What are the types and orders of tests that you think will be the most efficient way to determine a type of unknown powder?
Use numeric and visual data to determine a chemical testing protocol for the CSI
Use decision modeling to design protocols for laboratory experiments
Make decisions about whether or not a solution meets the needs of a client
Communicate the solution clearly to the client
This activity has the potential to address many mathematics and science standards. Please see page 4-7 for a complete list of mathematics and science standards.
RECOMMENDED SUPPLIES FOR ALL MODEL-ELICITING ACTIVITIES
It is recommended to have all of these supplies in a central location in the room. It is recommended to let the students know that they are available, but not to encourage them to use anything in particular.
Overhead transparencies and transparency markers/pens or whiteboards and markers or other presentation tools such as a document camera.
Rulers, scissors, tape
Markers, colored pencils, pencils
Construction paper, graph paper, lined paper
Paper towels or tissues (for cleaning transparencies)
Manila folders or paper clips for collecting the students’ work
Optional: Computers with programs such as Microsoft Word and Excel
WHAT ARE MODEL-ELICITING ACTIVITIES (MEAs)?
Model-Eliciting Activities are problem activities explicitly designed to help students develop conceptual foundations for deeper and higher order ideas in mathematics, science, engineering, and other disciplines. Each task asks students to mathematically interpret a complex real-world situation and requires the formation of a mathematical description, procedure, or method for the purpose of making a decision for a realistic client. Because teams of students are producing a description, procedure, or method (instead of a one-word or one-number answer), students’ solutions to the task reveal explicitly how they are thinking about the given situation.
THE MYSTERY POWDER MEA CONSISTS OF FIVE COMPONENTS:
1) Newspaper article: Students individually read the newspaper article to become familiar with the context of the problem. This handout is on page 8.
2) Readiness questions: Students individually answer these reading comprehension questions about the newspaper article to become even more familiar with the context and beginning thinking about the problem. This handout is on pages 9.
3) Problem statement: In teams of three or four, students work on the problem statement for 45 – 90 minutes. This time range depends on the amount of self-reflection and revision you want the students to do. It can be shorter if you are looking for students’ first thoughts, and can be longer if you expect a polished solution and well-written letter. The handouts are on pages 10-12. Each team needs the handouts on pages 10-12.
4) Process of sharing solutions: Each team writes their solution in a letter or memo to the client. Then, each team presents their solution to the class. Whole class discussion is intermingled with these presentations to discuss the different solutions, the mathematics involved, and the effectiveness of the different solutions in meeting the needs of the client.
In totality, each MEA takes approximately 2-3 class periods to implement, but can be shortened by having students do the individual work during out-of-class time. The Presentation Form can be useful and is explained on page 4 and found on page 16.
5) Extra Materials: Pages 13-14 contain information regarding a link to the newspaper article, additional materials needed for the Mystery Powder MEA, and optional reading material you can choose to give students to provide further information on anthrax.
RECOMMENDED PROGRESSION OF THE MYSTERY POWDER MEA While other implementation options are possible for MEAs, it is recommended that the MEA be implemented in a cooperative learning format. Numerous research studies have proven cooperative learning to be effective at improving student achievement, understanding, and problem solving skills. In this method students will complete work individually (Newspaper article and readiness questions; as well as initial thoughts on the problem statement) and then work together as a group. This is important because brainstorming works best when students have individual time to think before working as a group. Students can be graded on both their individual and group contributions. Social skills’ discussion at the beginning of the MEA and reflection questions at the end of the MEA are also essential aspects of cooperative learning.
Social Skills (3 -5 minutes)
Students must be taught how to communicate and work well in groups. Several social skills that are essential to group work are decision- making, asking questions, and communicating and listening. The teacher can show part of a YouTube video and discuss aspects of these skills before beginning the MEA. (http://www.youtube.com/user/flowmathematics)
Newspaper Article and Readiness Questions:
The purpose of the newspaper article and the readiness questions is to introduce the students to the context of the problem.
(10 minutes): Give the article and the questions to the students the day before for homework. Then, in the next class, discuss as a class the answers to the readiness questions before beginning to discuss the problem statement.
You may want to read the problem statement to the students and then identify as a class: a) the client that the students are working for and b) the product that the students are being asked to produce. Once you have addressed the points above, allow the students to work on the problem statement. Let the students know that they will be sharing their solution to the rest of the class. Tell students you that you will randomly pick a group member to present for each group. Tell the students that they need to make sure that everyone understands their group’s solution so they need to be sure to work together well. The group member who will present can be picked by assigning each group member a number.
