Saturday, July 30, 2011

Strengthening Language Skills While Reviewing Graphing Inequalities

While working to figure out from context which words have been removed from a paragraph explaining systems of inequalities, students will both reinforce their understanding of graphing systems of inequalities and their ability to use and understand academic English. Students first fill in the teacher created cloze dealing with systems of inequalities. Then, they make and share one of their own. A systems of inequalities cloze worksheet and key (based on a paragraph from NROC's Algebra 1--An Open Course, Unit 6, Lesson 3, Topic 1: Graphing Systems of Inequalities) are provided.

Learning Objective(s)
• Understand how graphing is used to represent solutions to systems of inequalities
• Recognize and use proper English grammar and syntax when communicating about algebra

Assessment Type
This formative assessment should be employed as part of a reinforcement activity or review after students are familiar with the terms and concepts referred to.
Assignment Details
A truly useful but often overlooked item in the NROC Algebra 1 course is the topic text. Written in a conversational style, the text re-explains the same concepts addressed in each lesson’s recorded presentation, providing more details and example problems. Unlike a traditional offline textbook however, it can be copy/pasted into presentations and lecture notes. So long as proper credit is given to its authors, you’re good to go. Here the topic text is used to make a “cloze” activity.

Used since the 1950’s, a fill-in-the-blank cloze exercise is designed to strengthen grammar and syntax skills. You will see the cloze worksheet (and key) on systems of inequalities were made by taking the NROC text and then removing every seventh word. Thus a puzzle rather than a fill-in-the-blank quiz is created—one in which a non-math preposition or verb is as likely to be omitted as a math term. In this assignment, as students first solve, then create, and finally trade-and-solve their clozes, they will use and discuss many aspects of the English language. This cloze activity could be used in many contexts, but this lesson assumes a 55 minute high school class session. Have on hand a class set of the systems of inequalities cloze worksheet and one copy of the key.

15min – As students enter, hand out the systems of inequalities cloze and have them begin work figuring out the missing words. After 10 minutes, have them compare answers with a partner. During this time, circulate, providing insight to any stuck students. Explicitly use grammar terms. If needed, you can brush up on prepositions and adverbs here or many other places online.

5min – Review answers as a whole class. Some suggested answers will be different but still technically correct based on the context. Discuss variance of answers, but accept all that work. Check the results with your key and discuss why the author(s) might have chosen one word over another. Explain that students will now have the make their own cloze puzzles and will then trade and complete them.

15min – If you have internet enabled computers available, have students go to the topic text portion of several of the previous lessons on the NROC Algebra 1--An Open Course. If you don’t have computers, this same activity can be done using a textbook’s text. Instead of “copy/pasting” as describe below, students will re-write and create a cloze paragraph by hand using their class textbook. They should note the textbook and page number as the text source and cloze key.

For those of you using the NROC text, this image shows where to click to find the topic text:

Since the example cloze deals with Unit 6, Lesson 3, Topic 1: Graphing Systems of Inequalities, text from Unit 6, lessons 1, 2, and 3 all make sense as text sources. This will provide the wanted review of the unit. Students should choose and copy/paste one paragraph from the lesson of their choice into a word processor and save it with a descriptive title (I recommend “NROCAlgebraUnitLessonTopic_Cloze”).

At the top of their document they should put (write the following on the board for them):
“Cloze and Key Created by: (First and Last Names)
Text Taken from: NROC Algebra 1—An Open Course Unit _(#)_ Lesson (#), Topic number: Topic Name
This gives credit to the original authors of the text as well as those creating the cloze.

Beneath this, the students should paste the paragraph’s text, making sure their selection will fit on the page twice and removing unwanted formatting (extra spaces and unwanted underlines from hyperlinks, for example). Then, they should bold and underline every seventh word. Now they have their key! They should copy/paste their edited paragraph below the first one, leaving about 5 spaces in between.

At the top of the second paragraph, they should write:
“Cloze Created by: (First and Last Names)
Cloze Solved by:_________ Date:________”

Now, they should delete every bolded/underlined word from the second paragraph, replacing what they’ve removed with a blank line. Finally, they should save their work and print out a copy.

10min--Once they have their copy printed, they should put their names in the appropriate places on the printout. Then, they cut the worksheet from the key and trade with another finished group who has done a different section of text. Each group races the other to complete the traded clozes. Afterwards, they should check their answers against the key. Groups that finish early can be given time to work on review homework or invited to make a cloze from scratch on any funny but classroom appropriate topic they want to share with the class and solve for fun.

5min--For wrap up, have students volunteer with which sentences were hardest to figure out and why. Summarize any key concept and/or syntax difficulties or vocabulary difficulties that were run into.

Instructor Notes
•Your students have just made you a large number of worksheets that can be used for future years. Save them! Either copy them off the computers or have them print out an extra hard copy for you.
•Encourage students to use and share hotkeys. In Microsoft word, for example, “CRTL+C” is copy, and “CRTL+V” is paste. “Shift+hypen” makes an underline.
•Remember, ELL students will have much more difficulty with a cloze. Offer them a bit more time and scaffolding for their work or pair that with a kind stronger student. Just be sure that the stronger student can explain why certain words are being chosen and does not just complete the worksheet solo.
• Since they’re making and solving puzzles, get them revved up. Pull out a timer when they solve each other’s clozes! They are racing each other within the class but also TOTAL time against other classes. Once you explain what they are to do after they’ve printed their work, start the timer. After the first group finishes, hand over timer and work collection duty to that group so you can help others.


