Materials: class set of algebra tiles Give points for homework
Transcript
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AIM: How do we solve 2 step equations using algebra tiles? OBJECTIVE: S.W.B.A.T. use algebra tiles or the puzzle method to solve 2 step equations Homework: 2 -step Equations Day 1 worksheet October 10, 2007 DO NOW Scales balance when the weights on them are equal. Which equation is represented by the balance scale below ?
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Using the properties of equality to solve equations –Do Now debrief OR x + x + -1 = x + 1 + 1 + 1 + 1 + 1 2x – 1 = x + 5
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Using algebra tiles to solve equations In Addition to puzzles we can also use algebra tiles to solve 2-step equations. However we must first know how to use the tiles and what they stand for. negative x positive x positive 1 negative 1
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Using algebra tiles to solve equations - The rules negative x positive x + = 0
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Using algebra tiles to solve equations – The rules + = 0 positive 1 negative 1
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Using algebra tiles to solve equations – Example 1 Solve - 5 = 2x + 1 Goal: Variables on 1 side, numbers on other side
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Using algebra tiles to solve equations – Example 1 continued Now we need to move all numbers to the left. -5 = 2x + 1 Add a red box to each side of the fence Red and yellow cancel out -6 = 2x
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Using algebra tiles to solve equations – Example 1 continued -6 = 2x Now we see that each green bar is equal to 3 red rectangles so we can remove half of each side
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Using algebra tiles to solve equations – Example 1 continued -3 = x Done! Now we see that one green bar is equal to 3 red rectangles
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Using algebra tiles to solve equations – Example 1 continued Now let’s check x = -3 using the original equation - 5 = 2x + 1
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Using algebra tiles to solve equations – Example 2 Solve -5 = - 3 x + 7
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Using algebra tiles to solve equations – Example 2 continued – 5 -3x + 7 Goal is to get all variables on one side of the fence Add three green bars to both sides to eliminate the red bars on the right
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Using algebra tiles to solve equations – Example 2 continued 3x + -5 7 Goal is to get one variable alone on the left All variables on the right cancel each other out.
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Using algebra tiles to solve equations – Example 2 continued 12 Now add five yellows to both sides to get rid of the numbers on the left. 3x Reds and yellows cancel
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Using algebra tiles to solve equations – Example 2 continued 12 Now we can see that each green bar is equal to four yellows 3x
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Using algebra tiles to solve equations – Example 2 continued x 4 Goal is to get one x on one side of the fence x = 4. Done ! Now let’s check using the original equation -5 = - 3 x + 7
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Using the Puzzle method to solve equations – Example 3 Let’s Solve - 5 = 2x + 1 using the puzzle method I’m thinking of a number. x Multiply the number by 2 2x Add 1 2x + 1 You get -5 2x + 1 = -5 What number am I ? -5 – 1 -2 Work backwards!
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Use algebra tiles or the puzzle method to solve and check the equations below