standard_description: Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
problem_activity: Problem 1
Two students are presented with the challenge of adding
$${2.5\times10^3}$$
and
$${1.3\times10^4}$$
. They have just learned how to multiply numbers in scientific notation, and they try out using similar strategies. They get two possible answers:
$${3.8\times10^4}$$
OR
$${3.8\times10^7}$$
a.   Explain or show to the students how both of the answers are incorrect.
b.   Why will the strategies used when multiplying numbers in scientific notation not work when adding?
c.   What are some strategies that can be used to solve this problem? Find the sum.
Problem 2
The Great Lakes are a series of freshwater lakes located on the US and Canadian border. Lake Superior has the greatest volume of water with
$${3.12\times10^{15}}$$
gallons of water. The smallest lake, by volume of water, is Lake Ontario with
$${4.26\times10^{14}}$$
gallons of water.
How many more gallons of water are in Lake Superior than in Lake Ontario?
Problem 3
A water molecule is made up of 2 hydrogen atoms and 1 oxygen atom, represented as H
2
O. One hydrogen atom has a mass of
$${1.7\times10^{-27}}$$
kg, and one oxygen atom has a mass of
$${2.7\times10^{-26}}$$
kg.
What is the total mass of a single water molecule?


aligns: no