Grade on effort and completeness, not on correct answers. Grade by looking at all the names on the completed clozes. Each student’s name should appear twice, once as a creator and once as a solver.

3pts – Student’s name appears on a correctly completed cloze key.
2pts - Key formatting is correct and answers provided in key.
5pts-- Student’s name appears on a correctly completed cloze.
(Partial points for an incomplete cloze)

10pts Total

Thursday, July 14, 2011

How to Record Your Own Step-by-Step Algebra Problems

The NROC Algebra 1 course includes many step-by-step worked example problems recorded by Salman Khan of Khan Academy. What do you do if you find yourself in need of an additional or alternate example? This post will help any teacher who wishes to create additional example problems for their students.

Learning Objective(s)

• For the Teacher: Learn how to create and distribute a recording of your own.

Assessment Type
This post is aimed at teachers, not students. It uses the worked examples relevant to NROC's Algebra 1--An Open Course, Unit 6 Topic 1: Solving Systems of Linear Equations by Graphing to show how one can add to the provided worked examples and supplement with examples made by the teacher.

Your finished example will look like the one linked to here:
Unable to display content. Adobe Flash is required.

Or, you can have students follow a link to reach a full size recording:

Assignment Details
The worked examples in “Unit 6 Topic 1: Solving Systems of Linear Equations by Graphing” jump right in with some deep word problems. An example that goes straight to graphing the intersecting equations might help. Let's record that example, showing step by step solving and reviewing graphing. Of course, you can apply the same techniques to any problem you choose.

Set aside a few hours for this so you won’t feel rushed, and then have fun with it. After you’re familiar with the tools, making recordings is fast and relatively easy.

First, make sure you have an internet connected computer equipped with a microphone headset and drawing tablet. I’ve had good luck with using a Logitech USB headset and a Wacom drawing tablet. This will improve your sound quality and allow you to write out your equations neatly as you present. If you cannot get a tablet, I suggest you type out your work on separate PowerPoint slides. If you only have an area or laptop mic, give it a try and see if you find the audio acceptable.

Next you’ll need recording software. Download the free version of Jing if you’re only going to do simple recordings lasting five minutes or less. If you’re looking for something more advanced, Camtasia Studio provides many more editing and presentation options. It costs a bit, but it does have a free trial period and frees you from the pesky 5 minute limit. Both programs have the ability to record a selected area of your computer screen and the audio to go with it. Also, new tools are coming out all the time. It's likely worth it to do a quick Google for new, free screencast software if you don't think these meet your needs.

Now, set up your graphics. Since we’ll be talking about line graphing, I’m going to want a coordinate axis set up in advance. I used screencapture (fn+f11 on my PC) to pull an image of a coordinate axis from one of the tests I use. I also plan to work with three slides, so I’ll paste the image I want into PowerPoint. I plan to have an introduction slide, a working the problem slide, and a summary or “right answer” slide. Since PowerPoint does not have a straight line tool available in presentation mode, when my problem involves graphing I like the neatness of a final answer screen. Now, my graphics are ready to go as Jing will allow me to play the PowerPoint while recording.

Work your problem. Before recording, take a moment to work your problem from beginning to end while taking notes on the problem’s key points. I also recommend talking through your problem aloud while you solve it, as you’ll be less likely to stumble later. Remember, you’ll need to keep things brief to stay under 5 minutes.

Secure the space. Make sure your phone is off, and put a sign on your office door saying, “If I’m talking I’m recording. Please leave me a note, but do not disturb!” You might want to invest in a small dry erase board or some Post-It notes for your door if you’re likely to do this often.

Record! Check your audio at the beginning of each recording session and have your practice notes on hand. Expect to make errors the first time you do it, but try to reach the end of the problem even if you mess up early. This will help you ensure you have your timing right. Keep your voice dynamic! You’ll improve with practice, so keep at it! Check your recording for good sound before publishing.

Publish your recording. Jing provides you with a file that you can save for viewing in your class or upload into a server of your choice. provides free accounts with 2GB storage and works well with Jing for this. Their sharing tutorial is linked to here. Essentially, once you upload to, you will have a URL that you can paste into a website or email to a student.

There you have it! You’ve created a recording that explores additional concepts for your students that they can access at home and any time that they’d like. Perfect!

Instructor Notes
• If you need multiple slides, use Microsoft PowerPoint, or a similar presentation tool. Most will allow you to do markup while presenting. If you just need one screen to markup, Microsoft Paint or any basic image editor will suffice.
• I allow myself one caught error per recording. Any more than that and I believe the recording needs to be redone.
• If you want to capture an image from your screen to use in a slide presentation, on a PC hit the “Fn+F11" hotkey combo or the "print screen” button. This takes a snapshot of your entire screen. You can paste that snapshot into a PowerPoint slide or paint program. You can even use this to grab an image from the NROC presentation or worked examples if you need to further explain an example used there.
• If you want your students to demonstrate that they’ve viewed a recording, assign them to take notes on it and email or upload to you a scan or digital photograph of it.
• If you’re using an online learning management system such as Angel and have published an example recording via a link, the system can track which users have viewed that link. Assuming no two students work together, you can use this to track which students have viewed a recording as well.
• Keep things short, breaking things up into multiple videos as needed. This helps you as well if you’re using the free Jing software. It’s sure frustrating to have made a great recording only to stumble in the last minute.

If you complete a recording and get it to your students, let me know about it here and give yourself an A!