Using Technology to Study Cellular and Molecular Biology
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National Center for Research Resources

Using Technology to Study Cellular and Molecular Biology

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Teacher's Guide

Lesson 2—Explore, Explain

Resolving Issues

At a Glance

Overview

This lesson consists of two activities linked by classroom discussion. In the first activity, which is similar to the game Battleship, students investigate the concept of resolution and the relationship between probe size and resolution. The second activity incorporates results from the first activity and classroom observation and discussion. Students discover that in order to understand the complete structure of an object, it is necessary to have information in three dimensions rather than just two.

Major Concepts

Doing research in cellular and molecular biology requires scientists to identify the right technology (tool) for the job. An important consideration is the technology’s ability to resolve structural details of biological objects. Two objects can be resolved by using a probe (radiation) of a size (wavelength) that is not larger than the distance separating the objects. Generally, the smaller the probe, the greater the structural detail, or resolution, that results. Detailed structural knowledge about biological objects requires information obtained in three dimensions.

Objectives

After completing this lesson, students will

Teacher Background

See the following sections in Information about Using Technology to Study Cellular and Molecular Biology:
3.1 Scale
3.2 Resolution

In Advance

Web-Based Activities
Activity Web Version?
1 No
2 Yes
Photocopies
Activity 1
  • Master 2.1, Probing for Answers Score Sheet, 1 copy per 2 students; 1 transparency for classroom demonstration
  • Master 2.2, Probes, 1 copy per 12 students (see Preparation)
  • Masters 2.3 to 2.8, Probing for Answers—Levels 1–6, 1 copy of each per 12 or fewer students; 2 copies of each for 1324 students; 3 copies of each for 2536 students
Activity 2
  • Master 2.9, Solution to Probing for Answers, 1 transparency (print version only)
Materials
Activity 1 manila folders (1 per group, optional)
Activity 2
  • 2 hard-crusted bread rolls, unsliced
  • knife to slice bread
  • food coloring
  • syringe with needle, or 1-mL pipette

Preparation

Activity 1
From Master 2.2, Probes, cut out each 3 × 3, 2 × 2, and 1 × 1 square (1 copy produces 6 of each size of probe).

Activity 2
Just before the class period in which students will do this activity, inject a small amount of colored food dye into two locations in each of two unsliced, hard-crusted bread rolls. One location should be to the right of center and the other, to the left of center. The same or different dye colors can by used. Injecting the dye can be accomplished several ways to meet the primary objective, which is to color the inside and not the outside of each roll. Use either a syringe with a needle long enough to reach well into the roll or a carefully inserted 1-mL pipette. Wipe the outside surface of the needle or pipette to remove any dye solution before inserting it into the roll. It may help to use a sharp object, such as the sharp, pointed portion of a compass, to make a small hole before inserting a pipette containing dye. Try not to leave traces of the dye on the outside of the rolls.

If you have Internet access, have at least one computer at the URL http://science.education.nih.gov/supplements/technology/student. This is a main menu page from which you can access this activity.

Procedure

Activity 1: Probing for Answers

assessment icon
Assessment:
Steps 1 to 5 are intended to be a quick method to assess students’ prior conceptions about the use of technology in biological science.
  1. Begin by stating or writing on the board, “Technology is a means of extending human potential or of extending human senses.” Ask students to raise their hands if they agree with this statement.
  2. Ask students to provide justification for their responses. Can students relate specific technologies to the extension of specific human attributes or senses?

Students will generally agree that technology extends human potential. Obvious examples include the wheel and other transportation innovations that extend our potential for movement, and electronic devices, such as TV, radio, and telephones, that extend our ability to communicate. Microscopes, telescopes, eyeglasses, and contact lenses extend and enhance our sense of vision. Computers and written materials can be seen as ways to extend memory. There are many other examples.

Tip from the field test: Some students correctly pointed out that technology is also used to extend animal potential.

  1. Ask students to consider only technologies that have increased our understanding of living systems. Do they extend any human attributes? If they do, which attributes are extended?

Students will probably focus on those that extend vision, since they are the easiest to recognize. Examples could include radar, eyeglasses, contact lenses, and telescopes. Students also know that microscopes allow us to see objects that we cannot see with the naked eye. Students should be familiar with the light microscope, and many may have heard of electron microscopes. Through figures in textbooks, they may know X-ray crystallography as a technology that helped us “see” the structure of DNA. Other technologies might be mentioned. Accept all responses and write them on the board. This is an opportunity to identify students’ current understanding of these technologies.

