Using Good Wrong Answers to Achieve Math Confidence

Using ‘Good Wrong Answers’ to Achieve Math Confidence and Success Robin Schwartz College of Mount Saint Vincent Math Confidence www. mathconfidence. com

Why ‘Good Wrong Answers’? • GWA are designed with common mistakes and misunderstandings in mind • The answer is there!! www. mathconfidence. com 2

Why ‘Good Wrong Answers’? • Showing students ‘the right way’ can be complemented with GWA • They are fun ; ) • The comparative is very instructive www. mathconfidence. com 3

Student Opinion • Looking at ‘good wrong answers’ with a student allows him or her to see a mistake that is easy to make, and thus learn not to do so in the future. Without ‘good wrong answers’, the student might never learn to look out for these simple mistakes that look like they will work. Solomon Spigel, 15, homeschooler, Riverdale, New York student since 2002 www. mathconfidence. com 4

Schools Bronx: Bronx Science Fordham Prep PS 81 SAR Academy Horace Mann Fieldston MS/HS 141 Riverdale/Kingsbridge Academy Homeschoolers Westchester: Maria Regina New Rochelle High School Solomon Schechter Ursuline Our Lady of Victory Eastchester Middle School www. mathconfidence. com 5

Schools Manhattan: Hunter College High School Beacon High School Hunter Sciences High School HS for Math, Science and Engineering York Prep Trevor Day Wagner Middle School Eleanor Roosevelt HS The Lab School Manhattan East Middle School United Nations International School www. mathconfidence. com 6

The Hot Stove and the Oven Mitt Learning by Fire www. mathconfidence. com 7

2 2 (x+3) – (x+2) = A) 13 B) 5 C) 2 x + 5 D) 10 x + 13 E) 10 x + 5 www. mathconfidence. com 8

The Lonely Girl at the Dance The Middle Term www. mathconfidence. com

No More SAT Quantitative Comparisons A B www. mathconfidence. com 10

Quantitative Comparison • A if A is always larger • B if B is always larger • C if A and B are always equal • D if the relationship cannot be determined www. mathconfidence. com 11

QC Example A B 3 www. mathconfidence. com 12

QC Example A B 3 www. mathconfidence. com 13

Factoring www. mathconfidence. com 14

Factoring With “The Lonely Girl” “Two sets of parentheses” “Two plusses, two minuses or one of each? ” A) (8 x + 1) (10 x + 1) EVEN B) (4 x +1) (20 x + 1) EVEN C) (2 x + 1) (40 x + 1) EVEN D) (16 x + 1) (5 x + 1)ODD!! www. mathconfidence. com 15

Factoring www. mathconfidence. com 16

Factoring Using “Evenness” vs. “Oddness” A) (4 x + 4) (10 x + 10) Even B) (4 x + 8) (10 x + 5) Even C) (4 x + 20) (10 x + 2) Even D) (8 x + 5) (5 x + 8) Odd www. mathconfidence. com 17

12 divided by… www. mathconfidence. com 18

QC Example A B www. mathconfidence. com 19

0 and 1 • What happens when you divide by 0? • P/E Ratio www. mathconfidence. com 20

QC Example (no calculator) A B www. mathconfidence. com 21

Quantitative Comparison A B www. mathconfidence. com 22

If you cancel x’s, beware The Math Police www. mathconfidence. com 23

Absolute Value Equality |x– 5|=3 • A) x = 8 • B) x = 8 or x = -8 • C) x = 2 • D) x = 2 or x = 8 • E) x = -2 www. mathconfidence. com 24

The Power of Zero A) 2 B) 16 C) 0 D) 48 www. mathconfidence. com 25

What is the value of • A) • B) • C) -9 • D) -6 www. mathconfidence. com 26

More Exponents www. mathconfidence. com 27

Word Problem Percent • A suit is on sale for $100 after a 20% discount. What was the original price? • A) $120 • B) $125 • C) $80 • D) $500 www. mathconfidence. com 28

Word Problem Average You drive uphill at 40 mph and downhill at 60 mph. What is your average speed (x)? A B x 50 www. mathconfidence. com 29

Mathematics Builds Attention to Detail, Frustration Tolerance and Critical Thinking Skills www. mathconfidence. com 30

Student Opinions • "It's helpful to look over the answers for a multiple choice test so you can learn from your mistakes and review what you already understand. By doing this, you can only improve and score higher on your next exam. " Josh Friedman, salutatorian, MS/HS 141 freshman, Boston University student 2003 -2005 www. mathconfidence. com 31

Contact Information: Robin Schwartz www. mathconfidence. com mathconfidence@aol. com www. mathconfidence. com