Aleksandra Fedorov Ryan Marchenko Ethan Soifer Dr.Victoria Kofman
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1 Aleksandra Fedorov Ryan Marchenko Ethan Soifer Dr.Victoria Kofman
2 MATH ENRICHMENT SCHOOL Mental math Organizing Information Communication Skills Logic Creative Thinking Popularity New Opportunities Why do I need more math knowledge, when I already know enough from school?
3 MENTAL MATH STRATEGIES VS ALGORITHMS
4 NUMBER SENSE I am fast, thanks to mental math!
5 ORGANIZING INFORMATION IS IMPORTANT Was really sloppy - became a bit neater. Organizing is a postbrainstorming techniqueputting information in a logical order. Brainstorming is not enough!
6 BRAINSTORMING VS ORGANIZING Two drivers were coming to a Lake On The Moon city. The first driver drove 3 hours and 40 minutes with the speed of 60 miles per hour. The second driver drove 2 hours and 8 minutes with the speed of 120 km per hour. Which driver lives closer to Lake on The Moon? How much closer?
7 COMMUNICATING PROBLEM TO MYSELF The ancient hero Abakkor decided to kill the dragon that was eating farm animals and frightening people. When a dragon eats, each head eats 3 sheep per week, so it s difficult for farmers to survive when a dragon is close by. Fortunately, the dragon that lives in Abakkor s village only had one head. What Abakkor and the villagers did not know is that every time one head is cut off, three new heads grow to replace it. Abakkor the hero was sent by his village to fight the dragon. He went to the mountains and began his fight. He fought, and fought, and fought, and finally cut off the dragon s head and went home. The next day the dragon had 3 heads. Again Abakkor went to the mountains and fought, and fought, and cut off all of the dragon s heads. He fought the dragon for an entire week. On the seventh day, the dragon had so many heads that they weighed more than his entire body, and the dragon fell over and died. Abakkor the hero became famous in all parts of the country. People from all over came to see the dragon and count its heads. How many heads did the dragon have when it died? How many heads did Abakkor cut off?
8 DATA EXTRACTION, CHUNKING, AND SHORTCUTTIG PREP
9 WHY PREP? The ancient hero Abakkor decided to kill the dragon that was eating farm animals and frightening people. When a dragon eats, each head eats 3 sheep per week, so it s difficult for farmers to survive when a dragon is close by. Fortunately, the dragon that lives in Abakkor s village only had one head. What Abakkor and the villagers did not know is that every time one head is cut off, three new heads grow to replace it. Abakkor the hero was sent by his village to fight the dragon. He went to the mountains and began his fight. He fought, and fought, and fought, and finally cut off the dragon s head and went home. The next day the dragon had 3 heads. Again Abakkor went to the mountains and fought, and fought, and cut off all of the dragon s heads. He fought the dragon for an entire week. On the seventh day, the dragon had so many heads that they weighed more than his entire body, and the dragon fell over and died. Abakkor the hero became famous in all parts of the country. People from all over came to see the dragon and count its heads. How many heads did the dragon have when it died? How many heads did Abakkor cut off? Data Extraction Chunking Shortcutting Grows 3 new heads for 1 head cut off. A cuts 1 heads the first day. The next day there are 3 heads A cut off the heads for 7 days D died having too many heads How many heads did D have when it died? How many heads were cut off?
10 LOGIC: BULLS AND COWS Bulls Cows Rules: Two players choose 4-digit numbers without zeros or repeated digits, keeping these numbers secret from each other. The players take turns guessing their opponent s 4- digit number. After each guess, the opponent tells the guessing player the number of bulls and cows. Bulls means the number of correctly guessed digits. Cows means the number of digits on the correct place. The player who finds the 4-digit number with the least attempts wins.
11 CREATIVE THINKING It s called Thinking Outside the Box or Lateral Thinking Solving problems through an indirect and creative approach instead of using a traditional step by step logic Creative models make it easier to solve the problem than traditional logic.
12 CREATIVE THINKING Five Integers. There are five integer numbers. The first number is 7 more than the second, which is 998 more than the fifth. The fifth number has 4 digits. The fourth number has two digits less and is 99 times the first number. It is known that the third number is additive inverse of the square root of 4,096. Find the first number.
13 BECOMING POPULAR WITH MATH Helping others = making new friends. Tutoring - Tutoring club - In class - After school Why math makes us popular? Widespread view: smartness is innate!
14 NEW OPPORTUNITIES Science Olympiad Math Club Scholastic Bowl
15 FUTURE PROFESSION Logic and Creative Thinking Preparation to higher Level Math General Problem Solving Organizing Communication Estimation Neurosurgeon Financial Analyst Lawyer
16 THANKS Contact info: Victoria Kofman Phone: 1 (847) drkofman@gmail.com Aleksandra Fedorov aleksandramath@gmail.com Ryan Marchenko ryanmarchenko2001@gmail.com Ethan Soifer ethan.soifer@gmail.com
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