In this MEA, students must select which material to use in the development of an advanced military scout robot. Students must analyze data about each material’s individual properties that would make it a valid choice for military or police service. Students must complete calculations to determine material density as well as the overall mass and weight of the robot. This lesson focuses on the characteristic properties of density, unit conversion, and differentiating between mass and weight.
Subject(s): Science, Mathematics, English Language Arts
The comprehension readiness questions and reflection questions can be used as formative assessment (for questions, see the Readiness questions section). Readiness questions will indicate whether the students understand the problem and the problem context. The readiness questions are asked of students after they read the attached client letter 1. If desired, the teacher can ask the class to respond to these questions and ensure understanding before students begin working with the data.
Feedback to Students
See Lesson Plan in the "Instructional Suggestions" section. Sections for feedback and class discussion have been indicated.
See attached rubric or grade each set of response letters and completed data charts as individual assessments for each group.
Differentiate between weight and mass by using mathematical calculations to show both the difference between the two values, as well as their direct relation to one another. Students will be able to explain that weight is a measure of the force of gravity acting upon an amount of mass.
Explore and describe the densities of various materials through measurement of their masses and volumes.
Classify and compare substances on the basis of the characteristic physical property of density as determined by measurable quantities such as mass and volume.
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations to solve these problems.
Produce clear and coherent writing as organized and styled to be appropriate for a professional audience with response to a specifically requested task.
Students must be comfortable with multiplication and division using integers and decimal values. A very basic understanding of variables represented as letters, such as used in the Density=Mass/Volume equation (D=m/V) is needed for this lesson.
Students must understand mass, volume, and the force of gravity before starting this lesson. The concepts of weight and density should have been introduced prior to this lesson. Reinforcing an understanding of both weight and density is the main scientific focus of this lesson.
This lesson is intended to be completed in 1.5 block days (approx. 3 hours). The lesson plan indicated below is presented in time-oriented breakdown:
(0-10 min.) Begin class with quick review of the concepts of mass, volume, weight, and density. The BrainPop "Measuring Matter" video or StudyJams "Properties of Matter" video are both excellent review sources. If you do not have access to these, a class discussion, read aloud (from an appropriate selection of text), or other video review would be appropriate.
(11-20 min.) Complete the BrainPop or Study Jams post-lesson quiz as a class. Do sample calculations of density using mass and volume on the board together as well.
(21-25 min.) Introduce the MEA lesson concept: Your students' help has been requested by the company Military Dynamics for the development of a new reconnaissance (scout) robot. Inform students that they will be completing mathematical calculations and assessing physical properties. Arrange students in groups of 3-4 to prepare for the project. (It may be helpful to have predetermined groups ready)
(26-30 min.) Pass out the Client Letter 1 and Data Set 1 sheets to each group. Allow students in each group to read the client letter.
(31-40 min.) Use the readiness questions to be sure each group understands the assignment. The first thing each group will have to do is to complete the missing information from their data chart. After completing the chart, the students must select which material they think is best for the robot based on the information presented in the Client Letter. They must develop a ranking system and be able to explain why they made their particular selection.
(41-50 min.) Equations & Unit Conversion: Density = Mass x Volume OR Mass = Density x Volume
Complete a sample problem or two with the class indicating the proper calculation of these values.
Note: The data chart given to students has the volume listed in Liters (L), the mass listed in kilograms (kg), and the density is listed in (g/cm3). Show students that 1 g/cm3 is the same value as 1kg/liter, because 1 kg is 1000g, and 1 liter is 1000 cm3. This allows a very simple calculation of Mass, requiring students to only multiply the indicated Density by the Volume. Don't let students forget that they will have to add +10kg to the mass, because the data indicates that the internal components of the robot have a mass of 10kg.
(51-80 min.) Once the students understand what is requested of them, allow them to work in their groups. At the end of this time, each group should have both filled out the data chart and made a material selection. They should have a written explanation of the steps used to make this selection. Use the guiding/reflective questions to guide students to a proper understanding.
(81-90 min.) Students must complete a response letter indicating the ranking system used to make their selection of the robot's body material. You may use Response Template 1.
Math assistance option (51-70 min.): As a class, work with your students on the board to properly complete the calculations for the density, total mass, and total weight columns of the data chart. While doing sample calculation, discuss the guiding/reflective questions to guide students to a proper understanding.
Math assistance option (71-80 min.): Once the data chart has been completed, allow your students to work in their groups to select which material they would use for the robot. Now, the students complete a response letter indicating the ranking system used to make their selection of the robot's body material. If the development of the ranking system is too complex for your students, you may also choose to do this section as a class, or simply allow the students to write a paragraph explaining why they feel their selected material is the best option.
(91-100 min.) Collect student response letters and data charts. Next, pass out collected data charts to different groups of students, so that each group has a paper completed by a separate group of students.
Indicate that the members of the correcting group must write their name at the bottom right-hand corner of the data chart, preferably in red pen. Allow the students of these groups to review and correct the data chart of the other group.
(101-110 min.) After you have allowed each group the opportunity to check over their classmates' work, project the teacher's edition of the Data Set 1 - Teacher overhead. Go over each section of the data chart to make sure every group knows the proper numerical value for each data block. Use this time to review any errors in calculations. Once all data has been reviewed, have the students indicate the number of data blocks that the other group calculated correctly at the top of this paper. Circle this value.
