Unit 1 Relationships Between Quantities and Expressions

Week 1

Lesson 3

Standards/Objective• A.SSE.1 – Interpret parts of an expression• A.APR.1 – Add, subtract, and multiply

polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations.

Objective: Students understand that the sum or difference of two polynomials produces another polynomial. Students add and subtract polynomial expressions to form polynomials in standard form.

Essential Questions

• If you add two polynomials together, is the result sure to be another polynomial?

• If you find the difference of two polynomials, is the result sure to be another polynomial?

Vocabulary

• Monomial• Binomial• Trinomial• Polynomial• Polynomial Expression• Like Terms

Read, Write, Draw, Solve

Jeremy is building a barn. He needs to buy some 6 foot posts. The posts cost $12.50 each.

A. Write an expression that can model this situation

B. Explain what each term meansC. How much will it cost if Jeremy buys 8 posts?

Activator

• What do we call this (3 + 4) * 5?• What would we call (x + 5) + (4x2 – x)7x• What do you think we call 5n?• What do you think we would call 5x + 4?• What do you think we call 5n2 + 3n – 6?

How would you find the sum or difference of each numerical expression below?

A. 153 + 236

B. 6,854 + 1,032

C. 3.5 - 0.4

D. 13.47 + 6.02

E. 578 – 324

When we talk about ‘like terms’ what are we talking about?

If we see 5x2 what could be a like term that we could add or subtract from it?

How would you find the sum or difference each expression below?

+ ☺ ☺2

M + M + M + R + H + S 2x + 3x + x3 5r – 7r + 12

3(x – 4) + 7x – 2

Simplify with Algebra Tiles

• Can we simplify polynomial expressions using Algebra Tiles 3x + 4x – 5 – x + 3x2?

Let’s try some with the Algebra Tiles.

A. 4x + 8 – 3x

B. 5x – 9 – 2 – 3x

C. –3x + 7 + x – 6

D. 3x2 + 2x – 4 + x – x2

E. -4 + 2x2 + 5 + 4x – 5x2

Let’s try a few some examples with or without

A. 3 + 2x – 5 – 5x

B. (2x2 + 4x – 3) + (x2 – x + 10)

C. (3x2 – 4x + 2) – ( 4x2 + x + 4)

We have been working with finding sums and differences, applying the Commutative, Associative, and Distributive properties to prove equivalency of expressions and combining terms that are alike.

Is each polynomial expression that you have simplified today, is the new expression equivalent to the original polynomial expression?

Is Polynomial B an equivalence of Polynomial A? Explain how you know.

If x = 2 for both polynomials do you think you will get the same answer? Why?

A. 3x2 + 2x + 4 – x – 1

B. 3x2 + x + 3

Look at the two Polynomials below. Are they equal? Will you get the same answer for both A and B if x = 3?

A. 3x + 4x – 5 – x + 3x2

B. 6x + 3x2 – 5

Exit Ticket – Lesson 2• What are like terms? Create a polynomial expression with

at least 2 like terms.

• When we simplify a polynomial expression does it change the meaning or value of the expression?

• If you substitute 2 for x in expression A and B would you get the same value for polynomial expression A and B? Explain why or why not. Test your prediction by substituting 2 for x and simplify each expression.

A. 2x + 3 – 2 + 4x B. 6x + 1