In the notes, there are examples of how to model solving equations using a scale or balance model. Here’s another example:
Problem 1: Show how to solve 3x+3=x+9 using balance pictures and equations
A fourth grade class used the story of Larry Walters who went up into the airspace above Los Angeles in a lawn chair lifted by helium balloons (the LAX air traffic controllers were not pleased) to talk about negative numbers. See
http://tlc.ousd.k12.ca.us/~acody/larry.html or http://www.myrem.com/showthread.php?t=8410
for more info on Larry.
They solved problems such as:
- John weighs 75 pounds. If she is holding helium balloons that pull up with a force of –5 and –8 pounds, how much would a scale show that John weighs now? (75+ -5+ -8= 62)
and
- John weighs 75 pounds. How many 5 pound balloons should he hold for the scale to show 15 pounds? (75+(-5)N=15)
Problem 2: Write a balloon story, and draw a picture to go along with the equation 2x-3=9:
Problem 3: On the trips program, the boy starts at 10 and walks forward at a speed of 2 feet per second. The girl starts at 0 and walks forward at a speed of 3 feet per second.
Write equations for the boy’s position after t seconds, and the girl’s position after t seconds.
Use the two equations to find out what how many seconds it has been when the girl catches up to the boy.
Problem 4: In a 20 foot classroom, a boy starts at the left wall, and walks across at a speed of 2 foot per second. A girl starts at the right wall, and walks across the room at a speed of 1 ft per second.
Write equations for the boy’s position after t seconds, and the girl’s position* after t seconds.
Use the two equations to find out what how many seconds it has been when the girl catches up to the boy.
*hint: use distance from the left wall for both boy and girl
Problem 5: Solve, and show your solution to: