Day 116: Pi Day

6th Grade Math Standards: 6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
MA.1.a.Use the relationships among radius, diameter, and center of a circle to find its circumference and area.
MA.1.b. Solve real-world and mathematical problems involving the measurements of circles.

6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

The Learning Objective: Discover a function rule based on an chart or picture; Define pi as an irrational number that is the ratio of the circumference to the diameter

Agenda:

1. Jumpstart with function rules and sequences
2. Review the functions homework from the previous class
3. Visual Patterns # 7, #1, and #22 (they got progressively more difficult)
4. Read the story of Sir Cumference and the First Round Table by Cindy Neuschwander and Wayne Geehan
5.  Pi Chains
6. Pass out WQ #20 for next week

The Assessment: I asked students to come up with one sentence that would describe how they would start solving visual pattern #7. A few of them said they would start with a chart. When we then proceeded to work on Visual Pattern #1 more students were using a chart immediately. I also went around the room looking at homework. Students had difficulty with the sequence 5, __, 10, 12 and 1/2...

Homework: Weekly Quiz #20 will be due not next class, but the following class.

My Glass Half-Full Take: We assigned a color to each of the ten digits in the number system and gave students 10 different colors of construction paper. From there, students were asked to make a "pi chain." We left the method to how they could go about doing this entirely up to the students. I enjoyed that aspect of the project very much as it gave the students the opportunity to think critically about division of labor and other strategies that would optimize the size of their chains. Students left class stating that it was an enjoyable math class. 

One Thing I Wish I Had Done Differently: I wish at the end of class I had done an index card sized formative assessment (exit ticket) and asked students what type of number pi was and if they could describe what ratio pi represented. I don't think the second objective was fully measured even though the chain is an exaggerated way of emphasizing pi is much more than 3.14.