Virtual Math Manipulatives for Algebra

When I last posted about the NROC text resources, I focused on the use of the written text itself, but did you notice the manipulatives? Take a look at Unit 4, Lesson 1, Topic 3 of NROC’s Algebra 1—An Open Course. There, you’ll see a manipulative that relates the slope “m” and constant “b” of a linear equation in slope intercept form to its graph. Below is a snapshot of the manipulative.


Like physical manipulatives, virtual manipulatives are awesome tools for students trying to really understand and internalize (I’d use the term “grok,” but I doubt that word is commonly understood, these days) how a mathematical concept works. Here is a way to use this tool in your classroom.

Learning Objective(s)
• Understand how graphing is used to represent solutions to a linear equation
• Recognize how changing coefficients and constants change the graphed solution.

Assessment Type
The formative assessment mentioned here should be employed as part of an introduction or reinforcement activity before students are thoroughly familiar with the concepts referred to.

Assignment Details
In a classroom with only one internet enabled computer, one can have one of NROC’s manipulatives running on through an overhead projector. Explain the basics of what they're seeing in the manipulative, and then ask them to predict what will happen when you toggle one of the variables.

For example, to use the manipulative mentioned, remind students of the y=mx+b form of linear equations, and possibly run them through how to graph one using an X,Y table. Hint that you’re going to be showing them a shortcut soon. Read the introduction to the manipulative aloud to the class and field any questions, but do not use any of the slider bars to change the manipulative. Then, ask “What will happen to the graph if we increase the value of b in the manipulative below? How about if we make B negative? ” Have them record their prediction and share their prediction with one partner. Then, “What will happen if we make ‘m’ greater? If ‘m’ is a fraction? Negative?”

If at all possible, though, these manipulatives should be given to students directly to explore on their own. You’ll need to give them basic direction on how to make the manipulative go, but once you have, allow them to have fun exploring the manipulative. Eventually, structure their investigation, asking them “What happens if…?” questions and “Why does…?” questions. I recommend having them write down their responses for you. (See the Example Questions below)

So, that’s a great way to use virtual manipulatives in your classroom. I hope you have fun with them! Yet, what do you do if you want a manipulative, but NROC doesn’t have it in its text?

I have two go-to sources, Wolfram Math Demonstrations and Geogebra, both of which have large libraries of manipulatives and a build-your-own option if you need something new. Both are absolutely free, although user accounts are required for Geogebra. Both can also be embedded in your webpage. In fact, Geogebra is what was used to make the demonstrations made in the NROC text.

See my hints and tips below for more information on getting started with these two great manipulative resources. If you build your own, give me a link to it in the comments section. I’d love to see it!

In summary, manipulatives are great because they instantly provide a playful math experience while allowing the student to explore and internalize “If I change one thing, what happens to another?” You can access manipulatives through NROC’s text, by visiting the Wolfram Math Demonstrations page, or making your own with Geogebra!

Example Questions
1. What do you think will happen to the graph if we increase the value of ‘b’ in the manipulative? How about if we make b negative? What really happened when ‘b’ changed?
2. What do you think will happen if we make ‘m’ greater? What if ‘m’ is a fraction? Negative? What really happened when ‘m’ changed?
3. Overall, describe what ‘m’ changes in a graph of y=mx+b? What about b?
4. *Extra Credit Challenge!* If you have two y=mx+b equations graphed on the same page and ‘m’ is the same in both, but 'b' is different, what is the special name for how these two lines’ relationship?


Rubric
4 Points for participating well in the class activity and discussion.
2 Points per question (6 total). The first point is for any honest attempt at a prediction given in a complete sentence. 2nd point is for noting the correct action of the graph when transformed. No penalty for skipping the Extra Credit, but take the opportunity to discuss the answer later as it introduces parallel lines.
Total: 10 points

Instructor Notes

Hints and Tips for Geogebra:
Download Geogebra and register with them to access their materials.

