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TAS Kids % Anne Hecht
Taipei American School
800 Chungshan Rd, N., Sec. 6, Taipei, Taiwan, R.O.C.

Solutions to the Mathmagic Problems, Cycle 3, 2nd 2nd Grade; Names of Students:  Mr  StensonÕs  Class; Anika Arya; John Bolton; Michelle Brody; Nicholas Chan; David Lo; Julia Cheong; Simone Gusta fsson; Cliff Jiang; Jim Kang; Frank Kuo;; Eunice Li; Alexis Liesman; Bernard Overmaat; Claus Reuter; Jay Roxas; Anthony Shing; Jessica Tiedemann; Angel Tsao; Jocelyn Soh;  Josh Hurdle

1.  State the Problem.  Edna has 9 pennies,  Her mom gives her 9 more pennies,  This doubles the amount of pennies that Edna has.  What we know; We know how many pennies Edna has and we know that in getting nine more it is called doubling.  What we donÕt know; How many pennies Edna has now. Assumptions; We assume she doesnÕt lose any Failed Strategies; One group said 20-2=18.  They knew the answer was 18 and they gave another way of saying 18, but it didnÕt relate to the problem. Another group said 9+9=18+
9=27+9=36 or 18+18=36.  This group doubled but didnÕt answer what was required in the problem. Successful Strategies; 1.  9 pennies plus 9 pennies =18 pennies.  This is making an equation.  Also the solution has a name-pennies.  Other groups said 9+9=18 in vertical form.  Other groups said 2x9=18, using the operation multiplication.  One group said, ÒIf  we draw 9 and 9 markers and group them 10 and eight it would be like saying 9+9 and 10+ 8 will give the same answer, 18.

1.  State the Problem.  Tom tells 2 friends a secret.  Each of these friends tells 2 more people the secret.  Including Tom, How many people know the secret? What we know; first Tom has a secret.  He tells two people.  They each tell two people. 2. What we donÕt know; How many people know the secret. Failed Strategies; Used Tom and the numbers in the problem to make an equation- 1+2+2=5; **+*****=7 was also a failed strategy.  Even although this grup got the right answer, the strategy of a group of 2 and a
 group of 5 was not explained in a way that matched the problem; Tom tells 2 friends equals 2, friends tell 2 more is now 2+2, and Tom makes 1 more, so 2+2+1+5.  This group did not understand that each friend told the secret to 2 more people. 3.  Successful Strategies; Drew a Picture- 0 (Tom)  00 (2 friends) 00 00 (each tells 2 more friends)0000000 (7 people in all know the secret); Drew a Picture and wrote an equation from the picture; 3 + 4 = 7 (first 3 people know the secret, then 4 more); another group
 used tally marks as they read the problem, i.e. 1 mark for Tom, 2 marks for the 2 friends, 2 marks for the next friends and 2 marks for the last 2 friends, /////  //.  The last tally mark in the first set was drawn across the first four marks, but our computer doesnÕt do that; Another group wrote numbers as the read the problem and ended up with an equation, i.e. 2+2+2+1=7 people.
 They started with the 1 and went to the left because they knew that right to left or left to right in addition gives the correct answer; Another group drew in pictures of faces, but also drew lines from each of the 2 friends to 2 sets of 2 friends.  This is draw a picture and draw a diagram.

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