the following blocks, then use your diagrams to write two equivalent expressions for the area. Verify algebraically that the expressions are equal.**

## Task 7.4 Question 3

**One side is 1" less than the standard size and the other side is 2" more than the standard size.**

## Draw your illustration: Click the buttons to add each element (blue, green, and yellow represent positive terms)

## Task 7.4 Question 3a

Write two different expressions for the area of the block. Use your diagram and verify algebraically that the two expression are equivalent.
*Use the ^ key to enter an exponent, if needed, when typing your expression.*

## Task 7.4 Question 4

**One side is 2" less than the standard size and the other side is 3" more than the standard size.**

## Task 7.4 Question 4a

Write two different expressions for the area of the block. Use your diagram and verify algebraically that the two expression are equivalent.
*Use the ^ key to enter an exponent, if needed, when typing your expression.*

## Task 7.4 Question 5

**One side is 2" more than the standard size and the other side is 3" less than the standard size.**

## Task 7.4 Question 5a

Write two different expressions for the area of the block. Use your diagram and verify algebraically that the two expression are equivalent.
*Use the ^ key to enter an exponent, if needed, when typing your expression.*

## Task 7.4 Question 6

**One side is 3" more than the standard size and the other side is 4" less than the standard size.**

## Task 7.4 Question 6a

*Use the ^ key to enter an exponent, if needed, when typing your expression.*

## Task 7.4 Question 7

**One side is 4" more than the standard size and the other side is 3" less than the standard size.**

## Task 7.4 Question 7a

*Use the ^ key to enter an exponent, if needed, when typing your expression.*

**An expression that has 3 terms in the form:**is called a trinomial. look back at the trinomials you wrote in questions 3 - 7.

## Task 7.4 Question 8

How can you tell if the middle term () is going to be positive or negative?

## Task 7.4 Question 9

## Task 7.4 Question 9a

One of the employees thinks that this rectangle will have the same areas as the original square since one side was decreased by the same amount as the other side was increased. What do you think?

## Task 7.4 Question 9b

*Use the ^ key to enter an exponent, if needed, when typing your expression.*

## Task 7.4 Question 10

**Try modeling these two problems, look at your answer to #8, and see if you can find a pattern in the result.**

## Problem A

Write a trinomial expression for the area of the block. Use your diagram and verify algebraically that the two representations are equivalent.
*Use the ^ key to enter an exponent, if needed, when typing your expression.*

## Problem B

Write a trinomial expression for the area of the block. Use your diagram and verify algebraically that the two representations are equivalent.
*Use the ^ key to enter an exponent, if needed, when typing your expression.*

## Task 7.4 Question 11

What pattern did you notice? What is the result of ?

## Task 7.4 Question 12

## Problem A

Write a trinomial expression for the area of the block. Use your diagram and verify algebraically that the two representations are equivalent.
*Use the ^ key to enter an exponent, if needed, when typing your expression.*