Once you register for Geogebra, go back and log in. Browse the wiki-library of resources, but be patient as things take a while to load. Geogebra's library is divided by language—you won’t see a list of manipulatives on the “Main” page. Look instead under the link that says “English.”

If you want information on how to create or embed a manipulative in your website, look in their "Introductory Materials" for orientation. Their format is do-it-yourself and share. Again, if you make a manipulative, please post me a link of your creation! I’d love to see it!

Hints and Tips for Wolfram Math:
You’ll need to download a CDF player (free) to use the demonstrations, but wow! It’s worth it.--CDF Player

To navigate, try looking within the topics list in the drop down menu linked to here.--
Wolfram Math Demonstrations Topics List. You can also do a keyword search.

If you get stuck or find yourself with questions on how to make your own demonstration--Wolfram FAQ.

Also, if you see a demo that’s almost what you want, but not quite, emailing them is very effective. I usually get a response within a week. Or, if you’re at all familiar with Mathematica and/or programming you can make a DIY manipulative here too! Have a great time!

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
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

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:


Or, you can have students follow a link to reach a full size recording:
SolvingSystemsofEquationsbyGraphing3

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. Screencast.com 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 screencast.com, 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.

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

Tutor Sim: Feedback While Reviewing Functions

The NROC tutor simulations can be used for individual review or whole class game play. As the student(s) answer a series of interactive multiple choice questions, the simulation first provides hints and then, at the end, suggests topics to review. With a little introduction and wrap up, the sims can be powerful review tools. This lesson plan uses the simulation from Unit Three - Tutor Sim: Snowboarding, which reviews the fundamentals of functions and their graphs. This lesson could be used with any NROC simulation. It describes the individual and whole class use of the tutor simulations.

Learning Objective(s)

• Review concepts before an exam.
• Identify areas for future study.
• Review slopes, proportionality, functions and their graphs.

Assessment Type

This assessment can be one of the last formative assessments done while preparing for a summative assessment. If done individually, it can help a student self-assess their learning needs. If done with a whole class, it can be used at the beginning of a class session to help the teacher get a sense of what the class still struggles with.

Assignment Details

Before beginning this with your class, take the time to run yourself through Unit Three's "Tutor Sim: Snowboarding." I recommend you get some answers wrong on purpose, so you can see how the simulation reacts. Upon completion, you'll also see the feedback given by topic at the end.

The two timed lesson plans below assume a 55 minute class session in a high school classroom.

If students can work individually with internet enabled computers:

1. 10 min– Warm Up. I have a warm up that I call, "Easy, Medium, Hard." Basically, as students enter the room I invite them to choose one easy, one medium, and one hard question from their homework and to write those three problems on the board for everyone to solve. After a few minutes working on the problems we share and discuss answers. If you have a trusted student or TA, it might help you to have them go around to each computer in your classroom and make sure the web page for the tutor sim is loaded and ready to go.
2. 15 min—Have students get out their note paper and introduce them to the NROC Tutor Sim: Snowboarding then have them work through it at their own pace on their computer. I recommend that you require them to summarize each question (draw any graph given, write down key data and what you're asked to find), and to show both their work and answers (not just the letter of the answer). They need to work through the sim honestly (not just guess and check) because at the end of the tutoring session the sim will use their wrong answers to identify areas is which they are having difficulty.
3. 15 min-- Having completed the tutor sim, students should copy down the suggested review sections as headings on a new sheet of paper, skipping 10 lines between each heading. They can then either fill those blank lines in with three example problems worked from their textbooks or with notes from going to and reviewing the presentations and problems from the NROC lessons dealing with the topic they had trouble with. If a student has no trouble, allow them to begin on their practice test or homework right away.
4. 10 min—Gather the class together for a discussion of what topics are still giving them the most trouble. Provide some review on topics with which many students are struggling.
5. 5 min—If you've not already done so, pass out any practice test or take home review sheet you have for students to complete. I often also offer 5% extra credit for 10 additional worked problems chosen by the student specifically to help them fill gaps that they realized they had today.

