Lesson 14Multiplying, Dividing, and Estimating with Scientific Notation
Learning Goal
Let’s multiply and divide with scientific notation to answer questions about animals, careers, and planets.
Learning Targets
I can multiply and divide numbers given in scientific notation.
I can use scientific notation and estimation to compare very large or very small numbers.
Lesson Terms
- scientific notation
Warm Up: True or False: Equations
Problem 1
Is each equation true or false? Explain your reasoning.
Activity 1: Biomass
Problem 1
Use the table to answer questions about different creatures on the planet. Be prepared to explain your reasoning.
creature | number | mass of one individual (kg) |
---|---|---|
humans | ||
cows | ||
sheep | ||
chickens | ||
ants | ||
blue whales | ||
Antarctic krill | ||
zooplankton | ||
bacteria |
Which creature is least numerous? Estimate how many times more ants there are.
Which creature is the least massive? Estimate how many times more massive a human is.
Which is more massive, the total mass of all the humans or the total mass of all the ants? About how many times more massive is it?
Which is more massive, the total mass of all the krill or the total mass of all the blue whales? About how many times more massive is it?
Activity 2: Info Gap: Distances in the Solar System
Problem 1
Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.
If your teacher gives you the problem card:
Silently read your card and think about what information you need to answer the question.
Ask your partner for the specific information that you need.
Explain to your partner how you are using the information to solve the problem.
Solve the problem and explain your reasoning to your partner.
If your teacher gives you the data card:
Silently read the information on your card.
Ask your partner “What specific information do you need?” and wait for your partner to ask for information. Only give information that is on your card. (Do not figure out anything for your partner!)
Before telling your partner the information, ask “Why do you need that information?”
After your partner solves the problem, ask them to explain their reasoning and listen to their explanation.
Pause here so your teacher can review your work. Ask your teacher for a new set of cards and repeat the activity, trading roles with your partner.
Activity 3: Professions in the United States
Problem 1
Use the table to answer questions about professions in the United States as of 2012. Express each answer in scientific notation.
profession | number | typical annual salary (U.S. dollars) |
---|---|---|
architect | ||
artist | ||
programmer | ||
doctor | ||
engineer | ||
firefighter | ||
military—enlisted | ||
military—officer | ||
nurse | ||
police officer | ||
college professor | ||
retail sales | ||
truck driver |
Estimate how many times more nurses there are than doctors.
Estimate how much money all doctors make put together.
Estimate how much money all police officers make put together.
Who makes more money, all enlisted military put together or all military officers put together? Estimate how many times more.
Lesson Summary
Multiplying numbers in scientific notation extends what we do when we multiply regular decimal numbers. For example, one way to find
Calculating using scientific notation is especially useful when dealing with very large or very small numbers. For example, there are about 39 million or
Comparing very large or very small numbers by estimation also becomes easier with scientific notation. For example, how many ants are there for every human? There are