EDSE 2700E Middle and Secondary School Mathematics: Teaching Developmentally Dr. Shana Elizabeth Henry 19 th of February 2015

ActivityMinutesTime 1 Reflection of Last Class 10 min7:30 – 7:35 2 Articles, Discussion Questions 25 min7:35 – 8:00 3 Survey 15 min8:00 – 8:15 4 Activity w/ Summary 45 min8:15 – 9:00 5 Review Info for next week20 min9:00 – 9:20 EDSE 2700E Middle and Secondary School Mathematics: Teaching Developmentally Dr. Shana Elizabeth Henry 19 th of February 2015

Weekly Topic: Proportional Reasoning Feb. 5 th, 2015

R&R Langrall & Swafford. (2000). Three balloons for two dollars: Developing proportional reasoning. McDuffie, 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 Find two numbers that approximate this proportion. A B A - B

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. Euclid's Elements Book VI Definition 3

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 is Phi?

is an irrational number

What is Phi? is an irrational number is a proportion

What is Phi? is an irrational number is a proportion is the solution to a quadratic equation

What is Phi? is an irrational number is a proportion is the solution to a quadratic equation is the ratio of the line segments that result when a line is divided in one very special and unique way.

What is Phi? is an irrational number is a proportion is the solution to a quadratic equation is the ratio of the line segments that result when a line is divided in one very special and unique way. is constructable (geometrically)

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:

DefineExamples w/ numbers Example w/ algebra a.k.a RatioComparison of two quantities # of girls to # of boys 3x : y Fraction, decimal, Percent ProportionAn equation that states ratios are equal

DefineExamples w/ numbers Example w/ algebra a.k.a RatioComparison of two quantities # of girls to # of boys 3x : y Fraction, decimal, Percent ProportionAn equation that states ratios are equal a and d (extremes)

DefineExamples w/ numbers Example w/ algebra a.k.a RatioComparison of two quantities # of girls to # of boys 3x : y Fraction, decimal, Percent ProportionAn equation that states ratios are equal a and d (extremes)

DefineExamples w/ numbers Example w/ algebra a.k.a RatioComparison of two quantities # of girls to # of boys 3x : y Fraction, decimal, Percent ProportionAn equation that states ratios are equal a and d (extremes) b and c (means)

DefineExamples w/ numbers Example w/ algebra a.k.a RatioComparison of two quantities # of girls to # of boys 3x : y Fraction, decimal, Percent ProportionAn equation that states ratios are equal a and d (extremes) b and c (means)

DefineExamples w/ numbers Example w/ algebra a.k.a RatioComparison of two quantities # of girls to # of boys 3x : y Fraction, decimal, Percent ProportionAn equation that states ratios are equal a and d (extremes) b and c (means)

A B A - B The line AB is cut in extreme and mean ratio at C since AB : AC = AC : CB.

Disproportionate thinking?

The average height of a woman in the United States is centimeters. If Barbie is 300 mm tall, compute her proportional measurements (i.e. her bust, waist, wrist, and inside leg). The average height of a woman in the United States is centimeters. If Barbie is 300 mm tall, compute her proportional measurements (i.e. her bust, waist, wrist, and inside leg).

Purpose: See an application of proportionality in our bodies and to discuss disproportionate body images. Proportional Reasoning

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, 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