- Course 1, Unit 2
|a.||Make sketches of at least five different graphs showing
different patterns relating change in two variables.
In this unit, students investigated linear, periodic, exponential, and quadratic patterns. These are not intended to be complete investigations at this stage, only to get some general graphical patterns and their accompanying symbolic forms available to students. The focus is on how the y-value changes in the table, at a constant rate or an increasing or decreasing rate, and how that appears in the graph. Students use NOW-NEXT equations which will probably be unfamiliar to you. This language is the precursor to work with sequences and series in Course 3, Unit 7, and focuses on how one y-value is related to the next, when x is an integer. Students also use "y = ..." equations, which you will probably find familiar. The situations investigated in the unit were:
|b.||For each graph write a brief explanation of the pattern
of change shown in the graph and describe a real life situation that
fits the pattern.
See sample graphs, possible equations, and descriptions below.
|1.||The graph is likely to look somewhat linear, with price
on the horizontal axis and number of customers on the vertical
axis. As the price rises, the number of customers falls.
|2.||The graph is likely to look somewhat linear, with stretches
reported for each weight. The table will show approximately a constant
rate of increase. The axes of the graph should be labeled with units
of weight on the horizontal axis and units of length on the vertical
|3.||This graph shows how the rider rises and falls as the
Ferris wheel turns. The rider's height cycles through the same up
and down pattern as the wheel continues to turn.
|4.||Because populations tend to grow at a percentage rate,
meaning that the actual increase depends also on the number of people
present at any time, the growth is likely to be exponential growth,
slow to begin with then faster and faster as time passes.
|5.||This graph shows a constant rate of change. For each
additional hour worked, the money earned increases by the same amount.
|6.||Assuming the payments are all equal, the balance will
fall at a constant rate.
|7.||Since each ticket sells for the same price, the income
will rise at a constant rate.
|8.||The profit may start as a negative until enough tickets
have been sold. The profit increases at a constant rate.
|9.||Since speed is constant, the distance traveled increases
at a constant rate.
|10.||The height of the ball increases and then decreases.
It starts out moving fast, slows down as it reaches its maximum height,
and then speeds up again as it falls back down.
|11.||As the ticket price goes up the profit goes up, but
when the ticket price becomes expensive the number of tickets falls
so the rate of increase of the profit becomes less. Eventually the
ticket price becomes so high that the number of tickets sold drops
off enough to make the profit fall. Profit depends on ticket price,
but also on number of tickets sold.
|12.||Assuming the speed stays constant, the gasoline consumption
will remain constant and the graph will decrease linearly.
If you would like to see specific problems from Course 1, Unit 2, a link is provided to Examples of Tasks from Course 1, Unit 2. If you are interested in following up on the Algebra strand in general, then the Scope and Sequence will help you see where different concepts are introduced. On the Algebra page, you can read an explanation of the main algebra concepts as they are developed in all four courses.