A Gary Larson Far Side cartoon, “Early Microbiologists,” can be used to engage students. Pictured is a caveman “laboratory,” in which several cavemen peer intently into Petri dishes filled with agar. Since they do not have microscopes, they hold the dishes in various ways, such as very close to the face. One of the cavemen imitates binoculars by holding his hands to his eyes. (The cartoon can be found in several published works, including The Prehistory of the Far Side, by Gary Larson, copyright 1989 by FarWorks, Inc., distributed by Universal Press Syndicate, published by Andrews McMeel, Kansas City, Kansas.)

  1. Ask students to focus on technologies as tools that allow us to “see” biological objects (the eye, microscopes of all kinds, and X-ray techniques). One at a time, ask the following questions:
    1. What technologies would you use to study a whole (intact) organism and why?
    2. What technologies would you use to study cells and why?
    3. What technologies would you use to study molecules and why?

Accept all reasonable responses, but challenge those that are incorrect. Students should understand that no single technology is useful at all levels of organization of biological organisms. In other words, no single technology is able to resolve structural details from the intact organism to the molecules that make up that organism. This discussion introduces students to the idea that there is a right tool for the job.

National Science Education Standards icon
Content Standard A:
Identify questions and concepts that guide scientific investigations.
  1. Ask students why a single technology cannot provide information at all levels of organization of biological organisms.

You might remind students that at the conclusion of Lesson 1, they were asked to speculate on what would make one technology more useful than another in a given situation. If students need prodding, you can ask whether they would use a microscope to study a whole organism, or whether they would use their eyes alone to study molecules. While a microscope is required to study single-celled organisms, such as bacteria and protists, most multicellular organisms can be observed with the unaided eye. High-resolution technologies, such as X-ray crystallography, are required for investigations of molecular structure.

  1. Tell students that what makes some technologies better than others for a given job relates to the concept of “resolution.” Ask them what resolution means.

Tip from the field test: Students generally had no concept of resolution as it relates to technologies used in biological science. Responses often related to resolution of computer monitors, personal resolve, or New Year’s resolutions.

  1. Tell students that they will investigate resolution. Organize the class into groups of two and then pair two groups.

This activity works best if you have a minimum of six groups so that each can receive one of the six Masters 2.3 through 2.8.

  1. Ask groups to arrange their seating so that one is directly opposite another:
Diagram of seating arrangement for this activity, showing three tables for six groups.

Allow sufficient room between tables so that groups do not interfere with one another.

  1. Explain to the class that this activity resembles the game Battleship, with which some of them might be familiar. Each group’s task is to locate and define the shape of an object or objects on the master held by the opposing group.

Tip from the field test: Field-testing indicated the need to point out that this activity is not exactly like Battleship. Students do not “sink” or “destroy” an opposition’s force. Rather, they use the Battleship strategy to locate and define the shape of a shaded region or regions on the master held by an opposing group.

  1. Give each group a copy of Master 2.1, Probing for Answers Score Sheet.

Students use this sheet to record hits and misses as they probe for the location of the opposing group’s shaded region(s).

  1. Randomly color several regions on a transparency of Master 2.1, Probing for Answers Score Sheet. Use this transparency and a 3 × 3 probe from Master 2.2, Probes, to demonstrate how this activity is done.
    1. Use this probe to locate areas 3 squares by 3 squares on the transparency. To save time, you may instruct students to probe only the nine nonoverlapping 3 × 3 regions, as shown on the following diagram:

      Diagram of Probing for Answers score sheet, divided into 9 rows of 9 squares each, labeled A to I horizontally and 1 to 9 vertically. The sheet is divided into sections of 3 squares by 3 squares, labeled 1 through 9 from the top left across and then down, with alternating sections shaded.
    2. One group begins by calling out the location of the 3 × 3 area they wish to probe, such as A-C, 1-3.
    3. If the opposing group’s Master (2.3, 2.4, 2.5, 2.6, 2.7, or 2.8) has a shaded square within the area called, they indicate this as a hit; if not, a miss.
    4. The first group records the result on their score sheet. Draw an X in 3 × 3 squares that are misses, and put an O in the 3 × 3 squares that are hits.
    5. It is then the opposing group’s turn to select an area to probe, which is then recorded as a hit or a miss.
    6. Groups take turns trying to locate the opposing group’s shaded squares
  1. Give each group a copy of one master selected from Masters 2.3 to 2.8. Instruct groups to hide this master from their opposing group.

