List of Objectives Involving Change, Rates, and Rate of Change

List for Math 503

Objectives (1):

  1. Traditional proportion problem. Three of the four numbers in the proportion are given and the student is to find the fourth. [two corresponding amounts and a third amount (which corresponds to an unknown amount)]
  1. Find the rate, given two change amounts (one change for the numerator and one change for the denominator, "d/t = rate"). Could be, but need not be, a rate of change. [delta-x and delta-y] (2)
  1. Convert units. (The units may be a "rate unit," e.g., miles per hour.)
  1. Find the rate, given two amounts and a time (or other amount for "the denominator"). Could be, but need not be, a rate of change. [x1, x2, and delta-y]
  1. State the rate in a different form, given the rate. (Find the reciprocal.) [rate]
  1. Find rate of change, given two ordered pairs (for example, two amounts at two different times) [x1, y1, x2, and y2]
  1. Find the average-which usually can be interpreted as a rate-given several successive amounts. [successive amounts]
  1. Multiply a rate and an amount to get a result ("r×t = d"). [rate and delta-y]
  1. Find an amount given a rate and a result ("d ÷ r = t"). [rate and delta-x]
  3. Multiply rates to find a rate. [two rates]


  4. Find a weighted average. [multiple rates and corresponding amounts]
  1. Combination of objectives.

Categories of Uses of Rates with Examples

Flow rate or speed

Use Rate

Production Rate

Density or pressure

Pay Rate


Size of a portion or subpart

Rate of Change

(*The categories are not mutually exclusive. Some of these examples can fall under other categories.)

Equivalencies (these equal 1)


1. School districts need to decide where (when) students will be introduced to these ideas, and when the ideas will be developed, mastered, and reviewed.

2. For those that like notation, the information that is given in the problem will be put in square brackets. When dealing with change, rates, and rates of change one works with the following quantities: x1; y1; x2; y2; delta-x (x2 - x1); delta-y (y2 - y1); rate = delta-y ÷ delta-x.

J.R.Olsen ~ W.I.U.