Coefficient Constant Equivalent expressions Equation. 3 A mathematical sentence containing an equal sign

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1 8.4.0 Lesson Date Algebra Vocabulary and Generating Equivalent s Student Objectives I can identify how many terms an expression has and what the coefficients, constants, and like terms of that expression are. Coefficient Constant Equivalent expressions Equation Word Bank: Like terms Simplest Form/Standard Form Terms Vocabulary Definition Example 1 A mathematical statement expressing something, can be a number or variable, or have an operation or operations with variables and/or numbers 2 s that have the same value, no matter what the value of a variable 3 A mathematical sentence containing an equal sign 4 Each part of an expression separated by addition or subtraction 5 The number that multiplies a variable 6 Terms with the same variable 7 A term without a variable 8 An algebraic expression without parentheses and no like terms

2 Student Objectives I can generate equivalent expressions using commutative property, associative property, and by rewriting subtraction as adding the opposite and dividing as multiplying by the reciprocal. I recognize that the commutative property does not apply to expressions mixing addition and multiplication, leading to the need to follow the order of operations. I recognize the properties of operations. Examples - Fill in the chart for each of the following expressions 17. 3a b + 7 4b 3 Number of Terms Like Terms Coefficients Constants 3. 5c 4c + c 1 Exercise 1 - Fill in the chart for each of the following expressions 1. 3a a 2 Number of Terms Like Terms Coefficients Constants 2. 8b 8b c c + 1

3 Give an example of the: Commutative Property of Addition Associative Property of Addition Identity Property of Addition Commutative Property of Multiplication Associative Property of Multiplication Identity Property of Multiplication Distributive Property of Multiplication over Addition or Subtraction Opening Exercise Dr. and Dr. Crannell had 3 children. Annalisa was born first, with Francesca coming 2 years later, and then Tasha coming 2 years after that. a) Do you know how old Annalisa is? Let a = Annalisa s age (we call this defining a variable). Write an expression to represent Francesca s age in terms of Annalisa s age. b) Write an expression to represent Tasha s age in terms of Annalisa s age. c) Write an expression to represent all their ages added together. d) Let s verify that our expressions work and that they are equivalent. Dr. Annalisa Crannell is years old.

4 Example 1: Commutative and Associative Property with Addition a. Rewrite 4x + 2x + 3 and 4x 2x 3 by combining like terms. Write the original expressions and expand each term using addition. What are the new expressions equivalent to? b. Find the sum of 2x + 1 and 5x. c. Find the sum of 3a + 2 and 5a 3. Exercise 1 Write the following expressions in simplest form. a) 3a a 2 b) 8b + 8 4b 3 c) 5c 4c + c 3c Example 2: Commutative and Associative Properties with Multiplication Find the product of 2x and 3. Example 3: Commutative and Associative Properties in s with Addition and Multiplication a. 3(2x)= c. 4 2 z= b. 4y(5)=

5 d. 3(2x) + 4y(5)= e. 3(2x) + 4y(5) z = f. Alexander says that 3x + 4y is equivalent to (3)(4) + xy because of any order, any grouping. Is he correct? Why or why not? Lesson Summary Terms that contain exactly the same variable symbol can be combined by addition or subtraction because the variable represents the same number. Commutative and associative properties can be used where terms are added (or subtracted) in order to group together like terms. Changing the orders of the terms in a sum does not affect the value of the expression for given values of the variable(s).

6 Advanced Math 7 Period Name Homework Set Homework Homework Date Homework Homework Homework Fill in the chart for each of the following expressions. Number of Like Terms Terms 1. 7j j 9 2. g + 8 9g x + 2 4x + 2 Coefficients Constants 4. 5a + 3b c + 2a 4b Name the properties of numbers and operations used in simplifying the following expressions (the first one has been done for you: 5. 2x + 3y 4 2x + 2 = 2x + 3y + ( 4) + ( 2x) +2 rewrite subtraction as adding the opposite = 2x + ( 2x) + 3y + ( 4) + 2 = (2x + ( 2x)) + 3y + ( 2) = 3y + ( 2) For problems 6 14, write the following expressions in simplest form. 6. 3a + 5a 7. 8b 4b 8. 5c + 4c + c 9. 3a b + 8 4b 11. 5c 4c + c 12. 3a a b + 8 4b c 4c + c 3c

7 Choose 1 of the previous problems and verify that your expression is equivalent to the original expression by evaluating each for the given values: a = 2, b = 5, and c = Write the following expressions in simplest form (6a) 19. 3b(8) + ( 2)(7c) 17. 5d(4) 20. 4(3s) + 2( t) 18. (5r)( 2) 21. 9(4p) 2(3q) + p 22. Jack got the expression 7x + 1, then wrote his answer as 1 + 7x. Is his answer an equivalent expression? How do you know? 23. Jill also got the expression 7x + 1, then wrote her answer as 1x + 7. Is her expression an equivalent expression? How do you know?