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Do Now Monday, December 16, 2013 James, Ken, Chris, and Jessie ordered a pizza from Lucia’s Italian Restaurant. They pizzas only come in one size and are in the shape of a square. James already had a burger a couple hours before and is not very hungry. James thinks that he can eat 10% of the pizza. Ken is very hungry and says he could eat half of the pizza. Chris thinks he will eat ¼ of the pizza, and Jessie says he is going to order a salad instead of eating pizza. If the friends eat the portions they have predicted, what percent of the pizza will be left over? Justify your thinking using the 10x10 grid above. James Ken

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What are we going to learn? What does dilation mean? Dilation means ____________ _________________________. CFU Students, you already know how to plot points onto a number line. Now, we will use that skill to identify figures on coordinate planes. Make Connection Identify each of the four quadrants. Describe what relationship exists between their ordered pairs (x, y). 1 enlargements or reductions in size Vocabulary We will use Dilations 3 to show Proportional Relationships on a Coordinate Plane. Learning Objective Activate Prior Knowledge QUADRANT NAME:__________________________ Monday, December 16, 2013 ‘B’ Week 1 QUADRANT 2 34 ( +, + ) enlarging or reducing size. ( -, + ) ( -, - ) ( +, - )

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12 3 45 678 910 2 4 5 6 7 8 9 3 1 x-axis y-axis The coordinate plane is a flat surface made by the intersection 2 of two perpendicular 3 number lines. An ordered pair describes 4 the location of a point on the coordinate plane using x- and y-coordinates. On your whiteboard, write an example of an ordered pair. Which number is the x- coordinate? Which is the y- coordinate? How do you know? Which of the following is the ordered pair that identifies the location of the point T? A (9, 7) B (7, 9) In your own words, what is an ordered pair? “An ordered pair is ______.” CFU Ordered Pairs on the Coordinate Plane 2 crossing (synonym) 3 crossing at a 90 degree angle 4 shows (synonym) Vocabulary Activating Prior Knowlegdge (Continued) “X is the point’s distance along the x-axis.” “Y is the point’s distance along the y-axis.” – the horizontal number line. – the vertical number line. The origin is where the x-axis and y-axis intersect. (4, 5) 5 4 “Y is the point’s distance along the y-axis.” “X is the point’s distance along the x-axis.” T Animated Ordered Pair (2, 3) x and y

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Determine 5 the x-coordinate of the point. (write) Hint: The distance along the x-axis. Determine the y-coordinate of the point. (write) Hint: The distance along the y-axis. Read the ordered pair aloud. “Point ___ is at the point (__, __)” Plot and locate points on a coordinate plane. 1 2 3 How did I/you determine the x-coordinate? How did I/you determine the y-coordinate? When the x-coordinate and the y-coordinate are put together, they form an _____________. CFU 1 2 Skill Development The coordinate plane is a flat surface made by the intersection of two perpendicular number lines. An ordered pair describes the location of a point on the coordinate plane using x- and y-coordinates. A B C D E F G H 1. Point A ( ___, ___ ) 2. Point B ( ___, ___ ) 3. Point C ( ___, ___ ) 4. Point D ( ___, ___ ) 5. Point E ( ___, ___ ) 6. Point F ( ___, ___ ) 7. Point G ( ___, ___ ) 8. Point H ( ___, ___ ) 26 33 61 29 910 76 20 0 5 figure out Vocabulary Ordered Pair (2, 3) x and y 3 Move Left / Right on x-axis. Move Up / Down on y-axis. ordered pair

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Skill Development/Guided Practice (continued) Determine the x-coordinate of the point. (write) Hint: The distance along the x-axis. Determine the y-coordinate of the point. (write) Hint: The distance along the y-axis. Plot and label the point at the correct coordinates. Plot and locate points on a coordinate plane. 1 2 3 How did I/you determine the x-coordinate? How did I/you determine the y-coordinate? How did I/you plot and label the point? CFU 1 2 The coordinate plane is a flat surface made by the intersection of two perpendicular number lines. An ordered pair describes the location of a point on the coordinate plane using x- and y-coordinates. Ordered Pair (2, 3) x and y 1. Point A ( 3, 10 ) 2. Point B ( 2, 7 ) 3. Point C ( 4, 6 ) 4. Point D ( 5, 9 ) 5. Point E ( 0, 5 ) 6. Point F ( 7, 0 ) 7. Point G ( 8, 8 ) 8. Point H ( 4, 3 ) C D E F G H A B 3

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Skill Development/Guided Practice (continued) How did I/you determine which figure is the original? What does a dilation show? If my figure is enlarged, I am multiplying by a factor greater than ______, which increases the size of my original. If my figure is a reduction, I am multiplying by a factor less than ______ (I could also divide), which decreases the size of my original. CFU 2 1 3 4 Determine which figure is the original. Determine which figure is the enlargement or reduction. Dilations show us enlargements or reductions. For the following example, the blue figure is a DILATION (enlargement or reduction) of the red figure. ORIGINAL: DILATION (NEW IMAGE): ORIGINAL: DILATION (NEW IMAGE): RED BLUE RED BLUE “The original RED figure has gone through a reduction to become the BLUE figure. The RED figure measured 9 x 9, the BLUE figure measures 3 x 3. What factor did the RED figure multiply or divide by? Divide by 3.Multiply by 2 1 1

