DO NOW 1.7.14

1. 1. You are asked to find the area of a 4x4 square (shown). Find the area. You are asked to dilate the square (DILATION of 2). Will the square be larger or smaller than the original? What operation is used Draw the new square in the space to the right. How does the area compare to the original? Will this work for any figure? DO NOW 1.7.14 Area: 64 square units Area: 16 square units

2. Learning Objective NAME:__________________________ Tuesday, January 7, 2014 ‘A’ Week We will use Dilations1 to show Proportional Relationships on a Coordinate Plane. What are we going to learn? What does dilation mean? Dilation means ____________ _________________________. CFU Activate Prior Knowledge Identify each of the four quadrants. Describe what relationship exists between their ordered pairs (x , y). enlarging or reducing size. 2 1 QUADRANT QUADRANT QUADRANT QUADRANT ( - , + ) ( + , + ) Make Connection Students, you already know how to plot points onto a number line. Now, we will use that skill to identify figures on coordinate planes. 1enlargements or reductions in size Vocabulary 3 4 ( - , - ) ( + , - )

3. Activating Prior Knowlegdge (Continued) 10 9 8 7 6 5 4 3 2 1 3 6 7 8 1 2 4 5 9 10 Ordered Pair The coordinate plane is a flat surface made by the intersection2 of two perpendicular3 number lines. An ordered pair describes4 the location of a point on the coordinate plane using x- and y-coordinates. (2, 3) xandy CFU 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 ______.” Ordered Pairs on the Coordinate Plane y-axis – the vertical number line. T Animated “X is the point’s distance along the x-axis.” “X is the point’s distance along the x-axis.” 5 (4, 5) 4 “Y is the point’s distance along the y-axis.” “Y is the point’s distance along the y-axis.” 2 crossing (synonym) 3 crossing at a 90 degree angle 4 shows (synonym) Vocabulary x-axis – the horizontal number line. The origin is where the x-axis and y-axis intersect.

4. Skill Development Ordered Pair 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. (2, 3) xandy CFU 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 _____________. Plot and locate points on a coordinate plane. 1 Determine5 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 (__, __)” 1 2 2 3 2 6 1. Point A ( ___, ___ ) 2. Point B ( ___, ___ ) 3. Point C ( ___, ___ ) 4. Point D ( ___, ___ ) 5. Point E ( ___, ___ ) 6. Point F ( ___, ___ ) 7. Point G ( ___, ___ ) 8. Point H ( ___, ___ ) 3 3 Move Left / Right on x-axis. 6 1 2 9 Move Up / Down on y-axis. 9 10 3 B C D E F G H A 7 6 ordered pair 2 0 0 10 5 figure out Vocabulary

5. Skill Development/Guided Practice (continued) Ordered Pair 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. (2, 3) xandy 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 Plot and locate points on a coordinate plane. 1 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. 1 2 2 3 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 ) B A C D E F G H 3

6. 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 Dilations show us enlargements or reductions. For the following example, the blue figure is a DILATION (enlargement or reduction) of the red figure. 1 Determine which figure is the original. Determine which figure is the enlargement or reduction. 1 2 3 1 4 RED RED ORIGINAL: DILATION (NEW IMAGE): ORIGINAL: DILATION (NEW IMAGE): BLUE 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? “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

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

8. DILATIONSenlarge 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) xandy Skill Closure CFU Which operations are used in dilations? Addition Subtraction Multiplication Division Identify the points given on a coordinate plane. 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. 1 2 3 Word Bank Word Bank DILATION OF 0.5 coordinates ordered pair dilation quadrant point plot enlargement reduction factor Y ( , ) R ( , ) T ( , ) -2 3 Y’ ( , ) R’ ( , ) T’ ( , ) -1 1.5 2 1 1 0.5 -1 -2 -0.5 -1 R’ Y’ T’ Because the dilation is less than 1, our new image will be smaller than the original, in this case ½ the size of the original. Summary Closure What did you learn today about dilations / plotting and locating points on a coordinate plane? (Pair-Share) Use words from the word bank.

9. DILATIONSenlarge 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 NAME________________PERIOD _____ 1.7.14 CLASSWORK Independent Practice Identify the points given on a coordinate plane. 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. 1 2 3 Word Bank DILATION OF 0.5 ORIGINAL FIGURE NEW FIGURE -2 2 -1 1 M ( , ) K ( , ) H ( , ) Q ( , ) M’ ( , ) K’ ( , ) H’ ( ) Q’ ( , ) 3 0 1.5 0 1 -4 0.5 -2 M’ Q’ H’ K’ -1 -1 -0.5 -0.5 less Because the dilation is ________ than 1, our new image will be ________ than the original, in this case _______ the size of the original. smaller half

10. DILATIONSenlarge 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 NAME________________PERIOD _____ 1.7.14 CLASSWORK Independent Practice Identify the points given on a coordinate plane. 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. 1 2 3 Word Bank DILATION OF 2 ORIGINAL FIGURE NEW FIGURE 0 2 0 4 A ( , ) W ( , ) H ( , ) L ( , ) A’ ( , ) W’ ( , ) H’ ( , ) L’ ( , ) 2 2 4 4 0 -1 0 -2 W’ H’ A’ L’ -1 1 -2 2 greater Because the dilation is _______ than 1, our new image will be ________ than the original, in this case _______ the size of the original. larger twice