Working on the Problem Statement (35-50 minutes): Place the students in teams of three or four. Students should begin to work by sharing their initial ideas for solving the problem. If you already use teams in your classroom, it is best if you continue with these same teams since results for MEAs are better when the students have already developed a working relationship with their team members. If you do not use teams in your classroom and classroom management is an issue, the teacher may form the teams. If classroom management is not an issue, the students may form their own teams. You may want to have the students choose a name for their team to promote unity.
Teachers’ role:As they work, your role should be one of a facilitator and observer. Avoid questions or comments that steer the students toward a particular solution. Try to answer their questions with questions so that the student teams figure out their own issues. Also during this time, try to get a sense of how the students are solving the problem so that you can ask them questions about their solutions during their presentations.
Presentations of Solutions (15-30 minutes): The teams present their solutions to the class. There are several options of how you do this. Doing this electronically or assigning students to give feedback as out-of-class work can lessen the time spent on presentations. If you choose to do this in class, which offers the chance for the richest discussions, the following are recommendations for implementation. Each presentation typically takes 3 – 5 minutes. You may want to limit the number of presentations to five or six or limit the number of presentations to the number of original (or significantly different) solutions to the MEA.
Before beginning the presentations, encourage the other students to not only listen to the other teams’ presentations but also to a) try to understand the other teams’ solutions and b) consider how well these other solutions meet the needs of the client. You may want to offer points to students that ask ‘good’ questions of the other teams, or you may want students to complete a reflection page (explanation – page 4, form – page 15 in which they explain how they would revise their solution after hearing about the other solutions. As students offer their presentations and ask questions, whole class discussions should be intermixed with the presentations in order to address conflicts or differences in solutions. When the presentations are over, collect the student teams’ memos/letters, presentation overheads, and any other work you would like to look over or assess.
ASSESSMENT OF STUDENTS’ WORK
You can decide if you wish to evaluate the students’ work. If you decide to do so, you may find the following Assessment Guide Rubric helpful:
Performance Level Effectiveness: Does the solution meet the client’s needs? Requires redirection: The product is on the wrong track. Working longer or harder with this approach will not work. The students may need additional feedback from the teacher.
Requires major extensions or refinements: The product is a good start toward meeting the client’s needs, but a lot more work is needed to respond to all of the issues.
Requires editing and revisions: The product is on a good track to be used. It still needs modifications, additions or refinements.
Useful for this specific data given, but not shareable and reusable OR Almost shareable and reusable but requires minor revisions: No changes will be needed to meet the immediate needs of the client for this set of data, but not generalized OR Small changes needed to meet the generalized needs of the client.
Share-able or re-usable: The tool not only works for the immediate solution, but it would be easy for others to modify and use in similar situations. OR The solution goes above and beyond meeting the immediate needs of the client.
IMPLEMENTING AN MEA WITH STUDENTS FOR THE FIRST TIME
You may want to let students know the following about MEAs:
MEAs are longer problems; there are no immediate answers. Instead, students should expect to work on the problem and gradually revise their solution over a period of 45 minutes to an hour.
MEAs often have more than one solution or one way of thinking about the problem.
Let the students know ahead of time that they will be presenting their solutions to the class. Tell them to prepare for a 3-5 minute presentation, and that they may use overhead transparencies or other visuals during their presentation.
Let the students know that you won’t be answering questions such as “Is this the right way to do it?” or “Are we done yet?” You can tell them that you will answer clarification questions, but that you will not guide them through the MEA.
Remind students to make sure that they have returned to the problem statement to verify that they have fully answered the question.
If students struggle with writing the letter, encourage them to read the letter out loud to each other. This usually helps them identify omissions and errors.
OBSERVING STUDENTS AS THEY WORK ON THE MYSTERY POWDER MEA
You may find the Observation Form (page 15 useful for making notes about one or more of your teams of students as they work on the MEA. We have found that the form could be filled out “real-time” as you observe the students working or sometime shortly after you observe the students. The form can be used to record observations about what concepts the students are using, how they are interacting as a team, how they are organizing the data, what tools they use, what revisions to their solutions they may make, and any other miscellaneous comments.
PRESENTATION FORM (Optional)
As the teams of students present their solutions to the class, you may find it helpful to have each student complete the presentation form on page 16. This form asks students to evaluate and provide feedback about the solutions of at least two teams. It also asks students to consider how they would revise their own solution to the Mystery Powder MEA after hearing of the other teams’ solutions.
