Proving Them wrong project

1. Proving Them wrong project

2. Thomas Jefferson’s Quote: “Comparing them by their faculties of memory, reason, and imagination, it appears to me that in memory Negroes are equal to the whites; in reason much inferior, …; and that in imagination they are dull, tasteless, and anomalous.”

3. Memory, Reasoning, and Imagination in Mathematics Mathematical thinkers, who are also excellent problem solvers, need to have a good memory, great reasoning skills, and a deep imagination. - In mathematics we need good memories to remember formulas, definitions, and facts. - The ability to reason in mathematics is essential when explaining topics and terms, drawing conclusions, and recognizing patterns. - To imagine in mathematics is to explore, predict, and question, which are all powerful actions in the problem-solving/decision-making process. To say that a person lacks these skills is to say that a person is not intelligent!

4. Your Task • You are to create a powerpoint presentation in which you choose a math term/topic to teach using the three essential mathematical skills. • Your presentation will include a title page, slides that display each skill, and a creative piece (extra credit) that better illustrates your term/topic. • “Memory” must include 3 items, “reason” must include 5 items, and “imagine” must include 3 items. • Powerpoints must be submitted to me via email at dsbullie@cps.edu no later than Wednesday, Jan. 25, 2012, at 7:00AM, or a late penalty will be assessed. • Some students will be selected to present their powerpoints to their class on Wednesday.

5. Example of Using Memory, Reason, and Imagination Think about when you had memorize the multiplication table. You just knew that 5 x 6 = 30. Later, as you began to reason, you understood that 5 x 6 meant “5 groups of 6 items” or “6 groups of 5 items.” You also started to notice patterns in the multiplication table that would enable you to multiply larger numbers. Finally, your imagination pushed you to explore deeper concepts like fractions, decimals, percent, exponents, radicals, integers, algebra, etc.

6. Memory Slide • The skill of memorization is the most basic and it allows us to restate or rename a term/topic, draw a picture to represent that term/topic, or give an example of that term or topic. • Restate/rename • Represent with picture • Give an example

7. Reason Slide • The ability to reason allows us to explain/describe a term/topic, draw conclusions about the term/topic, and make analogies and connections about the term/topic. • Explain/describe • Draw conclusions • Make connections/analogies

8. Imagine Slide • The ability to imagine allows us to make predictions, ask questions, compare and contrast, and develop extensions. • Make predictions • Ask questions • Compare and contrast • Extend

9. Examples The following slides will be presentations on the topics of ratios, perpendicular lines, and slope.

10. Ratios: Memory a:b – a to b 4:3 – 4 to 3

11. Ratios: Reason • Comparison of a part to another part or a part to a whole • Ratios are also represented by fractions when comparing a part to a whole • Proportions are created when ratios are set equal to each other • When comparing a part to another part, use “to” • When comparing a part to a whole, use “out of”

12. Ratios: Imagine • Can we use fractions when comparing parts to parts? • What are some real-life applications of using ratios? • What is the relationship between ratios and rates? • How are ratios and slope related? • Converting units involve rates • How do rations and ratios compare?

13. Perpendicular Lines: Memory

14. Perpendicular Lines: Reason • Perpendicular lines are two lines that intersect at a right angle • Perpendicular lines look like a cross • The x- and y- axes are perpendicular to each other • A square at the vertex of an angle indicates that there are perpendicular lines • The slopes of perpendicular lines are opposite reciprocals

15. Perpendicular Lines: Imagine • How are the slopes of perpendicular lines opposite reciprocals? • What is the slope of a line perpendicular to the line whose equation is 4x + 2y = 8? • If the transversal line is perpendicular to the parallel lines that it crosses, then what can we say about the angle relationships formed?

16. Slope: Memory

17. Slope: Reason • Slope is the “steepness” of a line • The steeper the line, the greater the slope • Reading from left to right, the slope is positive if the line goes up and negative if the line goes down • The slope of a horizontal line is 0 • The slope of a vertical line is undefined

18. Slope: Imagine • Prove that the slope of a vertical line is undefined • If two or more lines have the same slope, then what are they? • Do curves have slopes? • In what professions is it important to know how to find and use slope? • How are slope and speed related?

19. Slope: Creative Piece I go by many names, pitch, speed, or rate of change Don’t want your brains perplexed, so let me explain my steps I’m the change in y divided by the change in x I’m rise over run, the steepness of a line Horizontally I’m zero and vertically I’m undefined

20. List of Topics to Present • Proportions • Percents • GCF • LCM • Exponents • Radicals • Expressions • Radicals • Exponents • Equations • Variables • Lines • Coordinate Plane • Distance Formula • Midpoint Formula • Parallel Lines • Pythagorean Theorem • Acute Angles • Obtuse Angles • Right Angles • Complementary Angles • Supplementary Angles • Adjacent Angles • Vertical Angles • Corresponding Angles • Alternate Interior Angles • Alternate Exterior Angles • Co-interior Angles