Dimensional Analysis Scientific Notation

Common Core Connection Objectives: Today I will be able to: Apply scientific notation to problem solving. Calculate multiplication and division problems using scientific notation. Apply dimensional analysis to solving metric coversions Informal Assessment – monitoring student interactions as they complete the scientific notation practice Formal assessment – math assessment/scientific notation practice and exit ticket Common Core Connection Make sense of problem and persevere in solving them Model with mathematics

Lesson Sequence Evaluate: Warm-Up Explain: Scientific Notation Notes Elaborate: Scientific Notation Practice Explain: Dimensional Analysis Notes Elaborate: Dimensional Analysis Practice Evaluate: Exit Ticket

Warm-Up Solve and record your answer to the correct number of sig figs. 12.3 + 14.06 + 4.0001 = _____________ 16.33 + 12.465 + 0.022 = ____________ 34.5 x 0.0001 = _____________ 150.00 x 65.4 = ______________

Objective Today I will be able to: Apply scientific notation to problem solving. Calculate multiplication and division problems using scientific notation. Apply dimensional analysis to solving metric coversions

Homework Complete the dimensional analysis practice Wear closed toed shoes for lab on Wednesday and Thursday

Agenda Warm-Up Scientific Notation Notes Scientific Notation Practice Dimensional Analysis Notes Dimensional Analysis Practice Exit Ticket

Scientific Notation Notes

In groups, brainstorm 3 examples of things that scientists/ engineers could study that would be large enough or small enough for scientific notation to be used to describe them

Standard Notation to Scientific Notation cont. Examples 489000000 (Standard Notation) Move the decimal to the left, exponent is positive 4.89 x 108 (Scientific Notation) Numbers greater than 1 always have a positive exponent in scientific notation 0.000123 (Standard Notation) Move the decimal to the right, exponent is negative 1.23 x 10-4 Numbers less than 1 always have a negative exponent in scientific notation

Scientific Notation to Standard Notation cont. Examples 3.47 x 105 (Scientific Notation) Exponent is positive, move to the right 347000 (Standard Notation) 7.82 x 10-4 (Scientific Notation) Exponent is negative, move to the left 0.000782 (Standard Notation)

Let’s Think… Place the following numbers into scientific notation

Multiplying/Dividing in Scientific Notation Multiply or divide the numbers first (don’t include x 10exp) When multiplying, add the exponents together When dividing, subtract the exponents Make sure there is only one number before the decimal place in scientific notation. You may have to move the decimal so there is only one

Multiplying/Dividing Scientific Notation cont. Examples: (2.0 x 105)(7.0 x104)= 1.4 x 1010 (15.0 x 107) / (3.0 x 109)= 5.0 x 10-2

Scientific Notation Practice Complete the practice at your desk. We will review selected answers as a class.

Dimensional Analysis Notes

Conversion Factor 12 inches 1 foot 7 days 1 week ½ A Fraction that is equal to the number one Two quantities that equal the same thing 12 inches 1 foot 7 days 1 week .5 ½

Dimensional Analysis 1 dozen 12 eggs 12 eggs 1 dozen Yes! Do these two fractions equal the same quantity? 1 dozen 12 eggs 12 eggs 1 dozen Yes!

Dimensional Analysis Problem Solving Tips Read the problem Write down what you are given, put it over 1 Write down what you are looking for List all possible conversion factors for the problem Make a road map Solve the problem

Practice Problem 1 10 hours 1 Q: How many minutes are there in 10 hours? 1. Read the problem 2. Write down what you are given, put it over 1 3. Write down what you are looking for. The number of minutes x minutes 10 hours 1

Practice Problem 1 Cont 1 hour 60 minutes 60 minutes 1 hour 4. List all possible conversion factors for the problem -We know that one hour = 60 minutes 5. Make a road map Hours ? Minutes 1 hour 60 minutes 60 minutes 1 hour

Practice Problem 1 Cont. 10 hours . 1 hour = 10 hours 2 6. Solve the problem We also know that when you multiply, if 2 quantities are placed in opposite corners of each other, they will cancel out For example, Incorrect, the units do not cancel out 10 hours . 1 hour = 10 hours 2 1 60 minutes 60 minutes

Practice Problem 1 cont. 10 hours . 60 minutes = 600 minutes 1 1 hour 7. Solve for Correct Answer! 10 hours . 60 minutes = 600 minutes 1 1 hour

Practice Problem 2 Q: How many minutes are there in 12 weeks? Weeks  Days  Hours  ? Minutes 12 weeks . days . hours . minutes = 1 week day hour 12 weeks . 7 days . 24 hours . 60 minutes = 1 1 week 1 day 1 hour

= 1,048,320 minutes or 1,051,200 minutes (365 days) Practice Problem 3 Q: How many minutes are there in 2 years? Years  Weeks  Days  Hours  Minutes 2 years . weeks . days . hours . minutes = 1 year week day hour 2 years . 52 weeks . 7 days . 24 hours . 60 minutes = 1 1 year 1 week 1 day 1 hour = 1,048,320 minutes or 1,051,200 minutes (365 days)

Practice Problem 4 500 mL . 1 Liter = 0.500 L 1 1000 mL Q: How many liters are in 500 mL? mL  ? L 500 mL . 1 Liter = 0.500 L 1 1000 mL

Practice Problem 5 20 kg . 1000 g . 1000 mg = 2 x 107 mg 1 1 kg 1 g Q: How many milligrams are there in 20 kg? kg  g  ? mg 20 kg . 1000 g . 1000 mg = 2 x 107 mg 1 1 kg 1 g

Dimensional Analysis Practice

Exit Ticket Activity Find your matching partner by finding the correct standard notation and scientific notation pair With your partner discuss the following questions: If you could have one special superhero power, what would it be? Would you rather have Cheetos fingers, or a popcorn kernel stuck in the back of your throat, for the rest of your life?