Make sure that each of these six masters is used by at least one group. In larger classes, the same master may be used by more than one group. You may choose to place each master in a manila folder. Students can use the folder in various ways (for instance, opened and stood on its edge) to keep their master from being seen by the opposing group.

  1. Give each group a 3 × 3 probe from Master 2.2, Probes. Instruct students to use this probe to locate areas 3 squares by 3 squares that contain the opposing group’s shaded area(s).

Limit the time allowed for this portion of the activity to no more than five minutes.

  1. Ask students whether they believe they have gathered enough information to specify the exact shape(s) and location(s) of the opposing group’s shaded object(s).

Make sure students in opposing groups do not share information about their shaded patterns. Students should realize from looking at their own shaded pattern that the 3 × 3 probe is too large to identify the shape and location of smaller objects; that is, the large probe cannot resolve the size and shape of the smaller objects.

  1. Ask students what would help them define the shape and location of the opposing group’s shaded object(s).

A smaller probe is required.

Tip from the field test: Field-testing indicated the importance of having students come to this conclusion on their own.

  1. Next, give each group a 2 × 2 probe. Groups are to focus on those areas that were determined to be hits with the larger probe.

Students are to repeat with this probe what they did earlier (see Step 13 above) and try to determine the structure and location of the opposing group’s shaded pattern. Limit the time allowed for this portion of the activity to no more than several minutes.

  1. Ask students whether they believe they now have enough information to specify the exact shape(s) and location(s) of the opposing group’s shaded object(s).

Make sure students in opposing groups do not share information about their shaded patterns. At this point, some students may believe they have sufficient information to predict the pattern held by the opposing group. Ask those willing to speculate on the opposing group’s pattern to provide their justification, especially how they know that all four squares in a 2 × 2 “hit” region are shaded.

  1. Next give each group a 1 × 1 probe.

Students should focus only on those areas determined to be hits with the 2 × 2 probe. They should continue to define the structure and location of the opposing group’s shaded pattern. Limit the time allowed for this portion of the activity to no more than several minutes.

  1. Ask students if they believe they now have gathered enough information to specify the exact shape(s) and location(s) of the opposing group’s shaded objects. Do they need another probe to complete the task?

Students should justify their responses. Students cannot know for sure what the opposing group’s pattern looks like, even though they see that their own pattern is composed of 1 × 1 squares. If they speculate that the opposing group’s pattern is constructed similarly, then no additional probes are required, since the objects being resolved (the 1 × 1 squares, both shaded and unshaded) are the same size as the final probe. Importantly, the final probe is not larger than the objects being resolved. If students believe that additional probes are required, they should justify this based on what they believe to be the size of the objects being resolved (shaded and unshaded). Their suggestion for an additional probe should indicate a probe size no larger than that of the objects being resolved. No matter what the response, ensure that students derive a general relationship between probe size and the size of the objects being resolved before proceeding. They should be able to explain that the size of the probe should be no larger than the objects being resolved.

assessment icon
Assessment:
Listening to students explain their answers, defend their reasoning, and modify their responses after listening to other students explain their logic will help you assess students’ understanding of resolution.
  1. Have opposing groups confirm that after using the series of three probes, they were able to determine the correct pattern on one another’s master.

Discussion Questions

  1. Why not use the smallest probe first?

A similar question is, Is there an advantage to using larger probes first and then using smaller probes? The larger probes allowed the students to quickly identify the general location of the object(s) being investigated. In some cases, even information about structure, albeit crude, can be obtained. Remind students of the procedure they follow when using a light microscope. They first use the lowest magnification to locate the object of interest and then switch to a higher magnification to gain more information. Using the smallest possible probe first can be time consuming and expensive. In some cases, using the smallest available probe also can be inappropriate—for example, when the probe is very much smaller than the objects being resolved. As an example, consider the time and expense involved in using an electron microscope rather than a light microscope to count yeast cells or to assess fruit fly traits in a genetics experiment.

  1. On the board, write these wavelengths:

Refer to Master 1.1, Searching for Scale, and ask students which of these they think would be appropriate probes (that is, provide the appropriate level of resolution) for the objects listed.

