Lesson 3 Building the Perfect Square Develop Understanding
Graph each function.
Find the square of a binomial expression.
Recognize a perfect square trinomial.
Create perfect squares from partial areas.
Find relationships between terms in a perfect square trinomial.
How can we use models to find equivalent expressions for perfect squares?
Open Up the Math: Launch, Explore, Discuss
Optima has a quilt shop where she sells many colorful quilt blocks for people who want to make their own quilts. She has quilt designs that are made so that they can be sized to fit any bed. She bases her designs on quilt squares that can vary in size, so she calls the length of the side for the basic square
If Optima adds
When Optima draws a pattern for the square in problem 1, it looks like this:
Use both the diagram and the equation
The customer service representatives at Optima’s shop work with customers and write up the orders based on the area of the fabric needed. As you can see from problem 2, there are two ways that customers can call in and describe the area of the quilt block. One way describes the length of the sides of the block, and the other way describes the areas of each of the
For each of the following quilt blocks, draw the diagram of the block and write two equivalent equations for the area of the block.
Block with side length
Block with side length
What patterns do you notice when you relate the diagrams to the two expressions for the area?
Optima likes to have her little dog, Clementine, around the shop. One day, Clementine got a little hungry, and started to chew up the orders. When Optima found the orders, one of them was so chewed up that there were only partial expressions for the area remaining. Help Optima by completing each of the following expressions for the area so that they describe a perfect square. Then, write the two equivalent equations for the area of the square.
What process can be used to find
Will this strategy work if
Will the strategy work if
One of the new customer service representatives thinks she doesn’t need to draw diagrams anymore because she found a great shortcut. She writes
Ready for More?
The square of a binomial:
An example is:
Adding Notation, Vocabulary, and Conventions
Squaring a binomial:
In this lesson, we connected area models for multiplication to show how to multiply binomials to get a perfect square trinomial. We learned to recognize a perfect square trinomial by looking for a relationship between the second and third terms. We also worked to create a perfect square when given the first two terms of a trinomial.
Each of the following equations has just one intercept; find it and state whether it is an