standard_description: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^(2) × 3^(–5) = 3^(–3) = 1/3^(3) = 1/27.
problem_activity: Task
Nia and Trey both had a sore throat so their mom told them to gargle with warm salt water.
$\hskip30pt$ Nia mixed 1 teaspoon salt with 3 cups water.
$\hskip30pt$ Trey mixed $\frac12$ teaspoon salt with $1 \frac12$ 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.”
Explain why the salt water mixtures taste the same.
Which of the following equations relates $s$, the number of teaspoons of salt, with $w$, the number of cups of water, for both of these mixtures? Choose all that apply.
$s = \frac13 w$
$s = 3w$
$s = 1\frac12 w$
$w = 3s$
$w = \frac13 s$
$w = \frac12 s$


aligns: no