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Teaching Math Blog

Strengthening Language Skills While Reviewing Graphing Inequalities

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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
Date:____________”
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.

Rubric

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

Links
How to Make a Playlist on HippoCampus:
A four-minute tutorial video
Open Textbook to Accompany NROC Algebra I--An Open Course (2011); FIrst Semester:
Open Textbook to Accompany NROC Algebra I--An Open Course (2011); Second Semester:
Open Textbook to Accompany NROC Developmental Math: Beginning Algebra:
Open Textbook to Accompany NROC Developmental Math: Intermediate Algebra and Trigonometry:
Open Textbook to Accompany NROC Developmental Math: Geometry and Statistics:
Learn more about the new NROC Algebra and Developmental Math courses:
HippoCampus Algebra & Geometry Study Group on OpenStudy.com:
National Library of Virtual Manipulatives--Line Grapher:
Finding Your Way Around the TI-83+ / Ti-84+ Calculator:
National Library of Virtual Manipulatives--Geometry Topics:
National Library of Virtual Manipulatives--Algebra Topics::

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