Standards-Based Lesson

Writing and Solving Word Problems from Real-World
TITLE:
Situations

LESSON DEVELOPER: Christian Curry

CONTENT AREA AND GRADE: Algebra 1 - Grade 8

This is a two-day lesson that involves writing and solving
SCOPE AND SEQUENCE multi-step equations and inequalities. (from the VSC:
1.B.2.a and 1.B.2.b)

TARGET TEACHING DATE: October 11 - October 12, 2006

SCHOOL: Perry Hall Middle School

STANDARDS:

Mathematics - Grade 8

Standard 1.0 Knowledge of Algebra, Patterns, and Functions: Students will algebraically represent, model,
analyze, or solve mathematical or real-world problems involving patterns or functional relationships.

Topic B. Expressions, Equations, and Inequalities:

Indicator 2. Identify, write, solve, and apply equations and inequalities

Objective g. Write equations and inequalities that describe real-world problems

PERFORMANCES:

The students will create an equation based on the following topic:

Sports: Students will then use predetermined data to solve their equations.

SETTING:

Real World Setting: Professional sports

You are a famous NFL agent. Your client, a famous quarterback, is at the end of his contract. You will
create a new contract for your client. You must create stipulations in your contract that include a base
salary, bonuses for reaching specific performance incentives (ex. $10,000 for every touchdown thrown), and
penalties for performing poorly (ex. losing $5,000 for each interception thrown). Once you have created the
equations, you will research to find your statistics for the 2005 season. Using these statistics, you will
determine your salary for the season based on the contract you have created.

SMARTSKILLS:

Level I: Acquiring Data - Data students will acquire in this standards-based task:

Vocabulary: Equation, Substitution, Base salary, Touchdown, Interception, Completion, Sack
Skills:
1. Create and solve an equation.
2. Use given information to solve a real world problem.

Level II: Visualizing Information - Data from Level I that are visualized as information in this standards-
based task:

Organizing: Using the information provided in the word problem to determine final salary of
quarterback.
Creating meaning: Determine the final salary of chosen NFL player.

Level III: Applying Knowledge - Visualized information from Level II that is applied knowledge in this
standards-based task:

Making decisions: Creating appropriate values to performance incentives.
Solving problems: Determining the final salary of NFL quarterback.

PREFERENCES:

Student Involvement - The students will complete the task in a project group to create an equation. The
students will then work on their own to determine the outcome of their equation given a set of data.
Students will then meet again to compare their results and create a poster to share their results.

Instruction - Activities will be organized and delivered in a multimedia presentation followed by large
group discussion and small group activities.

Special Education Accommodations - Students with special needs will require the following electronic
devices: Calculator

Special Education Accommodations - Students with special needs will require the following presentation
of information: Extra processing and response time and written copies of orally presented instructional or
assessment materials

Use of Resources - The school will provide classroom time to complete the task

Use of Resources - The students will provide classroom materials such as pencils, paper, notebooks
homework time

Customer for Student Work - The student will present their work as evidence of task completion to peers
and teachers

Assessment of Student Work - The following people will be involved in assessing student work generated
to complete the task: The student's teacher and peers

Assessment of Student Work - The following forms of assessment will be used to determine progress and
results: Formative Performance Assessment consisting of poster and presentation made by groups

Reporting Results - The assessment results will be reported as a score point on a rubric

Timeline - The estimated time needed to plan, teach, and score this task is two class periods
(From October 11 to October 12 for 2 class periods)

ACTIVITIES:

Teaching for Understanding in Mathematics

Activity 1: The teacher reviews yesterday's lesson and assigns a problem that was not finished. The
students present solution methods they have developed and the teacher summarizes.
(Estimated time: 10 minutes)

Step 1: Upon entering the room, students will solve one problem shown on the TV screen. The problem will
give students a real-world situation and equation. They will be asked to solve for an unknown (knowing they
have been provided with all necessary components to solve).