STUDENT REFLECTION FORM
You may find the Student Reflection Form (page 17) useful for concluding the MEA with the students. The form is a debriefing tool, and it asks students to consider the concepts that they used in solving the MEA and to consider how they would revise their previous solution after hearing of all the different solutions presented by the various teams. Students typically fill out this form after the team presentations.
NCTM Mathematics Standards
Numbers and Operations:
Compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line
Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules
Understand how mathematical ideas interconnect and build on one another to produce a coherent whole
Recognize and apply mathematics in contexts outside of mathematics
Create and use representations to organize, record, and communicate mathematical ideas
Use representations to model and interpret physical, social, and mathematical phenomena
NRC Science Standards
Use appropriate tools and techniques to gather, analyze and interpret data
Develop descriptions, explanations, predictions, and models using evidence
Think critically and logically to make the relationships between evidence and explanations
Recognize and analyze alternative explanations and predictions
Communicate scientific procedures and explanations
Use mathematics in all aspects of scientific inquiry
Substances react chemically in characteristic ways with other substances to form new substances (compounds) with different characteristic properties. In chemical reactions, the total mass is conserved. Substances often are placed in categories or groups if they react in similar ways
Science and Technology
Design a solution or product.
Implement a proposed design.
Evaluate completed technological designs or products.
Communicate the process of technological design.
Science in Personal and Social Perspectives
The potential for accidents and the existence of hazards imposes the need for injury prevention. Safe living involves the development and use of safety precautions and the recognition of risk in personal decisions. Injury prevention has personal and social dimensions.
Scientists and engineers work in many different settings, including colleges and universities, businesses and industries, specific research institutes, and government agencies.
Common Core State Standards
5.MD 1 Convert like measurement units within a given measurement system.
5.MD2 Represent and interpret data.
7.SP Use random sampling to draw inferences about a population.
1. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
2. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.
Draw informal comparative inferences about two populations.
3. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
4. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book
G-CO G-MG Apply geometric concepts in modeling situations
1. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).
2. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).
3. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).
S-IC Understand and evaluate random processes underlying statistical experiments
1. Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
2. Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?
Make inferences and justify conclusions from sample surveys, experiments, and observational studies
3. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
4. Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.
5. Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
Standards for Mathematical Practices integration with MEAs
How it occurs in MEAs
1. Make sense of problems and persevere in solving them.
As participants work through iterations of their models they continue to gain new insights into ways to use mathematics to develop their models. The structure of MEAs allows for participants to stay engaged and to have sustained problem solving experiences.
2. Reason abstractly and quantitatively
MEAs allow participants to both contextualize, by focusing on the real world context of the situation, and decontextualize by representing a situation symbolically.
3. Construct viable arguments and critique the reasoning of others.
Throughout MEAs while groups are working and presenting their models.
4. Model with mathematics.
This is the essential focus of MEAs; for participants to apply the mathematics that they know to solve problems in everyday life, society, or the workplace. This is done through iterative cycles of model construction, evaluation, and revision.
5. Use appropriate tools strategically.
Materials are made available for groups as they work on MEAs including graph paper, graphing calculators, computers, applets, dynamic software, spreadsheets, and measuring devices.
6. Attend to precision.
Precise communication is essential in MEAs and participants develop the ability to communicate their mathematical understanding through different representations including written, verbal, symbolic, graphical, pictorial, concrete, and realistic.
7. Look for and make use of structure.
Participants in MEAs can use their knowledge of mathematical properties and algebraic expressions to develop their solutions.
8. Look for and express regularity in repeated reasoning.
As participants develop their models the patterns they notice can assist in their model development.
Wall Street Journal Anthrax Scare: Newspaper Receives 10 Envelopes Containing White Powder
Colleen Long—The Huffington Post
January 21, 2009
NEW YORK — Authorities investigating white powder found Wednesday in envelopes at the Wall Street Journal in New York and Harvard Law School in Massachusetts said it was harmless.
Police evacuated about 250 people from the Journal's Manhattan newsroom and executive offices after about a dozen envelopes were found. FBI spokesman James Margolin said five employees were decontaminated as a precaution.
They had been released from quarantine and were in good health, a newspaper spokeswoman said.
A newspaper spokeswoman said the New York mail was addressed to several executives. The postmark was Knoxville, Tenn., but each letter had a different return address. Each contained a blank piece of paper with the powder.
The New York Police Department said the envelopes might be linked to mail with white powder, also declared harmless, sent Dec. 2 to Fox News and to a number of conservative media commentators. Additional tests will be done on the powder, which was thought to be flour.
