School Year Session 11: March 5, 2014 Similarity: Is it just “Same Shape, Different Size”? 1.1

Agenda Similarity Transformations Circle similarity Break Engage NY assessment redux Planning time Homework and closing remarks 1.2

Learning Intentions & Success Criteria Learning Intentions: We are learning similarity transformations as described in the CCSSM Success Criteria: We will be successful when we can use the CCSSM definition of similarity, and the definition of a parabola, to prove that all parabolas are similar 1.3

1.4 An approximate timeline The Big Picture

Someone in your group has recent experience Do not “bonk with the big blocks” 1.5

Introducing Similarity Transformations With a partner, discuss your definition of a dilation. Activity 1: 1.6

Introducing Similarity Transformations (From the CCSSM glossary) A dilation is a transformation that moves each point along the ray through the point emanating from a common center, and multiplies distances from the center by a common scale factor. Figure source: ometry/GT3/Ldilate2.htm Activity 1: 1.7

Introducing Similarity Transformations Two geometric figures are defined to be congruent if there is a sequence of rigid motions (translations, rotations, reflections, and combinations of these) that carries one onto the other. Two geometric figures are defined to be similar if there is a sequence of similarity transformations (rigid motions followed by dilations) that carries one onto the other. Two geometric figures are defined to be congruent if there is a sequence of rigid motions (translations, rotations, reflections, and combinations of these) that carries one onto the other. Two geometric figures are defined to be similar if there is a sequence of similarity transformations (rigid motions followed by dilations) that carries one onto the other. Activity 1: (From the CCSSM Geometry overview) 1.8

Introducing Similarity Transformations Read G-SRT.1 Discuss how might you have students meet this standard in your classroom? Activity 1: 1.9

Circle Similarity Consider G-C.1: Prove that all circles are similar. Discuss how might you have students meet this standard in your classroom? Activity 2: 1.10

Circle Similarity Activity 2: 1.11 Begin with congruence On patty paper, draw two circles that you believe to be congruent. Find a rigid motion (or a sequence of rigid motions) that carries one of your circles onto the other. How do you know your rigid motion works? Can you find a second rigid motion that carries one circle onto the other? If so, how many can you find?

Circle Similarity Activity 2: 1.12 Congruence with coordinates On grid paper, draw coordinate axes and sketch the two circles x 2 + (y – 3) 2 = 4 (x – 2) 2 + (y + 1) 2 = 4 Why are these the equations of circles? Why should these circles be congruent? How can you show algebraically that there is a translation that carries one of these circles onto the other?

Circle Similarity Activity 2: 1.13 Turning to similarity On a piece of paper, draw two circles that are not congruent. How can you show that your circles are similar?

Circle Similarity Activity 2: 1.14 Similarity with coordinates On grid paper, draw coordinate axes and sketch the two circles x 2 + y 2 = 4 x 2 + y 2 = 16 How can you show algebraically that there is a dilation that carries one of these circles onto the other?

Circle Similarity Activity 2: 1.15 Similarity with a single dilation? If two circles are congruent, this can be shown with a single translation. If two circles are not congruent, we have seen we can show they are similar with a sequence of translations and a dilation. Are the separate translations necessary, or can we always find a single dilation that will carry one circle onto the other? If so, how would we locate the centre of the dilation?

Break 1.12

1.17 Engage NY Redux Activity 3: Last time, we left unanswered the question: “Is the parabola with focus point (1,1) and directrix y = -3 similar to the parabola y = x 2 ?” Answer this question, using the CCSSM definition of similarity.

1.18 Engage NY Redux Activity 3: Are any two parabolas similar? What about ellipses? Hyperbolas?

Learning Intentions & Success Criteria Learning Intentions: We are learning similarity transformations as described in the CCSSM Success Criteria: We will be successful when we can use the CCSSM definition of similarity, and the definition of a parabola, to prove that all parabolas are similar 1.19

1.20 Find someone who is teaching similar content to you, and work as a pair. Think about the unit you are teaching, and identify one key content idea that you are building, or will build, the unit around. Identify a candidate task that you might use to address your key idea, and discuss how that task is aligned to the frameworks (cognitive demand/SBAC claims) we have seen in class. We will ask you to share out at 7:45. Planning Time Activity 4:

1.21 Homework & Closing Remarks Homework: Prepare to hand in your assessment and task modification homework on March 19. You should include both the original and the modified versions of both tasks (the end-of-unit assessment and the classroom task), your assessment rubric, and your reflections on the process and the results. Begin planning your selected lessons. You will have time to discuss your ideas with your colleagues in class on March 19. Bring your lesson and assessment materials to class on March 19. Activity 5: