# NC Math 1 MVP 7.3: Factor Fixin'

- Author:
- Douglas Bynum, Tim Brzezinski

- Topic:
- Algebra, Area, Quadratic Equations

*Optima’s Quilts*only made square blocks for quilters and Optima spent her time making perfect squares. Customer service representatives were trained to ask for the length of the side of the block, , that was being ordered, and they would let the customer know the area of the block to be quilted using the formula . Optima found that many customers that came into the store were making designs that required a combination of squares and rectangles. So,

*Optima’s Quilts*decided to produce several new lines of rectangular quilt blocks. Each new line is described in terms of how the rectangular block has been modified from the original square block. For example, one line of quilt blocks consists of starting with a square block and extending one side length by 5 inches and the other side length by 2 inches to form a new rectangular block. The design department knows that the area of this new block can be represented by the expression: . The diagram that represents the area and dimensions of the new block is drawn like this

## Task 7.3 Question 1

Label each of the areas of the diagram in your printed copy of the MVP task and use them to find a different expression to represent the area of this new rectangular block two ways. The first way is: . What is a second expression for the area? Use the ^ key to enter an exponent when typing your expression and remember to write is as A(x)=____.

## In this portion of the task you will use the Geogebra Applet to draw each diagram.

*Optima’s Quilts*has introduced. Find two different algebraic expressions to represent each rectangle, and illustrate with a diagram why your representations are correct.

## Task 7.3 Question 2

**The original square block was extended 3 inches on one side and 4 inches on the other.**

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

## Task 7.3 Question 2a

The original square block was extended 3 inches on one side and 4 inches on the other. 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 and remember to write it as A(x)=_____.

## Task 7.3 Question 2b

The original square block was extended 3 inches on one side and 4 inches on the other. 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 and remember to write it as A(x)=_____.

## Task 7.3 Question 3

**The original square block was extended 4 inches on only one side.**

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

## Task 7.3 Question 3a

The original square block was extended 4 inches on only one side. 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 and remember to write it as A(x)=_____.

## Task 7.3 Question 3b

The original square block was extended 4 inches on only one side. 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 and remember to write it as A(x)=_____.

## Task 7.3 Question 4

**The original square block was extended 5 inches on each side.**

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

## Task 7.3 Question 4a

The original square block was extended 5 inches on each side. 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 and remember to write it as A(x)=_____.

## Task 7.3 Question 4b

The original square block was extended 5 inches on each side. 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 and remember to write it as A(x)=_____.

## Task 7.3 Question 5

**The original square block was extended 2 inches on one side and 6 inches on the other.**

## Task 7.3 Question 5a

The original square block was extended 2 inches on one side and 6 inches on the other. 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 and remember to write it as A(x)=_____.

## Task 7.3 Question 5b

The original square block was extended 2 inches on one side and 6 inches on the other. 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 and remember to write it as A(x)=_____.

**,**

*diagrams***and**

*written descriptions***of the area of the rectangles in using expressions representing the lengths of the sides.**

*algebraic descriptions*## Task 7.3 Question 6

## Task 7.3 Question 6a

Write a description of the following "order" For instance, *"**The original square block was extended __ inches on one side and __ inches on the other."*

## Task 7.3 Question 6b

Find an expression to represent the area, , as a product of two factors. When typing your expression and remember to write it as A(x)=_____.

## Task 7.3 Question 6c

Find an expression to represent the area, in simplest form. Use the ^ key to enter an exponent when typing your expression and remember to write it as A(x)=_____.

## Task 7.3 Question 7

## Task 7.3 Question 7a

Write a description of the following "order" For instance, *"**The original square block was extended __ inches on one side and __ inches on the other."*

## Task 7.3 Question 7b

Find an expression to represent the area, , as a product of two factors. When typing your expression and remember to write it as A(x)=_____.

## Task 7.3 Question 7c

Find an expression to represent the area, in simplest form. Use the ^ key to enter an exponent when typing your expression and remember to write it as A(x)=_____.

## Task 7.3 Question 8

## Task 7.3 Question 8a

Write a description of the following "order" For instance, *"**The original square block was extended __ inches on one side and __ inches on the other."*

## Task 7.3 Question 8b

Find an expression to represent the area, , as a product of two factors. When typing your expression and remember to write it as A(x)=_____.

## Task 7.3 Question 8c

Find an expression to represent the area, in simplest form. Use the ^ key to enter an exponent when typing your expression and remember to write it as A(x)=_____.

## Task 7.3 Question 9

## Task 7.3 Question 9a

*"**The original square block was extended __ inches on one side and __ inches on the other."*

## Task 7.3 Question 9b

## Task 7.3 Question 9c

## Task 7.3 Question 10

## Task 7.3 Question 10a

*"**The original square block was extended __ inches on one side and __ inches on the other."*

## Task 7.3 Question 10b

## Task 7.3 Question 11

## Task 7.3 Question 11a

*"**The original square block was extended __ inches on one side and __ inches on the other."*

## Task 7.3 Question 11b

## Task 7.3 Question 12

## Task 7.3 Question 12a

*"**The original square block was extended __ inches on one side and __ inches on the other."*

## Task 7.3 Question 12b

## Task 7.3 Question 13

## Task 7.3 Question 13a

*"**The original square block was extended __ inches on one side and __ inches on the other."*

## Task 7.3 Question 13b

## Task 7.3 Question 14

## Task 7.3 Question 14a

*"**The original square block was extended __ inches on one side and __ inches on the other."*

## Task 7.3 Question 14b

## Task 7.3 Question 15

## Task 7.3 Question 15a

*"**The original square block was extended __ inches on one side and __ inches on the other."*