Mathematics I (College)

Everything you missed in high school.

This course has been recommended for ACE CREDIT®, which means it is considered for credit at thousands of colleges and universities across the country. For more information, click here.


We know what you're thinking. Mathematics I (a.k.a. Integrated Math) is a pretty dry sounding name for a course. Not to mention it implies that there's probably an Integrated Math II and maybe even a third course. 

We hate to break it to you, but there is.

This course is all about getting your feet wet with a variety of math topics one toe at a time. You wouldn't dive into the deep end of a pool without first spending time in the shallow end, strapped with floaties, would you? We didn't think so.

But enough talk. It's time to size up what's in store for us. Here's a spattering of what's to come:

  • Getting to know units up close and personal. We're talking meters, liters, inches, and the Wu-Tang Clan. Well maybe not them—we're talking about a different kind of unit.
  • Solving one- and two-variable equations of all shapes and sizes. We'll focus on those of the linear and exponential variety.
  • Graphing functions of many different varieties. After all, it is the spice of life.
  • Analyzing rates of change and comparing different functions. Sometimes even the most ornery of functions can find common ground.
  • Use statistics to study data. We'll use all sorts of charts to bring our data to life and tell us an intriguing story.
  • Getting a nice introduction to geometry. We'll even use our new found algebra skills to help us solve some of these shapely problems.

With all this in mind it's time to buckle down, suit up, and realize that Math I is happening with or without us. This will course will probably go a lot better if we give it our full, undivided attention, though.

Objectives

By the end of this course, you should be able to

  • understand how units work in equations and graphs
  • be able to convert between measurements made with different units.
  • interpret parts of linear and exponential expressions.
  • solve equations and inequalities in one or two variables.
  • create linear and exponential equations and inequalities.
  • identify the domain and range of a function.
  • model real-world situations with equations and inequalities
  • use tables and sequences to graph functions.
  • understand the relationship between arithmetic sequences and linear functions, and geometric sequences and exponential functions.
  • identify the effects of adding constants into functions.
  • calculate average rates of change to compare functions and graphs.
  • solve systems of linear equations and inequalities.
  • solve systems of exponential equations and inequalities graphically and with technology.
  • organize and interpret data using frequency tables, box plots, histograms, and scatterplots.
  • fit functions to data on a scatterplot.
  • distinguish between correlation and causation.
  • understand the undefined notions in geometry.
  • solve geometry problems in the coordinate plane.
  • use algebra to solve a variety of geometric problems.
  • perform rigid motions in the coordinate plane.
  • identify congruence in triangles and other shapes.

Unit Breakdown


  1. Mathematics I (College) - Units and Quantities

    Confused about centimeters and inches? Bushels and kilograms? Okay, nobody knows what a bushel is anymore, but we will cover all sorts of units in this unit, and most importantly, how to convert between them. You'll never see the metric system the same way again.

  2. Mathematics I (College) - Equations and Inequalities in One Variable

    Now it's time to get those algebra chops ready. Here we'll be doing what mathematicians do best: solving for x. For now, we'll keep things simple and stick with just one variable.

  3. Mathematics I (College) - Linear and Exponential Functions

    We're ready to beef things up a bit now. Here we'll be dealing two-variable equations and diving right into functions. We'll try not to harm any cows in the process.

  4. Mathematics I (College) - Graphing Equations and Inequalities

    We're declaring an open season on equations and inequalities. Now we're going to stick them in the coordinate plane to see if that does anything for us (it totally does). This is also a great time to formally introduce you to sequences; they'll make our lives a lot easier when it comes to making graphs.

  5. Mathematics I (College) - Graphing with Functions

    This unit is for the visual learner in all of us. We'll take the functions we've been working with and finally put a face to the name by graphing them. With a graph in hand, it'll be a lot easier to see how our functions behave...or misbehave.

  6. Mathematics I (College) - Rate of Change

    What do seasons, feelings, and Facebook's privacy policy all have in common? They all change. We're talking about changes in graphs, though. We'll take all the functions we've looked at so far and figure out how tell up them apart based on how they change. It's just another tool in our function-y toolbox.

  7. Mathematics I (College) - Systems of Equations and Inequalities

    What happens when we smoosh a few equations or inequalities together? It's less devastating than you might think. Instead of just solving one equation or inequality, we'll take a stab at finding values for x that work for a whole system of them. We promise it's not as hard as it sounds.

  8. Mathematics I (College) - Statistics

    We're gonna switch gears a bit in this unit, and move into statistical territory. After all, this course wouldn't be integrated if we didn't integrate some other material into the mix. Sometimes we all need a change of pace.

  9. Mathematics I (College) - Algebra In Geometry

    Another U-Turn is in order for this unit, but we promise it's a legal one. After a brief intro to geometry, we'll take all the algebra skills we've been honing throughout the course and apply them to a whole new shapely set of problems. More puns are definitely in store...

  10. Mathematics I (College) - Congruence and Rigid Motions

    We'll end the course by dealing with some nice, aesthetically-pleasing shapes. It'll be a nice intro and overview for what's to come in our more geometry focused sequel, Mathematics II: The Quest for Curly's Gold.

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