(02/05/96) ************************************* MathMagic Cycle 20: Level K-3 Regular ************************************* Triangular Numbers Suppose [] represent stairs or blocks. The [] [] [] [] total amount of [] blocks used in making S1 [][] [][] [][] the stairs are called TRIANGULAR NUMBERS: S2 [][][] [][][] 1, 3, 6, 10... S3 [][][][] S4 If S1 (one stair) needed one [] block, S2 1=1 3=2+1 6=1+2+3 10=1+2+3+4 needed 3, S3 needed 6,how many blocks are you going to need for S8? How many for S12? Make a table and try to predict Sn: Stairs| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | n | ------|----|----|----|----|----|----|----|----|----|----|----|----|----| Guess | | | | | | | | | | | | | | ------|----|----|----|----|----|----|----|----|----|----|----|----|----| Blocks| | | | | | | | | | | | | | ------|----|----|----|----|----|----|----|----|----|----|----|----|----| ************************************** MathMagic Cycle 20: Level K-3 Advanced ************************************** Sliding Ends Star A o Join the "o"s with a thin marker line to form a five point star: AC,AD,BE,BD and EC. Use the cutouts from a hole puncher and select FOUR bright ones (use some left over construction paper). Your job is to come Eo oB up with modified step-by-step instructions to help anyone solve this challenge: "Put the first dot on any point of the star, and o o then slide it along one of the (straight) marker D C lines to another star point, and leave it there. Put a second dot on another star point that is empty, and slide it along the marker line to another empty corner. Simple! Do the same with the third dot and TRY to do the same with the fourth, so that you will end up with four dots that have been slid into four empty corners". Not that easy, once you try it. ============================= Good luck MrH