EDSE 2700 E Middle and Secondary School Mathematics
- Slides: 44
EDSE 2700 E Middle and Secondary School Mathematics: Teaching Developmentally Dr. Shana Elizabeth Henry 19 th of February 2015
EDSE 2700 E Middle and Secondary School Mathematics: Teaching Developmentally Dr. Shana Elizabeth Henry 19 th of February 2015 Activity Minutes Time 1 2 3 4 5 Reflection of Last Class Articles, Discussion Questions Survey Activity w/ Summary Review Info for next week 10 min 25 min 15 min 45 min 20 min 7: 30 – 7: 35 – 8: 00 – 8: 15 – 9: 00 – 9: 20
Weekly Topic: Proportional Reasoning Feb. 5 th, 2015
R&R Langrall & Swafford. (2000). Three balloons for two dollars: Developing proportional reasoning. Mc. Duffie, Wohlhuter, & Breyfogle. (2011). Tailoring tasks to meet students’ needs.
Have you seen proportional reasoning in your placements? Which levels/strategies occurred? Do you agree with the four different levels of strategies for proportional reasoning? Tailoring Tasks to Meet Students Needs: “thread small changes seamlessly into high-level reasoning tasks to reach all students”. A) switch to a familiar context b) supplement foundational gaps c) incorporate overarching goals d) adjust for reading levels
Warm Up a = b b a-b Find two numbers that approximate this proportion.
Warm Up a = b b a-b A - B B A Find two numbers that approximate this proportion.
Euclid's Elements Book VI Definition 3 A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less.
Warm Up 2 Your height (α): ______ Your height to your belly button (β): ______ The ratio of α : β = ______ : _______ = ______ Find five classmates who have a similar ratio to you. Measure in centimeters & round to the nearest hundredth
What? What is Phi?
What? What is Phi? üis an irrational number
What? What is Phi? üis an irrational number üis a proportion
What? What is Phi? üis an irrational number üis a proportion üis the solution to a quadratic equation
What? What is Phi? üis an irrational number üis a proportion üis the solution to a quadratic equation üis the ratio of the line segments that result when a line is divided in one very special and unique way.
What? What is Phi? üis an irrational number üis a proportion üis the solution to a quadratic equation üis the ratio of the line segments that result when a line is divided in one very special and unique way. üis constructable (geometrically)
What is Phi as a ratio?
What is Phi as a ratio? divide a line in mean and extreme ratio.
What is Phi as a ratio? Line segments that result when a line is divided in one very special and unique way.
What is Phi as a proportion?
Phi as a proportion • the ratio of the length of the entire line (A) to the length of larger line segment (B)
Phi as a proportion • the ratio of the length of the entire line (A) to the length of larger line segment (B) is the same as • the ratio of the length of the larger line segment (B) to the length of the smaller line segment (A- B).
Phi as a proportion • the ratio of the length of the entire line (A) to the length of larger line segment (B) is the same as • the ratio of the length of the larger line segment (B) to the length of the smaller line segment (A- B). a = b b a-b
Phi as a proportion • the ratio of the length of the entire line (A) to the length of larger line segment (B) is the same as • the ratio of the length of the larger line segment (B) to the length of the smaller line segment (A- B). a = b b a-b • This happens only at the point where:
Define Examples w/ Example numbers w/ algebra a. k. a Ratio Comparison of two quantities # of girls to # 3 x : y of boys Fraction, decimal, Percent Proportion An equation that states ratios are equal
Define Examples w/ Example numbers w/ algebra a. k. a Ratio Comparison of two quantities # of girls to # 3 x : y of boys Fraction, decimal, Percent Proportion An equation that states ratios are equal a and d (extremes)
Define Examples w/ Example numbers w/ algebra a. k. a Ratio Comparison of two quantities # of girls to # 3 x : y of boys Fraction, decimal, Percent Proportion An equation that states ratios are equal a and d (extremes)
Define Examples w/ Example numbers w/ algebra a. k. a Ratio Comparison of two quantities # of girls to # 3 x : y of boys Fraction, decimal, Percent Proportion An equation that states ratios are equal a and d (extremes) b and c (means)
Define Examples w/ Example numbers w/ algebra a. k. a Ratio Comparison of two quantities # of girls to # 3 x : y of boys Fraction, decimal, Percent Proportion An equation that states ratios are equal a and d (extremes) b and c (means)
Define Examples w/ Example numbers w/ algebra a. k. a Ratio Comparison of two quantities # of girls to # 3 x : y of boys Fraction, decimal, Percent Proportion An equation that states ratios are equal a and d (extremes) b and c (means)
The line AB is cut in extreme and mean ratio at C since AB : AC = AC : CB. A - B B A
Disproportionate thinking?
Disproportionate thinking? The average height of a woman in the United States is 166. 624 centimeters. If Barbie is 300 mm tall, compute her proportional measurements (i. e. her bust, waist, wrist, and inside leg).
Proportional Reasoning Purpose: See an application of proportionality in our bodies and to discuss disproportionate body images.
Hybrid Course Timeframe: 30 minutes per task Task: Create online a portfolio of mathematical tasks that use manipulatives to engage students in their mathematical development. Deadline: Post the link to your online portfolio by the beginning of class, May 15 th, 2015. Gallery Walk: May 15 th, 2015
Minimum Requirements a) Image of manipulative b) Mathematical task c) Appropriate grade range d) Topic(s) that the task develops e) Solution f) Cite your source(s)
Review Info for next week
Review Info for next week
Manipulative Online Portfolio