Why Are Literal Equation So Hard?

literal-equations

Parks and Rec has to be one of my favorite shows and Rob Lowe is very cute, STILL! If you’ve never seen the show, put this on your to-do list! You’ll think it’s weird at first but the characters are hilarious. Rob Lowe joins the show during the second season. He literally says literally 20 times a show…maybe I’m exaggerating, but he does say literally a lot! Watch it…you’ll love it. It’s a nice way to relax and get your mind off school.

So why am I thinking about literal equations? The physics teacher is telling me that the kids can’t solve literal equations! I could have told him that :), but why can’t they? I know my students can solve 4x = 8, but they can’t solve d = rt for r. What’s the issue? I think it’s several things:

  1. They are solving 4x = 8 in their head. They know that 4 times 2 is 8, so x has to be 2. They aren’t thinking about inverse operations. I’m realizing some students still do not know that 4x means 4 times x.
  2. When students see a problem with only letters in it, they automatically think that it’s hard. They are not making the connection that really all that is happening is that r is multiplied by t. If they knew the operation taking place in the problem, then they should ask what is the inverse operation.
  3. Students are not understanding that all they are “UNDOING” the operations to solve for one of the variables…which leads me to wonder if anyone has ever explained that when you solve equations, you are actually doing PEMDAS backwards.

 

I’ve created a lesson that addresses all three of the issues above. At first, I think the student should analyze the problem by writing the equation in words so I can see if they understand what operations are taking place. I then ask them to circle the variable they are solving for so they can have a visual of what needs to be by itself. The notes below are what I give the students to get them started on this process.literal-equation-explained

I take them through a problem similar to the one above and then I let them practice 4 problems that are similar to this. Below is a sample:literal-eq-with-wordsIf you like collaboration, these problems would be good for a sage and scribe activity. The sage tells the scribe what to write. The scribe has to stay quiet for a while and let the sage describe the steps and what needs to be written. I eventually let the scribe have some input because sometimes they are dying to help the sage. We switch roles for each problem.

Next, I give them a worksheet that has a regular equation with a literal equation that looks just like it. They do the regular one first and then the literal equation (they are solving for c). I keep telling them to remember what they did on the regular equation and follow those same steps. Here’s an example:comparison-of-equations

The final activity in this lesson is to help the students in their science class. I give them some science equations mixed in with a few math equations. I’m hoping by now, these problems will be easy.

science-lit-equ

There is one more reason students do not understand literal equations and it’s our fault as teachers.

4. Teachers work on literal equations for one day maybe two and that’s it. How can they really get it?

Let’s not make that same mistake again. I plan on recycling literal equations back into my lessons. I plan on using them in bell-ringers and I plan on putting them on assignments and tests in the future. How many people can understand something, especially in math, after one or two days? Remember that when a student first sees a literal equation, it looks foreign to them. They are not going to make the connection that they are just equations (at first).

We can help make the student more successful in math and science if they learn to solve literal equations. Don’t take this topic lightly. Ask your science teachers what else students have a hard time with when it comes to math in their class. Bring something to write with, because you’ll get a list of items. Other things that my physics teacher has mentioned is conversions, graphing linear equations (knowing slope, independent and dependent) as well as being able to graph bar graphs.

Good luck and if you would like to purchase my literal equations activity, click below:

literal-equations-pic

Literal Equations for Math and Science

Two-Column Proofs and Logical Reasoning

The second unit in Geometry for me is Logical Reasoning. I do three things: 

  1. Inductive and Deductive Reasoning
  2. Conditional Statements
  3. Two-Column Proofs

Monty Python

I have fun teaching inductive and deductive reasoning. I usually start the lesson by having students watch a YouTube clip of Monty Python and the Holy Grail. It’s a pretty hilarious demonstration of how drawing conclusions based on patterns can lead you to the wrong conclusion. This would be a great place to talk about stereotyping if you would like to go a little deeper into how people base information sometimes from the media or gossip. This lesson has 12 task cards to practice reasoning and knowing the difference between the two types. 