Step 2: The Yellow Cab Taxi Company uses the equation c = .35m 1.25 to determine the cost of a taxi ride.
If c represents the total cost of a taxi ride and m represents the number of miles traveled in the taxi, use
the equation to determine the cost of a 12 mile ride. Use what you know about mathematics to justify your
answer. Use words and/or numbers to support your answer.

Step 3: Students will orally present their solution to the problem. A student will model their solution on the
board as students at their seat check their own work. Teacher will monitor student progress by walking
around the room and visually check student work.

Technology: Power point hooked up to TV monitor
Materials: Paper, pencil, chalk, chalk board, graphic organizer created and provided by teacher
Student product or performance: Solving the situation using the equation and information provided.
Links or connections between different parts of the lesson: Solving an equation given a real-
world situation.
Scoring: The teacher will have selected a student to put their answer on the board because it showed
all necessary components. Students will compare their work with the example and make any needed
corrections. Formative assessment will be used. The teacher will walk around the room to answer any
questions and make sure students are correcting their work.

Activity 2: The teacher introduces a teacher-directed activity modeling the task students will
complete later in the period. This activity is used as a benchmark.

Step 1: Ask students to write down the grade they think they will have earned at the end of the marking
period for the following subjects: English, Science, Math, History.

Step 2: Tell the students that a new rewards program has been set up by the principal. He has told the
students that at the end of the marking period they will earn $3 for each A, $1.50 for each B, $0.50 for
each C, $0.00 for each D, and the students will have to pay the principal $1.00 for each F.

Step 3: As a teacher-guided activity, the students will create an equation which will model this situation.
After the equation has been created, the entire class will find out how much a few students will have earned
(or owe) using teacher created data. Once a few situations have been modeled, the students will find out
how much they have earned (or owe) using their own data. Using their own data gives students motivation
to complete the activity.

Step 4: Ask the students which scenario will earn the most money:

Scenario 1: 1 A, 2 B's, and 1 C
Scenario 2: 2 A's, 1 C, and 1 F

The teacher will model how mathematics is used to justify their answer. The ECR rubric will also be
presented so students know how they can earn all possible points. All students will receive a copy of the
rubric.

Materials: Paper, pencil, graphic organizer created and provided by teacher
Student product or performance: Creating an equation. Solving the situation using the equation and
information provided.
Links or connections between different parts of the lesson: Writing an equation. Solving an

equation given specific data.
Scoring: Students will use the ECR rubric to evaluate how well they think they scored. They will give
themselves a score out of four points. The teacher will then ask for volunteers to justify their score.
This will be a formative assessment.

Activity 3: The teacher presents the task for the day and asks the students to work on it
independently (Task is to invent a problem for classmates to solve.)

Step 1: The teacher will assign six groups of five students. You are a famous NFL agent. Your client, a
famous quarterback (each group will choose a quarterback), is at the end of his contract. You will create a
new contract for your client. You must create stipulations in your contract that include a base salary,
bonuses for reaching specific performance incentives (ex. $10,000 for every touchdown thrown), and
penalties for performing poorly (ex. losing $5,000 for each interception thrown). Once you have completed
your contract, your group will create research actual statistics from the 2005 season. Using your statistics,
each member of the group will determine your quarterback's final salary based on the salary you have
created.

Step 2: Students will be given a list of performance incentives (both positive and negative) that will be used
to create the contract. The positive incentives include number of completions and touchdowns thrown. The
negative incentives include number of interceptions thrown and number of times sacked.

Step 3: On their own, students will create appropriate values to coincide with the specific incentives.

Student product or performance: List of monetary values associated with positive and negative
performance incentives.
Links or connections between different parts of the lesson: This information will be used to
create an equation.
Scoring: Monitored by teacher

Activity 4: The teacher suggests that students continue their work in small groups. Leaders of groups
share their problems with the teacher, who makes them public, e.g., writes them on the board.
Students copy the problems and begin working on them.

Note: It is unusual for students to work this long without a class discussion. Also, it is typical for students
to struggle with the task before the teacher intervenes.


