1. Use Properties of Operations to Generate Equivalent Expression Common Core: Engage New York 7.EE.A.1 and 7.EE.A.2

2. What does 7.EE.A.1 cover? Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

3. What does 7.EE.A.2 cover? Understand 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.

4. Table of Contents DateTitlePage 12/9/13Post Investigation 1- Check Up HW Assignment Due THURSDAY 12/12/13 HW Accuracy Grade (not completion only) 12/10/137.EE.1- Engage NY Lesson 1: Generating Equivalent Expressions *Attach the Problem set worksheet* # 12/13/137.EE.1- Engage NY Lesson 2: Generating Equivalent Expressions Fresh left

5. Focus 6 Solving Equations Learning Goal Students will be able to write and manipulate algebraic expressions and solve two-step linear equations.

7. Today, my learning target is to… Generate equivalent expressions using the fact that addition and multiplication can be done in: any order (commutative property) and any grouping (associate property) Recognize how any order, any grouping can be applied in a subtraction problem by using additive inverse relationships (adding the opposite) to form a sum and likewise with division problems by using the multiplicative inverse relationships (multiplying by the reciprocal) to form a product. Recognize that any order does not apply to expressions mixing addition and multiplication, leading to the need to follow the order of operations.

8. MY PROGRESS CHART Before we start the Learning Target Lesson, think about the Learning Target for today…. How much prior knowledge do you have regarding that goal? Chart your prior knowledge using your pre-target score icon.

9. Lesson 2- Math Standard 7.EE.A.1 Generating Equivalent Expressions

13. Opening exercise  Can we generalize a rule for the opposite of a sum? Yes, the rule is… “The opposite of a sum is the sum of its opposites.” You can use this property as justification for converting the opposites of sums as you work to rewrite expressions in standard form.

14. Example 1 (6 minutes): Subtracting Expressions Students and teacher investigate the process for subtracting expressions where the subtrahend is a grouped expression containing two or more terms. Opposite of a sum is the sum of its oppositesOrder of Operations 40 + 9 + (-(30 + 2)) 40 + 9 + (-30) + (-2) 49 + (-30) + (-2) 19 + (-2) 17 (40 + 9 ) – (30 + 2) (49) – (32) 17

15. Example 1 (6 minutes): Subtracting Expressions Students and teacher investigate the process for subtracting expressions where the subtrahend is a grouped expression containing two or more terms. Example 1 b. Subtract: (3x + 5y – 4) – (4x + 11). From the methods used in Ex 1(a), which will we have to use in Ex 1(b) and why? Check the equivalency of the expression by substituting 2 for x and 6 for y. IMPORTANT TO REMEMBER! When the subtraction is changed to addition, every term in the parentheses that follows must be converted to its opposite! 3x + 5y + (-4) + (-(4x + 11)) 3x + 5y + (-4) + (-4x) + (-11) 3x + (-4x) + 5y + (-4) + (-11) -x + 5y + (-15) -x + 5y – 15 1.Subtraction as adding the opposite 2.Opposite of a sum is the sum of its opposite 3.Any order, any grouping 4.Combining like terms 5.Subtraction replaces adding the opposite

16. INCOMPLETE PRESENTATION