There are 10 blank data blocks on the data chart. If a group correctly calculated 7 blocks, their paper should have a "7" at the top of the paper in a circle. Collect the graded papers.
(111-120 min.) Wrap up: Ask students which choice they made and why they chose it. Did any students make a selection based upon damage resistance? What about replacement time? What did your students think about this robot? How do they think it will be used? This should be a fun discussion with the class to keep them mentally engaged without them feeling too much pressure.
Block Day 2
(0-10 min.) Inform your students that you have heard back from Military Dynamics. They have more work for you! Arrange your students in the groups from the first section of this MEA. Pass out Client Letter 2 and Data Set 2. Allow students in each group to read the client letter.
(11-20 min.) Once again, the group will have to complete the missing information from their data chart. After completing the chart, the students must select which material they think is best for the robot based on the updated information presented in the Client Letter 2.
If needed, use this time to once again review the calculation of density, mass, volume, or weight to assist them with their new data chart.
(21-40 min.) Once the students understand the new requirements, allow them to work in their groups. At the end of this time, each group should have both filled out the data chart and made a material selection. They should have a written explanation of the steps used to make this selection.
Use the guiding/reflective questions for Part 2 to help students update or modify their choice or ranking system as needed.
(41-50 min.) Students must complete a response letter indicating the ranking system used to make their selection of the robot’s body material. You may use the Response Template 2.
(51-60 min.) At this point, the teacher may elect to do either of the following:
Collect all of the student response letters then have each group correct and grade another group's data chart. Project and review the answers as a class using the Data Set 2 - Teacher.
Collect all data charts and student response letters. These materials will be graded by the teacher. Project the completed data Chart 2 overhead and discuss/review the proper calculations.
(61+ min.)TheMEA has been completed. If using block scheduling, this allows you approximately 1 hour of the same class day to review concepts with the class, do reading on related topics, watch an educational video, or any other desired lesson reinforcement.
For classes with low-level mathematics students, this extra time may be introduced into the lesson plan, extending the time and methods used to assist your students with calculations and unit conversions, or further covering the conceptual difference between mass and weight.
What piece of data from the chart do you feel is most important for the robot? Why do you think so?
Which statistic do you think is least important? Why do you think it is not important?
Can you explain the process you used to make your selection?
Which material provides the greatest amount of protection for the robot?
How do you calculate the total mass of the robot?
Which material provides the robot with the lowest total weight?
Sample Answers to Guiding/Reflective Questions:
We feel that the most important piece of data is the damage resistance because the robot can't help anybody if it gets blown up by the enemy.
We think the service life is the least important statistic because the army can just buy a new robot and the army has a lot of money.
In our selection process, we decided which piece of data in each column was the best. We then calculated which of the materials had the highest amount of "best" selections. The material with the most is the one that we selected.
The stainless steel provides the highest amount of protection.
The total mass of the robot is calculated by multiplying the volume of the robot times the density of the robot. After you get that answer, you have to add 10kg for the internal parts of the robot to get the total mass in kilograms.
The material with the lowest total weight is Carbon-Fiber.
What things do you need to include in your solution?
Do you think there is more than one correct answer to what the client is asking? Why or why not?
Sample Answers to Readiness Questions:
We have to put a list of materials used to make the body of a robot in order from best to worst.
Our client is a company called Military Dynamics.
Our client wants us to look over information about the materials used to make a robot and make a rating system to help us decide which material is the best one to use.
We need to include the order that we ranked the materials and why we put them in that order. We also have to include a step-by-step process that explains how we made our decision.
Yes, I think there is more than one correct answer because some of the materials last longer and some are more protective, and some of them may be really heavy for a person to carry. A heavy robot might not be good for the soldier to carry, but it might be really good to use if it gets shot by bad guys.
Did you have to make any changes to your ranking system after receiving the second letter? Explain why you did or did not have to do so. (This question will be covered in the response letter)
What do you think this robot looks like?
Accommodations & Recommendations
As indicated in the "Instructional Suggestions" – this lesson allows for a 60 minute time extension to be completed in 2 full blocks if needed due to any modifications or accommodations your students may require.
As indicated in the "Instructional Suggestions." If focusing more on the mathematics of this lesson, it is suggested that extra time and attention be placed on proper completion of the data chart. A follow-up lesson involving reinforcement of unit conversions could be helpful.
If focusing on the scientific aspects of density, mass, volume, and weight, a follow up hands-on lab calculating the densities of various items is strongly suggested.
Suggested Technology: Computer for Presenter, Basic Calculators, LCD Projector, Microsoft Office
Special Materials Needed:
While this MEA can be completed without any assistance from computers or technology if needed, overhead projection from a computer and promethean board will make instruction and review of data much easier for the teacher and students.
This MEA is designed to be used in either a 7th or 8th grade science or mathematics class. If focusing more on the mathematics, this lesson aligns most closely to the 7th grade math standards. It focuses on unit conversion, specifically between mass and weight in the SI system, as well as calculation of mass using density and volume. These calculations involve multiplication and division of decimals.
If focusing more on the scientific aspects, the lesson aligns with the 8th grade science standards of properties of matter. However, the difference between mass and weight is covered in 6th and 7th grade science as well. The concept of density may be introduced in the 6th and 7th grade levels, just with less focus than the 8th grade pacing guide.
I personally feel that this MEA most properly suits an 8th grade science class working on density, while also using it as a review and refresh of 7th grade math concepts. It would also function well in a 7th or 8th grade physical science class.