If one internet enabled computer and projector setup is available:

1. 10 min– Warm Up. Do the "Easy, Medium, Hard" warm up described above. If you have a trusted student or TA, it might help you to have them get the projector setup and working while you help students with the warm up.
2. 15 min—Have students in teams of four with one volunteer student running the sim for the whole class. As each question is presented, the teams should work together to solve the problem for a set amount of time. When time is called, the teams should show their answer to the student at front. Whichever answer appears the most, that is the answer picked. If your students like to be competitive, you can keep score. Require that the person writing down the answer switches with each question and remind students that all team members need to understand and agree on the answer.
3. 5 min – Check in with the class about the topics covered with the sim and take a moment to summarize concepts and field questions. Now is a good time to pass out a practice exam or to introduce a set of review questions.
4. 20 min—Allow the students to work in small groups on the review questions. If you've noticed a subset of students struggling on a particular topic, you can pull that group aside to work with you or on one of the NROC lessons. If another group finishes early, you can encourage them to play a math game from the section.
5. 5 min—Check in with students before they go. Ask them to reiterate and summarize some of the key concepts on their test. They can write on a slip of paper the topic they plan to study most and one strategy (flash cards, choose extra problems from the book, work in a study note, review online) they can use to study their chosen topic.

Instructor Notes

• Warning: The simulation does not have a back button. If needed, one can reload the web page and begin again.
• Students will want to test the sim--meaning give wrong answers on purpose--to see what the sim does. Such curiosity is great! I would encourage students to do so AFTER going through the sim once earnestly.
• If a student answers all sim questions correctly and has no topic that needed more work, they should show you the completion screen. You can then initial their paper so you know that they did not just skip that part of the assignment and can give them full credit.
• One could make an assignment asking students to design their own tutor sim. Students could present the answer options as a flow chart and even look into creating a basic simulation using linked web pages.

Rubric

If students worked individually, have them turn in their notes and problems from the tutor sim along with their completed practice test.

10 Point Scale: Tutor Sim Notes

2pts – Problems from the tutor sim are numbered and organized clearly.

2pts – All problems are written out with key data and answers shown.

3pts – Follow-up topics are identified OR student showed you they'd made no errors on the tutor sim and had you sign off on their paper before leaving that day.

3pts – All follow-up notes or problems (three per topic) are written out and solved correctly OR your signature shows they were not required to do the follow questions.

Total= 10pts

10 Point Scale: Practice Test

5pts – Practice test is complete, readable, and received. Work is clear and understandable. Give an approximate percentage of 5 points based on what percentage of problems meet this criteria.

5pts – Answers are correct. Give an approximate percentage of 5 points based on what percentage of problems meet this criteria.

Total= 10pts

Algebra Equations to Budget a School Party

Having learned the basics of making and solving equations, students use their knowledge to budget for an imaginary school event. Students can follow up with budgeting for a real event or fundraiser.

Learning Objective(s)

• Translate real life situations into word problems.
• Translate word problems into algebraic expressions and equations.
• Apply algebra principles to everyday problem solving.

Assessment Type

This middle through high school appropriate summative project from NROC's Algebra 1--An Open Course, Unit 2 Team Project: Students Rule can act as a capstone assessment in which students showcase their skills by presenting results from their algebraic comparison of different pricing plans for a school event. Alternately, the problems from the project can be used as a standalone single class assignment.

Assignment Details

Before beginning this with your class, take the time to read through "Team Project: Students Rule" completely. You’ll find three interesting class party budgeting problems followed by a larger project based on presenting findings. Decide if you want to do this as a small, single class exercise (just doing and discussing the three word problems), or do you want to follow through with a full project. If you’re just doing the problems, you can paste them into a separate document from the overall project and print them as a worksheet that omits mention of the larger project. Otherwise, you’ll want to print the whole project prompt, one copy for each group.