The FBI in Knoxville said another letter with powder and a Knoxville postmark was received at Harvard Law School in Massachusetts, addressed to political commentator Alan Dershowitz. He recently published an opinion piece in the Journal defending Israel's actions in Gaza.
Police closed the fifth floor of the building that houses Dershowitz's office, and classes were moved to another part of the campus, a university spokesman said.
Harvard Law School said in a statement Wednesday evening that preliminary tests by the state police lab found the material was not hazardous, and the building would be open Thursday.
The FBI Joint Terrorism Task Forces in New York and Knoxville in partnership with the United States Postal Inspection Service were investigating the incidents. The Department of Homeland Security was monitoring the situation.
Why did the authorities need to test the powder?
Why is it important to be efficient when testing unknown substances?
What are some other reasons not in the article for why an unknown powder would have to be tested?
What are precautions you should take when testing an unknown powder?
Budget cuts require CSI department to make a new tool kit and manual for testing mystery powders
It was announced today that the CSI (crime scene investigation) unit will have its funding cut. The government has to make cuts everywhere and police units are included. One area that was deemed as having cost too much money was crime scene analysis. Too many tests were being run and processes were not efficient enough. Making sure that tests only have to be run if necessary will save money. Your job is to create a manual that has information that would help someone who works for CSI know what tests to run on an unknown powder. The manual should have an order of tests that you think will be the quickest way to determine a type of powder. The manual could have a different order of tests depending on the result of a test. Scientists try to get results with the fewest tests possible because materials for tests and the time to perform them cost money.
Read through the definitions below to help you. You will be given some powders to experiment with and a list of tests to conduct to help you find the most efficient order of tests to identify a powder. Write a letter to the head of the CSI department that describes your process for an order of tests you think will be the quickest way to determine the identity of a powder.
Density - the amount of mass in a cubic centimeter of volume. When the density of an object is greater than the density of the liquid it is in, the object will sink.
Acid –a sour substance, reacts with (corrodes) certain metals. Strong acids burn skin. Acids are 1 to 6.9 on the ph scale, the lower the number the stronger the acid.
Base –a bitter substance, slippery to the feel. Strong bases (higher numbers on the ph scale) burn skin. Bases are 7.1 to 14 on the ph scale.
Salt – The chemical reaction product when an acid and base combine. The other product is water.
pH Scale –a scale measuring how acidic or basic a substance is. A substance with a pH of 7 is neutral (neither acidic or basic). Below 7 is acidic. Above 7 is basic. Liquid or paper pH indicators change color (chemical change) when touching a substance that is either an acid or base. A color key shows how acidic or basic the substances are.
Chemical Reaction- when different kinds of substances come in contact and make new products. Signs that a chemical reaction have taken place:
1) a new substance is produced.
2) Energy (heat, sound, light) is absorbed or given off.
3) a gas or solid is formed.
Crystalline Solid – a solid made ofrepeating patterns of atoms that form a type of crystal shape. Salt is an example, forming cubic shapes.
Perform each of the following tests for each of the known powders, recording your observations in a data table. You may record any other observations you make while testing powders:
Color, Shape, Texture Test –
1. Put a spatula amount of known powder in a Petri dish, record color.
2. Spread a small amount to form a single layer and inspect with magnifying lens recording by drawing and/or words the shapes of particles you see.
3. Feel a small amount of the powder between your fingers, record how it felt…smooth, gritty, sticky.
Gross Density Test – place a spatula amount of powder into a beaker of water, record if the sample sinks (more dense than water) or not (less dense than water), and any other useful observations about its reactions with water.
Starch Test – on a small portion of your Petri dish powder sample put a drop of iodine and record if the iodine turns black (telling starch is present) or not.
Acid-Base Reaction Test – on a small portion of your Petri dish sample put a drop of vinegar (a weak acid) and record if a bubbling occurs, telling of a chemical reaction with a base. What is the product of the chemical reaction between an acid and base?
Litmus test –
Mix a small of your Petri dish powder sample with a couple of drops of water and either
Touch litmus paper to the mixture. Record the paper’s color, then use the key to determine acid (below pH of 7) or base (above pH of 7) and record results.
Put a drop of purple cabbage juice on. If the mixture turns green record the color and that it’s a base. If the mixture turns pink record the color and that it’s an acid.
