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Transcript
1-12 6th grade math Solving Addition and Subtraction Equations Objective • To solve one-step linear equations in one variable. • Why? To master another aspect of Algebra and Functions in 6th grade math (and beyond). Being able to solve equation is a key component in Algebra and other higher math. California State Standards AF 1.1 : Write and solve one-step linear equations in one variable MR 3.3: Develop generalizations of the results obtained and the strategies used and apply them in new problem situations. Vocabulary • Expression - A mathematical phrase made up of a combination of variables and/or numbers and operations. Expression with variables are also called algebraic expressions. Expressions with variables must have a number to substitute the variable and then solve. • 5n, n = 4. 5 x 4 = 20; 4x – 7; (5 x 2) – 6/3; … • Equation – A number sentence stating that two expressions are equal. Solving equations is like balancing a scale. Of you add or subtract a number to one side, you must also add or subtract that number to the other side in order to maintain the equality (or balance). Your goal is to ‘isolate the variable’ on one side of they equation. • 3 + 5 = x; 8x = 32; … • Inverse Operations – Two operations with an opposite effect. Addition and subtraction are inverse operations. Multiplication and division are inverse operations. Inverse operations ‘undo’ each other. You solve equations by using inverse operations. How to Solve Equations with Addition or Subtraction 1) Read the equation and understand what you need to do to ISOLATE THE VARIABLE. 2) First undo the subtraction to BOTH sides. 3) Carefully solve and check your work by substituting the solved number into the equation. A) x – 26 = 85 x - 26 + 26 = 85 + 26 x = 111 B) w + 41.8 = 55.9 w + 41.8 – 41.8 = 55.9 – 41.8 w = 14.1 C) 0.6 = p + 0.5 0.6 – 0.5 = p + 0.5 – 0.5 0.1 = p Try It! Solve each equation. 1) 26 1) a + 17 = 43 2) 88 2) x – 22 = 66 3) 138 + g = 150 4) y + 8.3 = 9.2 3) 12 4) 0.9 Objective Review • You can now solve one-step linear equations in one variable. • Why? You have now mastered another aspect of Algebra and Functions in 6th grade math (and beyond). Being able to solve equation is a key component in Algebra and other higher math. You can solve addition and subtraction equations by adding or subtracting the same amount on both sides of the equations. REMEMBER TO ISOLATE THE VARIABLE! Independent Practice • Complete problems 617, 19. • Copy original problem first. • Show all work! • If time, complete Mixed Review: 20-28. • If still more time, work on Accelerated Math.