The afternoon session for mathematics focused on Grade 8 Module 3: Similarity. The first four lessons explore what it means for two objects to be similar, with the precision of language playing a key role as students describe what they observe. Lesson 4 allows students to paraphrase the Fundamental Theorem of Similarity (FTS) after a hands-on activity exploring dilation factors and their effect on segments, distance from the center, and the preserving of parallel lines and angle measures. Students actually measure and confirm the relationships of the corresponding ratios of the corresponding segments.
In Lesson 5, Exercise 3 puts everything together. Students need to apply the FTS and their understanding of dilations and scale factors in order to come up with the coordinates of a dilated point. The trick is that the coordinates do not end up being integer coordinates. Students get a chance to predict if there is a multiplication effect on coordinates if the center is at the origin. These lessons do a nice job transitioning from the concrete to the abstract.
Lesson 7 discusses and presents why dilations preserve the degree of angles. This lesson pulls from prior knowledge involving angles formed by parallel lines cut by a transversal. This lesson is optional but recommended.
Looking forward to looking at Module 4 tomorrow!