# NC Math 1 MVP 7.5: The Wow Factor

- Author:
- Douglas Bynum, Tim Brzezinski

- Topic:
- Algebra, Area, Quadratic Equations

*Optima’s Quilts*sometimes gets orders for blocks that are multiples of a given block. For instance, Optima got an order for a block that was exactly twice as big as the rectangular block that has a side that is 1” longer than the basic size, ,and one side that is 3” longer than the basic size.

## Task 7.5 Question 1

**Draw a diagram of this block.**

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

## Task 7.5 Question 1a

Find an expression to represent the area as a product of two factors. Use the ^ key to enter an exponent, if needed, when typing your expression.

## Task 7.5 Question 1b

Find an expression to represent the area as a sum or difference of terms. Use the ^ key to enter an exponent, if needed, when typing your expression.

## Task 7.5 Question 2

## Task 7.5 Question 2a

Find an expression to represent the area as a product of two factors. Use the ^ key to enter an exponent, if needed, when typing your expression.

## Task 7.5 Question 2b

Find an expression to represent the area as a sum or difference of terms. Use the ^ key to enter an exponent, if needed, when typing your expression.

## Task 7.5 Question 3

What do you notice when you compare the two equivalent expressions in problems #1 and #2?

## Task 7.5 Question 4

## Problem A

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

Find an expression to represent the area as a product of two factors. Use the ^ key to enter an exponent, if needed, when typing your expression.

## Problem B

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

## Problem C

## Problem D

## Problem E

## Task 7.5 Question 5

Find an expression to represent the area as a sum or difference of terms. Use the ^ key to enter an exponent, if needed, when typing your expression.

## Task 7.5 Question 6 - Problem A

## Task 7.5 Question 6 - Problem B

## Task 7.5 Question 6 - Problem C

## Task 7.5 Question 7

What are some patterns you see in the two equivalent expressions for area that might help you to factor?

## Use this tool to help you answer the following questions. Click the Trash Can and then each object and anchor point to clear the workspace between problems.

## Task 7.5 Question 8

## Task 7.5 Question 8 - Problem A

## Task 7.5 Question 8 - Problem B

## Task 7.5 Question 8 - Problem C

## Task 7.5 Question 8 - Problem D

## Task 7.5 - Question 9

In *The x Factor, *you wrote some rules for deciding about the signs inside the factors. Do those rules still work in factoring these types of expressions? Explain your answer.

## Task 7.5 - Question 10

Explain how Optima can tell if the block is a multiple of another block or if one side has a multiple of in the side length.