Lynn Grimm

Seventh Grade Mathematics

Thomas Jefferson Middle School

Menomonee Falls, Wisconsin

Thomas Jefferson has a student population of approximately 660 students. I teach seventh grade mathematics in one of the three “house” systems. This assessment focuses on the percentage unit in the seventh grade curriculum.

Lynn Grimm

Menomonee Falls School District
Thomas Jefferson Middle School
Grade Seven/ Mathematics

Grade: Seven
Level: Accelerated, Regular, and Basic

Subject: Mathematics
Focus: Percentage Unit

MATHEMATICS CONTINUITY STANDARDS
FOR THE MENOMONEE FALLS SCHOOL DISTRICT

---GRADE SEVEN

I.) Ability as Outcome or Standard B:

Number Operations and Relationships; Students will use numbers effectively for various purposes, such as counting, measuring, estimating, and problem solving.

II.) Components (or Generic Criteria):

B 7.2 Students will: (Compute with real numbers (fractions, decimals, integers)

B 7.3 Students will: Generate and explain equivalences among fractions, decimals, and percents

B 7.5 Students will: Apply proportional thinking in a cariety of problem situations that both include, but are not limited to:

B 7.7 Students will: In problem-solving situations, select and use appropriate computational procedures with rational numbers such as:

Unpacking the Standards Further:

B 7.3 (2) Convert percent to decimal

B 7.5 (6) Find the percent of a number

B 7.5 (11) Find the amount of sales tax and the total amount

B 7.7 (6) Estimate sales tax and tip…use mental computation

B 7.2 (4) Round the product to the given place (hundredths place value---to the nearest penny)

III.) Performance Instrument or Process (Stimulus/Contex)

Lesson(s) Preceding Assessment:

The students have practiced together as a class and individually how to convert percents to decimals and decimals to percents. They also learned how to compute with percents. Lastly, they learned how to figure out tax of an item based on various tax percentages and tip for a service based on various tip percentages. The students practiced these skills as a class with several demonstrations and role playing situations. They also practiced these skills with a written assignment (worksheet and textbook assignments).

Assessment:

In groups of four the students create identical menus for fictitious restaurants. The students take turns role playing being a waiter or waitress for the restaurants. The other students take on the role(s) of patrons to the restaurant. The students pretending to be food servers take the other students orders. The students pretending to be customers determine the percent of the tip they plan to leave based upon the quality of the waiter/waitress' acting performance. The students are given a range of 5%-25% to leave for the tip. Each student is required to figure tax and tip correctly (to the nearest penny) on five separate orders using calculators. For the fifth and sixth order, the tip has to be estimated for 15% of the total of the bill. It is a simulation activity. The students rotate as a group from restaurant to restaurant taking turns with the various roles.

IV.) Specific Criteria

Directions for Learners:

The students were given specific instructions on how to make the menus and what to include. They were shown several examples. The students were given the packets in advance and three practice examples were done using an overhead copy of the menu pad. Two students volunteered to pretend they were seventeen and on a date. They ordered food and discussed the tip involved. The class figured out the tax and tip as a class. The teacher demonstrated three examples of how they could "act" as waiter or waitress. Oral directions were given and demonstrated the day before and the day of the assessment. Finally, after the first round took place, everyone froze and questions were answered regarding procedures before continuing the assessment.

V.) Self-Assessment

Self-Assessment:

After receiving feedback from the other students in their groups, the students fill out a group assessment and reflection packet. It asked them to express in writing what they learned, what they felt best about, what they still find hard to do, how their grouped worked together, and how they feel about a career that works with the public. It is a form of both reflection and self-assessment.

VI.) Feedback

Feedback:

In the same group of four, the students assessed each others "bills." In a real restaurant situation, many times, if patrons feel there is an error on the bill, they pass it around the table and various people recalculate the bill checking for errors. This form of feedback simulates this "real life" scenario. The students were directed to pick one of the front four sheets for the group to check and one of the last two pages. They put a star on the top of the two pages they chose to have corrected. The students chose one of the four roles of cooperative work (they have experienced this in class prior in a different activity). The four roles were: facilitator, reader, checker, and recorder. Every student was required to be an encourager. As a group, they each calculated and re-solved the order. They figured the tax and tip according to the percent listed. Second, the students calculated the exact answer for the estimated page. They determine whether or not the estimation was within $1.00, $2.00, or more of the actual result. All four students compared their answers and checked one of the choices from the rubric. The recorder wrote down the reason the packet was put into the specific category. Each student had their packet checked and each student was able to help assess the other three students' packets.