Powders: baking powder*, baking soda, talcum powder, aspirin (pulverized), salt, sugar (crystal and powdered*), white bleached flour*. (*not necessary but interesting)
1. pH paper or red cabbage juice (shred cabbage and heat-not boil- in water…pour off purple water for use…turns green means base, pink means acid)
2. Iodine for starch indication (turns black when contacts starch)
3. Vinegar (weak acid) – to test for the presence of Sodium bicarbonate
4. Water – gross density test
Tools: Magnifying lenses, spatulas, beakers (indicator holders, density tests), test tubes, (powder holders), data table, Petri dishes (powder inspection, testing), eye droppers, paper towels.
Additional Information for Students (optional)
Chemical properties of materials are demonstrated in reactions with other materials. When liquids are added to powders, students can observe bubbles and fizzing that indicate that a gas has been formed by the reaction. Color changes can indicate the presence of particular substances. Many chemicals react differently when heated. Heating can cause both physical and chemical changes. Vinegar indicates the presence of carbonates by fizzing and bubbling. Carbon dioxide gas is produced in such reactions. (Baking soda and vinegar will produce this gas.) Iodine can be used to indicate the presence of a starch by turning purple. Cornstarch mixed with iodine solution shows this reaction. Heating sugar causes it to form a liquid and then turn black. This type of change does not occur when heating the other powders in this activity. Salt does not react with vinegar, and iodine does not form a liquid nor turn black when heated.
Timeline: Anthrax through the ages
(CNN) --Although it's surfacing anew as a terrorist weapon, the deadly anthrax disease has plagued the world for centuries, with reports of it dating back to biblical times.
Anthrax is blamed for several devastating plagues that killed both humans and livestock. Soon after scientists learned more about it in the late 1800s, it emerged in World War I as a biological weapon.
Several countries, including Germany, Japan, the United States, the United Kingdom, Iraq and the former Soviet Union, are believed to have experimented with anthrax, but its use in warfare has been limited.
1500 B.C. -- Fifth Egyptian plague, affecting livestock, and the sixth, known as the plague of boils, symptomatic of anthrax
1600s -- "Black Bane," thought to be anthrax, kills 60,000 cattle in Europe
1876 -- Robert Koch confirms bacterial origin of anthrax
1880 -- First successful immunization of livestock against anthrax .
1915 -- German agents in the United States believed to have injected horses, mules, and cattle with anthrax on their way to Europe during World War I
1937 -- Japan starts biological warfare program in Manchuria, including tests involving anthrax
1942 -- United Kingdom experiments with anthrax at Gruinard Island off the coast of Scotland. It was only recently decontaminated.
1943 -- United States begins developing anthrax weapons
1945 -- Anthrax outbreak in Iran kills 1 million sheep
1950s and '60s -- U.S. biological warfare program continues after World War II at Fort Detrick, Maryland
1969 -- President Richard Nixon ends United States' offensive biological weapons program. Defensive work continues
1970 -- Anthrax vaccine approved by U.S. Food and Drug Administration
1972 -- International convention outlaws development or stockpiling of biological weapons
1978-80 -- Human anthrax epidemic strikes Zimbabwe, infecting more than 6,000 and killing as many as 100
1979 -- Aerosolized anthrax spores released accidentally at a Soviet Union military facility, killing about 68 people
1991 -- U.S. troops vaccinated for anthrax in preparation for Gulf War
1995 -- Iraq admits it produced 8,500 liters of concentrated anthrax as part of biological weapons program
1998 -- U.S. Secretary of Defense William Cohen approves anthrax vaccination plan for all military service members
2001 -- A letter containing anthrax spores is mailed to NBC one week after the September 11 terrorist attacks on the Pentagon and World Trade Center. It was the first of a number of incidents around the country. In Florida, a man dies after inhaling anthrax at the offices of American Media Inc.
While the presentations are happening, choose TWO teams to evaluate. Look for things that you like about their solution and/or things that you would change in their solution. You are not evaluating their style of presenting. For example, don’t write, “They should have organized their presentation better.” Evaluate their solution only.
What I liked about their solution:
What I didn’t like about their solution:
What I liked about their solution:
What I didn’t like about their solution:
After seeing the other presentations, how would you change your solution? If you would not change your solution, give reasons why your solution does not need changes.
STUDENT REFLECTION FORM – Mystery Powder MEA
Name _________________________________ Date__________________________________
1. What mathematical or scientific concepts and skills (e.g. ratios, proportions, forces, etc.) did you use to solve this problem?
2. How well did you understand the concepts you used?
Not at all A little bit Some Most of it All of it
Explain your choice:
3. How well did your team work together? How could you improve your teamwork?
4. Did this activity change how you think about mathematics?