Step 1: Students get together in their groups and choose one quarterback. Each group must have a different
quarterback. Then, students will discuss the incentive values and come up with one list of monetary values
for each incentive. The team leader from each group will be asked to share their values with the class and
justify their choices. As a class, we will narrow these down to the best choice for each incentive so each
group will be working with the same values. Each student will write these values down so each student has
the same information for the activity.

Step 2: Groups will now work together to create the equation which will be used to determine the
quarterback's salary.

Step 3: As a group, students will use 2005 season statistics from the following web site to determine the
stats for their quarterback.:

http://www.nfl.com/stats/playersort/NFL/QB-PASSING/2005/regular

If internet access is not available, the teacher will provide the students with a hard copy of their
quarterback's statistics. The teacher must be prepared with this material for all quarterbacks. This
information will be presented in table form.

Each member of the group will use their equation and data to determine the player's salary. After four
minutes, the group will get back together and agree upon a final salary based on their statistics. Once they
have completed the work individually, they will work together to confirm the final salary of their

quarterback. Groups will then present a poster of their solved equation. The leader of the group will present
their findings to the class.

As a class, students will respond to the following prompt outloud: Which quarterback would most benefit
from this contract? Which would benefit least from the contract? Use what you know about mathematics to
justify your answer. Use words and/or numbers to support your answer.

Technology: Power point hooked up to TV monitor, computer, internet access
Student product or performance: An equation used to determine the final salary.
Links or connections between different parts of the lesson: Writing and using an equation to
solve a problem.
Scoring: Teacher will use the ECR rubric to make sure students are giving complete answers. This
will be a formative assessment.

Activity 5: The teacher highlights a good method for solving these problems.

Step 1: The teacher will ask the students to pick one more quarterback to be used as a final example. After
data has been collected, the teacher will lead the group in a discussion on how to solve this problem using
the ECR rubric as a guide. The teacher will discuss each component of the rubric and give examples of how
students can receive the maximum value.

Source: Lesson template adapted for my classroom from:

1. The 1996 Third International Mathematics and Science Study (TIMSS)
2. Stigler, J. & Hiebert, J. (1999) The teaching gap: Best ideas from the world's teachers for improving
education in the classroom. New York: The Free Press.

BENCHMARKING:

Student Performance One: (Students will create an equation and use predetermined data to solve their
equation.)

Assessment Benchmarking Example:

As a class, the teacher will complete an activity with the students that will be used as a model later in class.
The example will benchmark the activity so students will know what is expected of them.

Ask students to write down the grade they think they will have earned at the end of the marking period for
the following subjects: English, Science, Math, History.

Tell the students that a new rewards program has been set up by the principal. He has told the students
that at the end of the marking period they will earn $3 for each A, $1.50 for each B, $0.50 for each C,
$0.00 for each D, and the students will have to pay the principal $1.00 for each F.

As a teacher-guided activity, the students will create an equation which will model this situation. After the
equation has been created, the entire class will find out how much a few students will have earned (or owe)
using teacher created data. Once a few situations have been modeled, the students will find out how much
they have earned (or owe) using their own data.

Ask the students which scenario will earn the most money:

Scenario 1: 1 A, 2 B's, and 1 C
Scenario 2: 2 A's, 1 C, and 1 F

The teacher will model how mathematics is used to justify their answer. The ECR rubric will also be
presented so students know how they can earn all possible points.

SCORING:

Scoring Approach: Holistic scoring will be used. Student performance will be scored on the overall quality
of the expected product or process, while paying attention to each of the criteria being examined. However,
strong performance on one criterion can offset weakness in another criterion.

Maryland High School Mathematics Rubric: Extended Constructed Response

The response indicates application of a reasonable strategy that leads to a
correct solution in the context of the problem. The representations are
correct. The explanation and/or justification is logically sound, clearly
Level 4
presented, fully developed, supports the solution, and does not contain
significant mathematical errors. The response demonstrates a complete
understanding and analysis of the problem.

