1. Factoring Linear Expressions Dr. Lee

2. Warm-Up 1 Find the error * Todd is finding (5x +3) – (2x + 1). Find his mistake. 5x + 3) – (2x + 1) = 5x + 3 – 2x + 1 = 5x – 2x + 3 + 1 = 3x + 4 ** How did you know that this solution was not reasonable? **What would be a more efficient strategy?

3. Common Core Standards 7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 7.EE.2Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”

4. Objectives “Given ten problems, students will be able to use properties of mathematics to factor linear expression.” Students must show their work and solve at least seven of the problems correctly to make mastery.

5. Targets I can factor a number by writing it as a product of its factors. I can find the GCF I can identify Monomials I can express a linear expression in factor form

6. Essential Question How do you know when monomials have common factors?

7. Terms Monomials, factor, factor form Monomials – is a number, a variable, or product of a number and one or more variable Factor – write it as a product of its factors Factored form – an expression expressed as the product of its factor

8. Launching the concept o Mona has 3 boxes of apples, 2 boxes of bananas, and 4 boxes of cups. Is it appropriate to ask how many total item Mona has? (Turn and talk) o What Level of Questioning is this? Respond

9. Launching the concept Troy has a box of apples and some apples outside the box. Is it appropriate to ask how many apples in total that Troy has? Explain your reasoning… What level of questioning is this? o What is the total number of apples that Mona has? What level of questioning is this? Is it possible to add 8 pencils to 7 books? Explain your reasoning. What level of questioning is this?

10. Launching the concept Mona was unable to add apples to bananas or even to cups. Why? Apples, bananas, and cups are three different terms. Suppose we use ‘a’ for the number of apples. ‘b’ for the number of bananas, and ‘c’ for the number of cups. a, b, and c are called variables. Variables are symbols or letters that can be used to represent numbers.

11. Launching the concept Mona has as 3a + 2b + 2c Terms Coefficients Suppose Mona has 5 dollars in her pocket. How would I display this within the current expression and what mathematical operation would you use? What level of question is this?

12. Launching the concept 3a + 2b + 2c + 5 Terms Coefficients Constants Are numbers that stand alone Variables **Hot ? How would you describe the problem in your own words? **How could you demonstrate a counter-example? * What level of questioning is this?

13. Guided Practice 1. What are the terms of 3a + 5b – 7c 8x – 10y – 20z - 1 10r – 28q + 5 Write the coefficients in Question 1 above. Write the constants.

14. Independent Practice Identify terms, like terms, constants, coefficients 1. 4e +7e + 5 2. 4 – 4y + y -3 3. 7 – 5y + 2 + 1 4. 2m + 3m – m 5. 8k + 3 + 4k 6. –b -3b + 8b +4 7. 5h – 6 – 8 + 7h 8. 5 – 2t + 5 9. 6m – 7 + 2m + 7 10. y – 8 – 4y + y

15. T.O.D Error Analysis Simplifying the expression 7(x + 1) + 2x. 7x + 1 + 2x = 7x + 3x Where did I go wrong? Explain your reasoning. What properties might you use to find a solution? Writing in Math Identify the like terms in expression 3x + 2 + x. Justify your response with drawing and an explanation. What level of activities are these?