The timed lesson plan below assumes you’re doing a standalone, 55 minute class session using and discussing the problems provided. Suggestions for fully implementing the project (with presentation and follow up investigations) follow.

1. 10 min– Have your students write to this prompt, “If you had $200 to throw you and ten of your friends a party, what would you do? How about if you had $2000 and threw a party for the school?” Have fun talking about options, ideas, and possibilities. While you do so, find ways to turn the ideas into equations and record these on the board.

2. 10 min—Today’s goal is to use algebra equations to answer real life questions about budgeting. Break students into small groups and hand out the instructions and three questions from the project. Students will record their answers individually even though they are working in a group. Expect to help them pretty heavily with the first problem, but do give them as much of an opportunity as possible to solve it on their own. I recommend giving them five minutes to read the problem to each other in their groups, then check in with them to see if they’ve come up with equations to represent the budget problem. If not, help them break it down into key points. Once equations are built that make sense, give them five more minutes to solve the equations they’ve come up with, and then again compare answers and discuss results.

3. 20 min (10 min per problem) – Students should now complete problems 2 and 3 in small groups while you circulate and help if needed. If a group finishes early, either check their answer yourself or have them check their answer against the results of another group when it finishes. If a group is completely stuck, but you’re already helping a group, you can invite the stuck group to send out one of its members as a spy to see what a more successful group has come up with. Groups that finish early (and correctly) should be invited to graph their cost equations from one of the problems on a white board or poster for others to see. Require correct axis labeling (recommend that the cost goes on the y axis, the variable appropriate for each problem on the x axis) and clarity as to which equation goes with which line.

4. 10 min—When all groups are finished, check that all have reached the same conclusions as to which vendors would be best to choose based on the budget numbers given. Discuss any discrepancies. Extend the discussion by referring to the graphs made by the groups that finished early. Have the students explain to you under what circumstances it would make sense to choose another vendor and justify it based on the graph. Ask them if to identify the point of intersection of the two equations from their problem. Can they tell you the meaning of that point? (Its where the cost and benefit would be the same regardless of which vendor was chosen.) This leads nicely into a discussion of systems of equations.

5. 5 min—Working individually students should summarize the results of the day in their own words. They can add this to the end of the page on which they solved their problems. I sometimes call these “Dear Me,” notes, as the goal here is for the students to take note of any realizations that they’ve had during class.

Instructor Notes

• If you’re working with a middle school class or lower level high school class, having them create presentations as described in the NROC project would be great. If your class has access to a computer lab completing the presentations should be do-able in about two more class sessions. I would ungroup the students for this part of the assignment, however, so each could learn the editing skills needed to make the presentation. A rubric is provided as part of the project.
• To extend this, have the students create a budget and use their algebra to compare options for a real life situation. Competing cell phone contracts can be good for this. Or, of course, they could really research and plan a school party.
• If you have a class interested in service learning, this would be a great introductory project for a charity fundraiser. Student groups could discuss and research a local need and create competing proposals for a fundraising event to meet that need. When all projects are presented, the class could vote on one project to actually attempt to bring to fruition.
• If you know you have a student who has really been struggling with group work or making algebra equations in general, you can have that student go online and use the NROC tutor simulation “Building a Swimming Pool” which is also part of Unit 2 and covers turning a real life situation into an equation.

Rubric

A rubric for the project itself is provided in the NROC assignment description.

Alternately, if using a 10 point scale for grading only the word problems and group work in class:

5pts -- Time on task. Students stayed engaged and on topic working to solve the problems. All students in the group supported one another and invited contributions from each other.

3pts – All three problems are written out and solved correctly.

2pts – A separate summary of what was learned in class that day is provided.

3pts – All three problems are written out and solved correctly.

Total= 10pts