The response indicates application of a reasonable strategy that may or may
not lead to a correct solution. The representations are essentially correct.
Level 3 The explanation and/or justification is generally well developed, feasible, and
supports the solution. The response demonstrates a clear understanding and
analysis of the problem.

The response indicates an incomplete application of a reasonable strategy
that may or may not lead to a correct solution. The representations are
fundamentally correct. The explanation and/or justification supports the
Level 2
solution and is plausible, although it may not be well developed or complete.
The response demonstrates a conceptual understanding and analysis of the
problem.

The response indicates little or no application of a reasonable strategy. It
may or may not have the correct answer. The representations are incomplete
or missing. The explanation and/or justification reveals serious flaws in
Level 1
reasoning. The explanation and/or justification may be incomplete or
missing. The response demonstrates a minimal understanding and analysis
of the problem.

The response is completely incorrect or irrelevant. There may be no
Level 0
response, or the response may state, "I don't know."

Notes: Explanation refers to the student using the language of mathematics to communicate how
the student arrived at the solution.

Justification refers to the student using mathematical principles to support the reasoning used to
solve the problem or to demonstrate that the solution is correct. This could include the
appropriate definitions, postulates and theorems.

Essentially correct representations may contain a few minor errors such as missing labels,
reversed axes, or scales that are not uniform.

Fundamentally correct representations may contain several minor errors such as missing labels,
reversed axes, or scales that are not uniform.

Source: http://www.mdk12.org/mspp/high_school/structure/algebra/index.html

METACOGNITION:

Attitude Information: I will collect the following information after we have completed the activity. I would
ask students to complete this survey on a separate sheet of paper (provided by the teacher) so their answers
are not influenced by their peers.

1. Do you feel that you are good in creating and solving equations?
2. Did you find this task to be difficult?
3. Did you see the usefulness of what you were asked to do in real life?
4. Did you enjoy the task?
5. What would you tell your parents/guardians about this task?
6. What would you tell your friends about this task?

RESULTS:

Organize: I will use the following chart to display student data for each time that I assess and score the
same learning standard(s):

Data-Driven Results Disaggregated by Gender and All Students

Directions: Complete this chart for each content standard and aligned scoring tool used to
measure student performance in classrooms. In order to judge student growth across assessments,
record data from only one scoring tool on one chart. Then, follow these steps:

1. For each student's performance on your scoring tool, enter his or her score in the
appropriate cell under the headings for Scoring Results, e.g., 3, 2, 1, or 0 on a four-point
rubric. The first example below shows that Jason Anderson scored a 3. His score is entered
under the male heading and under all students.
2. Enter the summary data at the bottom of each assessment column for male and female
students and for all students.
3. Analyze the results and relate them to the instructional processes used to teach the
standards-based lesson to all students, to female students, to male students, e.g., what
worked well, what needs improvement, what was learned for improving instruction and
student learning?
4. Edit this table on the TaskBuilderOnline Design Page to add student names, to rename
disaggregated groups, or to make other modifications. Also, you may delete these directions
from this table after you become familiar with this data analysis process.

Content Standard: Write equations and inequalities that describe real-world problems

Students Scoring Results

Last Name and First Name Male Female All Students

1. Example: Anderson, Jason 3 3

2. Example: Anderson, Susan 2 2

3.

4.

5.

6.

7.

8.

9.

10.

# Of students at the Advanced Performance Level

# Of students at the Proficient Performance Level

# Of students at the Basic Performance Level

% of Students equal to or greater than the Proficient Level
(Total # of students at the proficient and advanced levels
divided by the total number of students)

% Distance above or below school Annual Measurable
Objective (AMO)

Analyze: I will examine the data in the chart to look for trends, contributing factors, and implications of
student performance over a series of assessments of the same learning standard.

Trends:
Contributing factors:
Implications for student performance:

Reflect: I will consider the following stems to reflect on the results and instructional practices I used and
others I might benchmark and apply in the future. Then, I'll write a brief summary about my findings,
contributing factors, and implications for improvement.

As I look at the results, I noticed that...
This connects to...
What was valuable?...not valuable?

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