Student Samples: (see attachments)

Why I chose this particular assessment to study:

I chose the particular assessment to study because I knew it was a creative and effective learning tool for students. However, I knew that there was more that could be done with it. In the past, I had the students complete it more as a class activity. What I did not include with it in the past was a form of self- or peer-assessment. In addition, I never included a way to check for comprehension of the standards. I went through the motions not really knowing if the students had completely learned the concept. I was able to make snapshot views of individual students learning as I walked around the room checking packets. Now, I have included important components to the activity making a truly authentic form of assessment. I am more clear on the exact standards which are being addressed. The students are more clear on the expectations. Better feedback and self-assessment is now a component which was lacking before. Overall, I took something which was mediocre and made it a successful learning and assessment tool. It was interesting to read in the course book, Student Assessment-as-Learning at Alverno College, on page 35, "If we have a favorite assignment that we have often given, but have never articulated criteria for, we might begin with that as a stimulus and then go back to criteria and relation to course outcomes." This is very similar to what I have explained as my reasoning for selecting this assessment to study!

Analysis of student performance on the assessment:

The results of the assessment were clumped into two levels. 75% of the students earned extremely high proficiency and 22% were not proficient. Only 3% of the students fell into a third category of low proficiency. Those 3% that fell into low proficiency were mostly due to not rounding to the nearest penny correctly and forgetting dollar signs. I do not feel that my rubric gave a fair assessment of the number of students who understood the concept of figuring tax and tip correctly. According to my rubric, if the students made a totaling error, they received not proficient. Also, according to my rubric if they made one mistake out of four for figuring tax and tip they were not proficient. After looking over all of the packets, the majority of students who received not proficient did accurately figure tax and tip on one page and then made a simple, sloppy error on the other page. Many students also were able to figure tip correctly but made a mistake on the tax. They used .5 instead of .055 for figuring 5.5% tax. I have since changed the rubric for next year (see attachment). Hopefully, this rubric will be a better form of assessing the students' work. I will reevaluate it next year. The three areas where most students seemed to make mistakes actually came from: 1.) not rounding to the nearest penny accurately, 2.) not figuring tax correctly (many students used .5 instead of .055 for 5.5% tax when figuring), and 3.) forgetting dollar signs and sloppy errors in general.

Follow-up Steps:

While many students already achieved high proficiency, a few students still need to work on being able to round money to the nearest penny correctly. Many students need to remember to put dollar signs on their money amounts. Also, a few students need more practice in figuring tax correctly. These concepts will continually be reinforced throughout the unit. The students will apply these to the lessons regarding mark-ups and discounts (percent of change). Again, simulation examples will be created by the students in the classroom to demonstrate how to mark-up or mark-down various items. The rules of rounding to the nearest hundredth will continually be reviewed throughout these simulations. The students will also go "shopping" in catalogs for items which need to be marked up or down (see example). This is another opportunity for the students to practice rounding correctly and to remember dollar signs. In addition, these concepts will be reinforced through lessons regarding commission and interest. Lastly, tax will be reviewed when we practice and discuss commission of total sales and inventories.

Second Assessment and Directions for Learners:

The students will be put into groups of four. They will choose a store to create. The choices, consists of a jewelry store, clothing store, sports store, electronics store, real estate company, and a car dealership. They will then create the stores on construction paper by cutting and pasting products from catalogs. The students will be shown examples of "stores." The students are also required to mark-down or "put on sale" eight items in their store. If they want to have a "sale rack," they can organize it in that fashion. Then the students randomly choose "roles." The roles consist of pretending to be various members of the community. Some examples of the roles are: 1.)married with five children, middle class, 2.) junior in college, on a tight budget, or 3.) famous actor/actress, rich, single. The students are instructed to shop according to their pretend roles. This is to simulate the "real world" population of shoppers. Finally, the students randomly choose percents for the commission under which they work. The students who choose the higher percents represent staff who has worked for the store or company longer. This shows a realistic example of the workplace. The students then take turns being store owners/clerks and shoppers!!! They need to use selling techniques to try to increase their sales and therefore their commission. In class discussion has taken place prior to the assessment covering various sales tactics. When the students are the store owners or clerks they are required to keep a inventory of their sales. They write down the sale, figuring in the sale price if necessary, and they figure the tax for the item to the nearest penny. They are required to use dollar signs for all money amounts.

Feedback and Self-Assessment:

Both the feedback and self-assessment are identical processes as presented earlier in the restaurant assessment (see rubric attached). The students peer-assess each others inventories. This simulates an accountant or bookkeeper reviewing your records. There is an added component or competition included where the student with the highest commission earns extra credit points. The students then fill out another reflection worksheet. They discuss the same previous points and they also discuss their desire to go into sales in the future for a career. These
reflections are then kept in their guidance career files.

Second Analysis of Student Performance:

There was a large improvement on the number of students who were able to accurately figure tax to the nearest penny. By practicing and repeating these concepts, a higher percentage of students were able to obtain extremely high proficiency on these standards. 97% of the students earned extremely high proficiency, 1% were medium proficiency, and 2% were not proficient. I individually reviewed how to figure commission with these students. I noticed a huge improvement in the understanding of figuring tax, rounding to the nearest penny, and being careful in totals, etc. The practice really showed in the students' ability to do the figures without help or review.

Questions Raised by this Analysis:

After reflecting upon the first assessment, I realized that the criteria/rubric which I created was not a useful tool in assessing the true
ability of each child. Therefore, I made changes on this assessment tool for next year. I will try the assessment again using this new rubric. It is
possible that I will need to tune it again. Overall, I was pleased with the better understanding the students had from the activity/assessment this year in comparison to previous years. In the past, I did not provide a rubric, time for self or peer-assessment, or reflection. I witnessed a much higher understanding of the standards this year. This experience really led me to believe in the powerfulness of sharing the standards and expectations with the students prior to teaching. This personal experience supports the information provided in class about standards (the slide show about a specific school district who immersed themselves in standards). Also, I saw the necessity of providing follow-up assessment for the students who did not achieve high proficiency the first time. I saw such growth in many students when allowed time to re-practice skills and concepts. The students figured tax and rounding money with better ease and ability during the store/commission assessment.

The Criteria or Rubric:

Original Rubric for Restaurant Assessment

Extremely High Proficiency:

The students accurately figured the tax and tip to the nearest penny (rounded correctly). The estimation tip was figured within a $1.00 limit of the exact answer. All totals were correct to the nearest penny. Dollar signs were used for all money amounts.

High Proficiency:

Medium Proficiency:

The students figured the tax and tip, but did not round to the nearest penny accurately. The estimation was figured within a $2.00 limit of the exact answer. All totals were correct, but were not rounded correctly to the nearest penny. Dollar signs were used for all money amounts.

Low Proficiency:

The students figured the tax and tip, but did not round to the nearest penny accurately. The estimation was not figured within a $2.00 limit of the exact answer. All totals were correct but were not rounded correctly to the nearest penny. Dollar signs were not used for all money amounts.

Not Proficient:

Estimations were more than $2.00 off of the accurate answer. Totals were written down. The page was completed.

The Criteria or Rubric:

Changed Rubric for Restaurant Assessment

Extremely High Proficiency:

High Proficiency:

Medium Proficiency:

The students figured the tax and tip, but did not round to the nearest penny correctly. The estimation was figured within a $2.00 limit of the exact answer. Dollar signs were not used for all money amounts.

Low Proficiency:

The students figured either the tax or the tip accurately. The tax and/or tip were not rounded to the nearest penny accurately. The estimation was more than $2.00 from the exact answer. Dollar signs were not used for all money amounts.

Not Proficient:

Estimations were more than $2.00 off of the accurate answer. Totals were written down. The page was completed.

The Criteria or Rubric:

Rubric for Store/Commission Assessment

Extremely High Proficiency:

The student accurately figured tax and commission to the nearest penny (rounded correctly). All totals were correct. Dollar signs were used for all money amounts.

High Proficiency:

The student accurately figured tax and commission to the nearest penny (rounded correctly). All totals were correct. Dollar signs were not used for all money amounts.

Medium Proficiency:

The student accurately figured tax and commission but did not round to the nearest penny accurately.

Low Proficiency:

The student accurately figured commission.

Not Proficient:

The student filled out the inventory sheet.

Check-off List
for
"Essentials for Assessment-as-Learning":

1.) Is it linked to the Menomonee Falls standards? YES, see pages one through three.

2.) Is the task authentic (something they might do outside of school)? YES, all students at one time or another have and will go out to restaurants with their family and friends.

3.) Does the assessment make clear what "counts" or given a standard of quality? YES, the students are shown several examples of the menus and they are shown several examples of how to solve the restaurant packets. They are shown the criteria prior to the assessment.

4.) Did the criteria/rubric use positive terms? YES

5.) Did the learners critique their own work? YES, the students were part of the peer group that critiques the packets. The students were able to defend their work. They were able to listen and participate in the assessment of their work. They were allowed time to reflect in writing.

6.) Were the students given feedback? YES, the peer group that assessed the packet with the given rubric gave verbal and written feedback
on the packets.

7.) Was there multiplicity? YES, the students participated in several activities and assessments which include figuring percents, rounding to the nearest penny, and using dollar and cent signs appropriately. These activities and assessments include: the restaurant assessment, written textbook and worksheet assignments, role playing in class, the catalog shopping worksheet, the store/commission assessment, and a written test.

8.) Can the students make a connection between what they are learning in class to "real world" life (externality)? YES, all students have been to and will go to restaurants and stores where they can witness the use of these skills.

9.) Is it cumulative in nature? YES, these activities and assessments require a culmination of skills to be successful.

10.) Is it expansive in nature? YES, (VERY!!!) the students can create a variety of menus in the restaurant assessment, they can act out any type of waiter or waitress, they get to act out various shoppers in the store assessment, they each get to use different selling skills which fit their personality in the shopping/commission assessment.