Conditional statements is also fun to teach. I love it when kids say that it doesn’t seem like we are learning math. We discuss where the hypothesis and conclusions are in the conditional statement so the students can write the converse, inverse and contrapositive. We also discuss counterexamples and biconditionals. This lesson has some hands-on activities where students create if/then statements and the related statements and tape them into their journals. 

conditional

The last part of this unit is spent on two-column proofs. This usually happens for me in October, sometimes earlier but close enough that I can show them a silly Halloween proof that I created. I made this up a long time ago after watching “It’s the Great Pumpkin, Charlie Brown.”  It’s got all the elements of a real proof. I’ve used this as a bulletin board in past years. Feel free to use this in your classroom.geometric-proofs-b

One thing that is in this lesson that helps my students is a set of matching cards. Students will match the property or definition with its name. I do this as a collaborative activity. Students enjoy this and it helps them to have some tools to use going into writing proofs. This is a beginning proof lesson. I only practice two-column proofs. In lessons that follow this one, I introduce the other types of proofs like paragraph and flowchart proofs. 

If you are teaching online, no problem. I’m in the process of making these lessons more online friendly. Teachers Pay Teachers has a new tool that can take a PDF and transform it into an interactive worksheet. Look for the “Use as a Digital Activity” button on products that are available for this. You as a teacher can modify it as you see fit then assign it to your students. 

I love this part of Geometry. It’s different from the norm in math. It’s always a fun time of year. If you’d like to use my lessons, then the best way to get them and save a little money is to purchase the Unit 2 Bundle

Good Luck and I hope you have a successful year!

Geometry – Transformations Hands-On Activity

I am excited after going through a transformations activity that I have created. I’m gonna have to say, it’s pretty good! (Just saying…)

The first thing I do is show my students a Mario Brothers Transformation PowerPoint that I created this year. It’s a free download on my TpT site. So FUN! I tell the students to number from 1 to 4 in their journal and then I go through the PowerPoint to see if they can name the different transformations. I want to know what they remember from middle school.mario-transformations

Next I have the students jot down a few notes and then I begin the hands-on part. I use patty paper and wikki stix. Every student was engaged, asking questions and YES….LEARNING! I show them pictures of me working on the transformations which is very helpful. I don’t have to stop and do it in front of them…pictures are worth a thousand words! The pictures are provide in the product and I think you will find them very useful.

transformations

What are wikki stix you ask? I think they are just thread or string that has been dipped into wax which means they will stick to things. I use them as my lines of symmetry as well as a tool for rotations as seen below:

transformations

transformations

If you haven’t done transformations this year, I hope you will check out my Transformations Activity. Included is a note page, pages for each type of transformation, a quiz, keys and pictures. You will have a great time working through this with your students. Let me know what you think! Hope to hear from you soon.

You Have TI-Nspires…Now What?

TI-Nspires are amazing calculators. There are so many features, don’t try to learn them all at once. First of all, get the teacher software! I can’t live without it. In my district, even the students have the software available on their laptops. It’s wonderful.

How do you get started? The first thing I learned was go to the HOME SCREEN and choose NEW DOCUMENT. If there is a screen that asks if you want to save, say no. Now choose what you want to do. If you are learning, you will only choose graph or calculator. This is what I still choose most of the time!

new-doc-screen  choice-screen

The calculator screen is easy to use. If you are looking for something specific it is probably here: (see below) I used this button to type in a cube root as seen in the next pic.

special-characters  calculator-screen

Let’s say you now want to graph something. You have a choice. Start completely over and go to the home button and go through the same steps explained above, or add a page to your document. Let’s add a page. Simply click CTRL (blue button) +Page (doc button below home.)

add-a-page   graphing-1

Choose Graph! Now you can type an equation. The x button is one of the white alphabet buttons at the bottom of the calculator. Hit enter when you are ready to graph. To graph a second equation, click the tab button and type in a new graph… or to change the first equation, after clicking tab, up arrow to the original equation. If you know this much, you are ready to use the calculator. The only other things that are nice to know at this stage is that ctrl t will pull up a table (and ctrl t will take the table off).

table

AND the menu button has many things that will help you. I suggest clicking the menu button and checking it out! I use #4 and #6 daily. #6 is where intersections and zeros are and #4 of course helps you change the window settings like on the 84+.

menu

My goal was to help you get started. If you will start using these features and become very familiar with the calculator, you will discover new things on your own. Your students will also help you discover things. The main thing is to get started! Don’t let those calculators just sit. They are really awesome and helpful!