 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum                 Session 6,
Homework

In the puzzles that follow, each shape stands for a number value of "weight." To solve these puzzles, make the weights in each part of the mobile balance from left to right, just as a sculptor might balance all the parts of a mobile. Here are the rules:

 a. The right and left sides of each horizontal beam must balance. b. Each shape has a unique and consistent weight within a puzzle, and no shapes weigh 0. c. Take the clues at face value. For example, if a clue says that the square's weight is a multiple of the triangle's weight, you can assume that the triangle does not weigh 1. d. All weights are either one- or two-digit, positive whole numbers. e. A piece hanging directly below the fulcrum does not affect the balance between the left and right arms. Although this piece has its own definite weight, it remains "neutral" for the purpose of balancing the other two arms. f. The size of the pieces has no relation to weight. g. These mobiles are exercises in balancing number values. They do not take into account the distance from the fulcrum.   Think about the total weight of each branch of the mobile, which may give you the values of certain weights or help you find equations relating weights. In tougher puzzles, make a list of possible values for a weight, then try to reduce that list to one correct value. Problem H4 is a system of equations with eight variables, and is very difficult.   Close Tip Think about the total weight of each branch of the mobile, which may give you the values of certain weights or help you find equations relating weights. In tougher puzzles, make a list of possible values for a weight, then try to reduce that list to one correct value. Problem H4 is a system of equations with eight variables, and is very difficult.  Problem H1 Discover the value of each of the shapes. The total weight is 36. All shapes weigh less than 10.  Problem H2 Discover the value of each of the shapes. The total weight is 80. Only one shape weighs more than 9.  Problem H3 Discover the value of each of the shapes. The total weight is 54. The three arms are equal in weight.  Problem H4 Discover the value of each of the shapes. The total weight is 180. Each of the three arms is equal in weight.  Problem H5 Marcus had some cookies. He wanted to give them all away. He gave one half of them to his friend David. They divided the remaining cookies evenly among David's three brothers, so each got 4. How many cookies did Marcus have originally?  Which of the methods of solving equations that you have learned in this session can be useful here? There is more than one answer.   Close Tip
 Balance problems excerpted from In the Balance, by Lou Kroner (New York: Creative Publications, Wright Group/McGraw-Hill, 2000). The above materials may not be reproduced without written permission of Creative Publications.  Suggested Reading: Stacey, Kaye. "Ideas about Symbolism That Students Bring to Algebra." Reproduced with permission from The Mathematics Teacher, © 1997 by the National Council of Teachers of Mathematics. All rights reserved. Download PDF file     Session 6: Index | Notes | Solutions | Video