Unit 1 Relationships Between Quantities and Expressions Week

Unit 1 Relationships Between Quantities and Expressions Week 3 Lesson 1 Dimensional Analysis N. Q. 1

Focus Standard • N. Q. 1 – Students will use units of measure as a way to understand problems • Objective: Students will determine the appropriate units of measure within a context and covert units and rates using dimensional analysis.

Essential Questions • Why do we have different forms of measurement? • When would you need to convert from one unit to another?

Vocabulary Words Dimensional analysis is a process that uses rates to convert measurements from one unit to another. A rate such as in which the two quantities are equal but use different units, is called a conversion factor. To convert a rate from one set of units to another, multiply by a conversion factor.

Read, Write, Draw, Solve • An engineer computes the ratio of these two measurements. • fuel efficiency, measured in miles per gallon • speed, measured in miles per hour She divides fuel efficiency by speed. What unit will the quotient have? A. gallons per hour B. hours per mile C. gallons per mile D. hours per gallon

Activator • Discuss with your partner the following questions. – How many hours are in 1 day? – How many minutes are in 1 hour? – How many seconds are in 1 minute? – If you work 40 hours a week, how many minutes would you work in 1 week?

How many seconds are in a day? 1. What units of measure will I be working with?

How many seconds are in a day? 1. What do we know? Let’s translate what we know into math terms starting with the lowest measure of time.

Is each ‘conversation factor’ equivalent to 60 seconds = 1 minute? Remember that the original question is “How many seconds are in a day” Look at the factors. Which three factors should we choose to help us find our answer?

1. Ok we have chosen our factors. Now let’s see which units we cancel. 60 sec 1 min 60 min 1 hr 24 hr 1 day 2. Now multiply the numbers. 3. Divide. 4. What is our answer?

How many hours are in a year? 1. Let’s get started! Write down all of the factors you can think that we may need. (which measure do we want on top/bottom) 24 hr 365 days 1 day 1 year

1. Ok we have chosen our factors. Which units cancel? 24 hr 1 day 365 days 1 year 2. Now multiply the numbers. 3. Divide. 4. What is our answer?

Practice • Practice some Dimenional Anaylsis