Sunday, May 4, 2008

Test Prep Idea #3: Calculator Tricks Every Students Should Know

To my fellow Texas teachers, I apologize for not writing this earlier--but I think you can relate, as you too have just made it through "testing week". Throughout the week, every high school student in Texas took at least one standardized test.

This article is about what every high school students needs to know about graphing calculators (focusing on Texas Instruments TI-83/84, the most widely used version). This idea is for anyone who hasn't tested yet, is preparing for final exams or next year, and for Pre-Algebra classes being introduced to graphic calculators. I'm covering only the basics, the stuff you must know for 9th grade/Algebra I standardized testing--in my opinion, everything else is extra.

Common Error Messages

This is just as important as anything else, since test administrators can't help students use the calculator just like they can't help them with the test itself.
  1. ERR: SYNTAX: You typed in something wrong. Instead of "Quit", select "Goto" to go to the place where the problem is. For my students, this happens frequently when they try to graph an equation, and use a subtraction sign instead of a negative sign in the front. However, you must also show them that sometimes when you confuse those signs, the calculator doesn't give you an error, it just graphs something different. (For example, graph x2 [minus] 5, then x2 [negative sign] 5 to illustrate the difference).
  2. ERR: INVALID DIM: One of the scatter plots (i.e. Plot1) on the top of the Y= screen has been turned on. Arrow up and hit ENTER to turn it off. This is a good opportunity to also show them how to toggle Y1, Y2, etc on and off.
  3. ERR: WINDOW RANGE: You messed up something in WINDOW. Fix it with ZOOM 6.
Besides using TRACE and checking the table, students need to know how to manipulate both the window and table settings to see whatever they need to see. However, your students should remember one thing: they can change any setting they want as long as they know how to change it back.
  1. ZOOM 6: This is the single most important button combination since the Konami Code. Your students must memorize this, and you must ask "How do I put the graph back to normal?" on a daily basis.
  2. Recenter with TRACE: Demonstrate moving around the graph with TRACE, and that ENTER will recenter the graph on that point, just like clicking a point on Google Maps or MapQuest. Sometimes this is better (and easier) than zooming in and out.
  3. ZoomIn/Out: Show students the most common pitfall of ZOOM IN/OUT, which is hitting ENTER more than once, which will continue to zoom in and out farther if they don't press any other buttons. If they're lost in the graph, ZOOM 6 baby!
  4. ZSquare: Explain that the calculator screen is streched out like a widescreen TV (point out how the spacing on the x-axis is wider than on the y-axis). To see perpendicular lines, for example, you must use ZSquare.
  5. ZoomFit: Good for fitting the graph in screen when other options don't work.
  6. You can show all of the Zoom options, as long as you continually remind them about ZOOM 6.
Table Settings
Show them how to change the table settings if they're trying to match an equation to a table or find specific values. TblStart can be set to anything (set to zero to reset it) and [delta]Tbl changes the increments, so when the independent variable increases by 0.5 or 50 you can quickly match the calculator's table to given data (set back to 1 when they want to go back to normal). I would recommend you leave the other two settings alone to avoid confusion.

Main Screen Editing Shortcuts
I see my students typing and retyping long equations and getting frustrated when they press the wrong button, for example. Teach them about:
  • 2nd, ENTER (ENTRY): Brings back the previous entry, so if they are plugging in values to an equation for example, they can just edit the part they need to.
  • DEL: Students don't always know they can delete something without deleting everything with CLEAR. I made an analogy to typing something in Microsoft Word--you don't delete an entire paragraph when you want to change one word, right?
  • 2nd, DEL (INS): I used the same analogy to explain the usefulness of INS. It's helpful when you have to solve a problem through trial and error or when you need to graph several similar equations.
Other Essentials
  • MATH, 1 or MATH, ENTER (Math>Frac): This function takes either a decimal or a given fraction and converts it to a fraction in simplest form. As far as the TAKS goes, most answers that can be expressed as fractions are fractions, and they're always simplified. So my students have to be able to convert answers by themselves or with the calculator.
  • Exponents: Make sure they know how to use the x2 key to square and the carat ^ for exponents other than 2.
  • Resetting: If all else fails, TI-83 Plus/TI-84 calculators can be reset by typing 2nd, +, 7, 1, 2. This should be their last resort, since it drains the batteries quite a bit.
  • Use parentheses: I tell my students to put parentheses around fractions and as often as necessary to avoid any problems with order of operations.
The "Equivalent Expression" Trick
I didn't actually show this to my students in the days leading up to the test, but I did mention it earlier this year. I know that many teachers think of this as cheating, or at the very least shows a severe weakness of our tests. There are many questions where students have to do nothing more than simplify an algebraic equation by using the distributive property, combining like terms, laws of exponents and so on.

Students can simply input the expression exactly as given as Y1 in the Y= screen, and input the answer choices as Y2, Y3, etc. The equivalent expression or equation will create an identical graph as the original expression, because, of course, it's actually the same equation in a different form. This means students don't actually need to know any algebra to do these problems! Despite what your kids might say, this is a bad thing.

What's worse is that you can actually type equations in the main screen, with X and everything, and the calculator will plug in its own value for X and give you a numerical answer. The right answer will give you the same numerical answer. The troubling thing is, many students don't understand why the numerical answer isn't one of the choices, nor do they have any idea where it came from.

I don't see an easy solution to this problem, but it's something the authors of these tests need to think about.

Another quick TI graphic calculator guide