An exercise ball has a diameter of 25 in. How many square inches of rubber are used to make the ball, in terms of pi?

constant of proportionality = 3 and the equation is c = 3p.

step-by-step explanation:

c = kp   where c = amount of caffeine in mg., p = oz of pepsi and k is the constant of proportionality.

substituting the values given:

24 = 8k

k = 3.

the same value of k will be obtained if we substitute the other given values.

large crystals result from very slow cooling.

evaporation of water: this would produce an evaporite which is a sedimentary rock. like a salt pan in a desert. not possible to have volcanic rocks originate this way.

crystalization in molten earth: slow cooling over time. (hundreds to millions of years)

crystalization at earth's surface: this results in fast cooling. (a few hours to a few months or years)

crystalization from cooling off hot water: that would be a hydrothermal deposit. while associated with volcanics they are not volcanic rocks themselves and usually occur fairly rapidly.

• before the lesson, students attempt the assessment task individually. you then review students’

solutions and formulate questions that will them improve their work.

• during the lesson, students work collaboratively in pairs or threes, plotting graphs, completing

tables of values and deducing equations. then, based on the number of common solutions,

students link these representations.

• in a follow-up lesson, students receive your comments on the assessment task and use these to

attempt the similar task, approaching it with insights gained from the lesson.