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Relevance (Continued) T. Alice is at the theater. She would like to go to the gas station. Write directions for her. S. Felix is at the hardware store. He would like to go to the bank. Write directions for him. 1 st 2 nd 3 rd 4 th 5 th 6 th 2 nd 6 th 3 rd 4 th 5 th 1 st Bank Gas Station Hardware Store Theater Application Alice should go RIGHT (travel EAST) 1 block, then turn LEFT (travel NORTH) 4 blocks How did I/you determine what the question is asking? How did I/you determine the math concept required? How did I/you determine the relevant information? How did I/you solve and interpret the problem? How did I/you check the reasonableness of the answer? CFU 2 1 3 4 5 Felix should go RIGHT (travel EAST) 1 block, then turn LEFT (travel NORTH) 2 blocks Ordered Pair (2, 3) x and y

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DILATION OF 0.5 I’ (, ) N’ (, ) S’ (, ) U’ (, ) I (, ) N (, ) S (, ) U (, ) Skill Development/Guided Practice (continued) DILATION OF 3 H (, ) K (, ) W (, ) T (, ) H’ (, ) K’ (, ) W’ (, ) T’ (, ) 1.Find your original coordinates for the pre-image (the original drawing). 2.Multiply the factor of dilation by the original coordinates, then plot the points. Ex.) A will become A’. Dilations show us enlargements or reductions. 0 1 0 1 1 -1 0 3 0 3 3 -3 H’ K’ W’ T’ -2 3 3 2 -2 -3 -2 -1 1.5 1.5 1 -1 -1.5 -1 I’N’ S’U’

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Plotting and locating points on a coordinate plane will help you understand information in real life. 1 Does anyone else have another reason why it is relevant to plot and locate points on a coordinate plane? (Pair-Share) How can a visual example make it easier to see the true changes in a DILATION? (Pair- Share) CFU Relevance We have talked about similar figures during the past week. We know that similar figures are not congruent, but have sides that maintain a common ratio. A DILATION describes the relationship between two similar figures as a reduction or enlargement in size. The relationship can be easily modeled on a coordinate plane using x- and y-coordinates. Dilations allow us to see enlargements or reductions visually. 2 Information in real life is often presented in graphs on a coordinate plane. Most maps use a grid system that works like a coordinate plane.

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What did you learn today about dilations / plotting and locating points on a coordinate plane? (Pair-Share) Use words from the word bank. Skill Closure Summary Closure Word Bank coordinates ordered pair dilation quadrant point plot enlargement reduction factor DILATIONS enlarge or reduce the size of a figure. We can manipulate ordered pairs based on the dilation given. DILATIONS greater than 1 will make a figure larger, while dilations less than one will make a figure smaller. Ordered Pair (2, 3) x and y Write ordered pairs for the each point shown. Apply the factor of the dilation to the ordered pairs. Identify and plot the new points, then sketch the figure. Identify the points given on a coordinate plane. 1 2 3 DILATION OF 0.5 Y (, ) R (, ) T (, ) Y’ (, ) R’ (, ) T’ (, ) -2 3 2 1 -1 -2 -1 1.5 1 0.5 -0.5 -1 Y’ R’ T’

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Independent Practice DILATIONS enlarge or reduce the size of a figure. We can manipulate ordered pairs based on the dilation given. DILATIONS greater than 1 will make a figure larger, while dilations less than one will make a figure smaller. Closure Write ordered pairs for the each point shown. Apply the factor of the dilation to the ordered pairs. Identify and plot the new points, then sketch the figure. Identify the points given on a coordinate plane. 1 2 3 DILATION OF 0.5 M (, ) K (, ) H (, ) Q (, ) M’ (, ) K’ (, ) H’ (, ) Q’ (, ) NAME________________ PERIOD _____ 12.16.13 HOMEWORK ORIGINAL FIGURE NEW FIGURE

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Independent Practice DILATIONS enlarge or reduce the size of a figure. We can manipulate ordered pairs based on the dilation given. DILATIONS greater than 1 will make a figure larger, while dilations less than one will make a figure smaller. Closure Write ordered pairs for the each point shown. Apply the factor of the dilation to the ordered pairs. Identify and plot the new points, then sketch the figure. Identify the points given on a coordinate plane. 1 2 3 DILATION OF 2 A (, ) W (, ) H (, ) L (, ) A’ (, ) W’ (, ) H’ (, ) L’ (, ) NAME________________ PERIOD _____ 12.16.13 HOMEWORK ORIGINAL FIGURE NEW FIGURE

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