Common Core High School Mathematics: Transforming Instructional Practice for a New Era 6.1

Learning Intentions & Success Criteria Learning Intentions: We are learning to deepen our understanding of the Common Core State Standards and the implications for teaching and learning mathematics. Success Criteria: We will be successful when we can describe how the content standards and math practice standards are evident in the implementation of a mathematical task. 6.2

Agenda Homework review and discussion Art class Reading 6.RP and 7.RP Triangle relationships Break Reading 8.EE.5-6, 8.G.5 Constructing the argument Homework and closing remarks 6.3

6.4 Homework Review and Discussion Activity 1: Table Discussion: Discuss your write up for the day 5 math tasks Modeling Kidneys and Basketball Bounces: Compare your strategies with others at your table. Reflect on how you might revise your own solution and/or presentation.

6.5 Art class Activity 2:

6.6 Reading 6.RP and 7.RP Read the Ratio and Proportion standards from Grades 6 and 7. Turn and Talk: How do these standards progress from one grade to the next? Which grade do you think aligns best with the activity you have just completed? Why? Activity 3:

6.7 Triangle Relationships With a partner, draw three new right triangles whose hypotenuse lies on the line. Each of your triangles should be a different size. Label each triangle with as much information as you can. What do your triangles have in common? What are some relationships among your triangles? Activity 4:

6.8 Triangle Relationships What if you draw a right triangle for this line with a horizontal change of 40? What will the vertical change be? What if the horizontal change is 1? What if the vertical change is 1? What if you draw one or more right triangles on a different line? Can you still use the same ratio to find a missing vertical or horizontal change? Activity 4:

Break 6.9

6.10 Reading 8.EE.5-6, 8.G.5 Read these content standards from the Grade 8 Expressions and Equations and Geometry domains. Turn and talk: Which of these content standards have you seen in the activities you have completed today? How do these Grade 8 standards build on the RP standards you read earlier? Activity 5:

6.11 Reading 8.EE.5-6, 8.G.5 What coherence do you see in the standards you have read from these two Grade 8 domains? Activity 5:

6.12 Constructing the Argument What arguments does this standard expect students to produce? Work in pairs to construct those arguments for yourselves. Activity 6: 8.EE.6: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

6.13 Constructing the Argument Parallel sides of the right triangles are parallel lines crossing a transversal. Therefore, the parallel lines make congruent angles with the traversals. Therefore, any two triangles are similar (AA~). Therefore, the ratios of corresponding sides are equal. This explains why the slope is the same between any two distinct points on a non-vertical line in a coordinate plane Activity 6:

Learning Intentions & Success Criteria Learning Intentions: We are learning to deepen our understanding of the Common Core State Standards and the implications for teaching and learning mathematics. Success Criteria: We will be successful when we can describe how the content standards and math practice standards are evident in the implementation of a mathematical task. 6.14

6.15 Homework and Closing Remarks Homework (to be included in journal): Day 6 Math Task: Equations of Lines Day 6 Class Reflection Reading CCSSM overviews of Grade 8 geometry (critical area (3) on p. 52) and of the High School Geometry conceptual category (p. 74) Activity 7: