Algebra 1 Dimensional Analysis

Standard: Reason quantitatively and use units to solve problems. MGSE9–12.N.Q.1 Use units of measure (linear, area, capacity, rates, and time) as a way to understand problems: b. Convert units and rates using dimensional analysis (English– to–English and Metric–to–Metric without conversion factor provided and between English and Metric with conversion factor); c. Use units within multi–step problems and formulas; interpret units of input and resulting units of output. EQ: How are unit conversions performed, and why is it important?

Let’s Begin to Talk about dimensional Analysis… What is the reciprocal of ? What is Mini Lesson

What is Mini Lesson

Our goal with dimensional Analysis is to make units cancel out to…… 1 Mini Lesson

STEPS: 1.Given quantity w/its unit 2.Set up conversion factor 3.Divide Units – only the desired unit should be left 4.Solve the problem Mini Lesson

Example 1 Let’s look at the metric problems a different way. Convert 35m to km. Mini Lesson

An aspirin tablet contains 325 mg of active ingredient. How much is this in cg? Example mg1 cg = mg 10 = 32.5cg of active ingredient Mini Lesson

Example 3 Bob studied for 2.5 hrs. How many minutes did he study for? Initial unit = hr.Final unit = _______ Mini Lesson

Initial unit Conversion Final factor unit 2.5 hr x 60 min = 150 min 1 hr How many minutes are in 2.5 hours ? Mini Lesson

Example 4 How many seconds are in 1.4 days? Unit plan: days hr min seconds 1.4 days x 24 hr x ?? 1 day 12 Mini Lesson

Solution Unit plan: days hr min seconds 1.4 day x 24 hr x 60 min x 60 sec 1 day 1 hr 1 min = 120,960 sec Mini Lesson

Example 5 John Isner serves 140 miles per hour. How fast is that in feet per second? Mini Lesson

Solution 140 miles x 5,280 ft. x 1 hr x 1 min = 1 hr 1 mile 60 min 60 sec. = ft/sec. Mini Lesson

Example 6 If a 3 day boating trip covers 150 miles and you are boating 5 hours a day, how many miles must you boat each hour? 10 miles per hour Mini Lesson

Work Session Practice setting up Conversions via Dimensional Analysis

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