standard_description: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
problem_activity: Problem 1
At a market, long-grain rice can be purchased in any weight, measured in pounds. The cost and weight are proportional, for example, 5 pounds of rice costs $4.
a.   Write an equation to represent the cost,
$$y$$
, to purchase
$$x$$
pounds of long-grain rice.
b.   Determine the cost of 1, 10, and 15 pounds of rice.
c.   Graph the relationship between cost and weight of rice in the coordinate plane.
d.   What is the slope of the graph? What does it mean as a unit rate?
Problem 2
Nia and Trey both had a sore throat so their mom told them to gargle with warm salt water.
Nia mixed 1 teaspoon salt with 3 cups water.
Trey mixed
$${1\over 2}$$
teaspoon salt with 1
$${{1\over2}}$$
cups of water.
Nia tasted Trey’s salt water. She said,
“I added more salt so I expected that mine would be more salty, but they taste the same.”
a.   Explain why the salt water mixtures taste the same.
b.   Find an equation that relates
$$s$$
, the number of teaspoons of salt, with
$$w$$
, the number of cups of water, for both of these mixtures.
c.   Draw the graph of your equation from part (b).
d.   Your graph in part (c) should be a line. Interpret the slope as a unit rate.


aligns: no