Proportional Relationships Unit 2, Lesson 2

Title your notebook Across the top of the page, write the following: Unit 2 Lesson 2 Proportional Relationships

Page 1: Opening  Write: When the ratio between two varying quantities remains constant, the relationship between the two quantities is called a proportional relationship. Multiply and divide only for proportions.  Example:

Real-life use of proportional relationships  The real Statue of Liberty is way too large to fit inside a room, but proportional relationships can be used to create a smaller model that looks like the real thing.

Real-life use of proportional relationships  You can measure the height, width, and length of a building and then use a proportional relationship to keep everything in balance. HeightWidthLength Real

 What happens if you do not use a proportional relationship?  If you only change one dimension, the model will not look the same. HeightWidthLength Real Model ÷10

 What happens if you do not use a proportional relationship?  If you change the dimensions by different ratios, it still gets stretched. HeightWidthLength Real Model ÷2 ÷5 ÷2

 What happens if you DO use a proportional relationship?  When you keep a constant ratio, the model looks like a smaller version of the real thing. HeightWidthLength Real Model6074 ÷5

`  Let’s start by figuring out the height of the model.  The scale ratio says that every 20 feet of the real building equals 1 foot of the model.  Should model’s height be more or less than the real? Based on that, which operation would make sense?

 Let’s figure out the width of the real.  The scale ratio says that every 20 feet of the real building equals 1 foot of the model.  Should real’s width be more or less than the model? Based on that, which operation would make sense?

 Let’s figure out the length of the model.  The scale ratio says that every 20 feet of the real building equals 1 foot of the model.  Should model’s length be more or less than the real? Based on that, which operation would make sense?

Page 4: Work Time  The problem says “assuming that he drove at a constant speed.”  Copy down the table and show the work you used to find the missing numbers. CHANGE THE 72.5 TO 72  Hint: Last problem told us the scale was 20:1. Here we need to figure it out. We know that it took 1.5 hours to travel 72 miles. How can you use this to figure out how many miles he went in just 1 hour?  Early finishers: Try to solve the original problem, which had 72.5 miles instead of 72

Page 5: Work Time  Answer the two questions  Early finishers: A taxi charges $5 to get in and then $2 for each mile. Is this a proportional relationship? Explain why or why not. # of miles123 Cost ($)7911

Page 7: Ways of Thinking  Write down the answers to the problems that you were not assigned.  Also write down any answers that you were not able to solve.