Transcript Dimensional Analysis

Significant
Figures/Dimension
al Analysis
• Objective:
• Today I will be able to:
• Apply significant figures to solving problems
• Apply dimensional analysis to solving problems
• Informal Assessment – monitoring student
questions and interactions as they complete the
practice problems
• Formal assessment – analyzing student
responses to the exit ticket and practice
problems
• Common Core Connection
• Make sense of problems and persevere in solving
Lesson Sequence
• Evaluate: Warm-Up
• Engage/Elaborate: Real life Dimensional
Analysis Problems
• Evaluate: Exit Ticket
Warm-Up
Solve and record your answer to the correct
number of significant figures:
1)
4.276 x 520 =
2) .0025 x 3.15 =
3) 1,538.914 – 390.2 =
Objective
• Today I will be able to:
• Apply significant figures to solving problems
• Apply dimensional analysis to solving problems
Homework
• Complete the dimensional analysis practice
• Study for scientific notation quiz on Thursday,
September 11
Agenda
• Warm-Up
• Dimensional Analysis Notes
• Real Life Dimensional Analysis Practice
Problems
• Exit Ticket
Dimensional
Analysis Notes
Conversion Factor
• 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
Q: Do these two fractions equal the same quantity?
1 dozen
12 eggs
12 eggs
1 dozen
Yes!
Dimensional Analysis
Problem Solving Tips
1. Read the problem
2. Write down what you are given, put it over 1
3. Write down what you are looking for
4. List all possible conversion factors for the
problem
5. Make a road map
6. Solve the problem
Practice Problem 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
10 hours
1
3. Write down what you are looking for.
The number of minutes
x minutes
Practice Problem 1 Cont
4. List all possible conversion factors for the
problem
-We know that one hour = 60 minutes
1 hour
60 minutes
60 minutes
5. Make a road map
• Hours
? Minutes
1 hour
Practice Problem 1 Cont.
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,
10 hours
1
.
1 hour
=
60 minutes
10 hours 2
60 minutes
• Incorrect, the units do not cancel out
Practice Problem 1 cont.
7. Solve for Correct Answer!
10 hours . 60 minutes
1
1 hour
=
600 minutes
Practice Problem 2
Q: How many minutes are there in 12 weeks?
Weeks  Days  Hours  ? Minutes
12 weeks .
days .
1
week
hours . minutes =
day hour
12 weeks . 7 days . 24 hours . 60 minutes =
1
1 week 1 day 1 hour
Practice Problem 3
Q: How many minutes are there in 2 years?
Years  Weeks  Days  Hours  Minutes
2 years .
1
weeks .
days .
year
week
hours . minutes =
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
Q: How many liters are in 500 mL?
mL  ? L
500 mL . 1 Liter
1
1000 mL
=
0.500 L
Practice Problem 5
Q: How many milligrams are there in 20 kg?
kg  g  ? mg
20 kg . 1000 g . 1000 mg
1
1 kg
1g
= 2 x 107 mg
Dimensional
Analysis Practice
Complete the practice at your desk. Show all work.
Write answer to correct number of sig figs.Will be
collected
Exit Ticket
•
Why don’t you count significant figures
in a conversion factor?
•
What do you base significant figures on
in a dimensional analysis problem.
•
Solve the problem below. Show all work
and round to the correct number of
significant figures.
•
How many seconds are in the 7 hour
school day?