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Use Properties of Operations to Generate Equivalent Expression

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

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Use Properties of Operations to Generate Equivalent Expression

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  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

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

  6. 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.

  7. 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.

  8. Lesson 2- Math Standard 7.EE.A.1Generating Equivalent Expressions Opening exercise (6 minutes) MP.8: Look for and express regularity in repeated reasoning Purpose: To complete the table in the Opening Exercise that scaffolds (builds on) the concept of opposite expressions from the known concept on opposite numbers to find the opposite of the expression 3x. Opening Exercise Directions: Additive inverses have a sum of zero. Multiplicative inverses have a product of 1. Fill in the center column of the table with the opposite of the given number or expression, then show the proof that they are opposites. The first row is completed for you. Time to complete: 3-4 minutes

  9. Lesson 2- Math Standard 7.EE.A.1Generating Equivalent Expressions Opening exercise discussion (2-3 minutes) • In the last two rows, explain how the given expression and its opposites compare. Recall that the opposite of a number, say , satisfies the equation We can use this equation to recognize when two expressions are opposites of each other. For example, , we conclude that must be the opposite of . This is because when either are substituted into the blank in the resulting equation is true for every value of Therefore, the two expressions must be equivalent; .

  10. Lesson 2- Math Standard 7.EE.A.1Generating Equivalent Expressions Opening exercise • Since the opposite of and the opposite of , what can we say about the opposite of the sum of We can say that the opposite of the sum is the sum of its opposites .

  11. Lesson 2- Math Standard 7.EE.A.1Generating Equivalent Expressions Opening exercise • Is this relationship also true for the last example ? Yes, because opposites have a sum of zero, so If the expression is substituted in the blank, the resulting equation is true for every value of . The opposites of and the sum of these opposites is ; therefore, it’s true that the opposite of the sum is the sum of its opposites . sumopposite

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

  13. Example 1 (6 minutes): Subtracting ExpressionsStudents and teacher investigate the process for subtracting expressions where the subtrahend is a grouped expression containing two or more terms. Example 1 • Subtract: • Subtract the expression first by changing subtraction of the expression to adding the expression’s opposite • Next, subtract the expressions using traditional order of operations. Does the difference yield the same number in each case? • Which of the two methods seems more efficient and why?

  14. Example 1 (6 minutes): Subtracting ExpressionsStudents 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!

  15. INCOMPLETE PRESENTATION

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