Thursday, June 30, 2011

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.

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

Friday, June 10, 2011

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.


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