## 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.

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