Visible light could be used to resolve cells, bacteria, and mitochondria. Longer-wavelength electrons are potential probes for viruses, small cell organelles such as ribosomes, and large molecules such as proteins. Shorter-wavelength electrons and short-wavelength X-rays are potential probes for molecules, even small ones like glucose. They also may be used to resolve adjacent atoms in molecules (which requires probes smaller than 2 × 10–10 m).

Teacher note: Whether or not a probe is useful in a given situation also depends on whether the technology actually exists to make use of the probe. For instance, are appropriate sample preparation techniques available? Are appropriate sample handling technologies available (for example, can the sample be rotated if necessary, and in a way that does not interfere with the rest of the procedure)? Can the probe be focused sufficiently? Is there technology to view and evaluate the results of such analyses?

Activity 2: More Than Meets the Eye

  1. Begin by holding one of the bread rolls up to the class. Make sure that no dye is showing. Ask students to describe what they see.

Students will recognize the object, and they may describe it by noting its color, shape, and apparent external texture. They should indicate that the roll is a three-dimensional object.

  1. Do students have maximum information about the roll? Is there anything they do not know about the bread roll from just looking at it?

Student responses will vary from, “Is it tasty?” and “Where does it come from?” to “What is inside?” Some students may realize that although they might have made an assumption about the roll’s interior (for example, it is just plain bread), they actually know nothing about what is under the crust.

  1. Focus discussion on what is inside the bread roll. Ask students how they would get that information.

Students will suggest cutting or tearing the roll.

  1. Slice the roll to reveal the presence of dye in one of the two dye locations. Hold the roll so the class can see the two cut edges. Do the students now feel they have complete information about this object? If not, what questions do they have?

Even though they know there is a dyed region inside the roll, students should realize that they do not know what this region looks like. What is the shape of the dyed region and how far does it extend in any given direction? Is there only a single dyed region, or are there multiple regions? If there is more than one dyed region, is it the same color as the region they can see?

Tip from the field test: Some students suggested cutting the roll as one would if making a sandwich. The second bread roll is helpful if this possibility is raised.

Illustration of the roll used for this experiment being cut open vertically.
  1. Ask students how they could obtain information to answer these questions.

A simple approach would be to make additional slices in the roll. Students may suggest more exotic means (for example, use a fiber optic light source connected to a minivideo device to view the roll’s interior on a remote screen). If suggestions fall in the latter category, congratulate students for their ingenuity. Ask them to think about how to gain the information required quickly and using simple, available technology. In the end, focus student attention on increasing the number of slices. This requires only a knife and can be done quickly.

  1. Ask the students how many slices would be required to define the dyed region(s) in the roll’s interior. What are their considerations in providing an answer to this question?

The actual number of slices that the students believe is correct is not the important issue. If students do provide a specific answer, ask them to justify it. It is important for them to understand the following. First, multiple slices are required to define the object’s properties. The size of the slices will determine the resolution used to define the object’s properties. Thicker slices will provide less resolution, just as the 3 × 3 probes provided low resolution in Activity 1. Thinner slices will provide greater resolution, just as the 1 × 1 probes did in Activity 1.

  1. Ask students to have their group’s Master 2.3 to 2.8 available. Explain that the “level” designation below the grid (Level 1, 2, 3, 4, 5, or 6) on the master indicates the location of a slice through an object.

Level 1 is the top slice, followed by 2, 3, 4, 5, and 6 (at the bottom).

  1. Ask students to visualize their pattern in three dimensions by imagining that their shaded pattern represents the top of a stack of gray blocks. Their level is a slice two blocks thick.
  2. Ask the groups to share their data (that is, the location of the shaded regions) and try to reconstruct the three-dimensional object that has been cut into six slices.

Do not provide additional guidance. Give students about five minutes to do this. Students may or may not be able to reconstruct the object in this time.

National Science Education Standards icon

Content Standard E:
Identify a problem or design an opportunity.

Content Standard E: Implement a proposed solution.

Content Standard A: Scientists rely on technology to enhance gathering and manipulating data.

For those using the Web version of this activity, proceed as follows:

  1. Were students able to arrive at a solution? What might have made the task of reconstructing the object in three dimensions easier?

Students might suggest that a computer could provide the technology to make reconstruction easier.

  1. Have students proceed to the URL http://science.education.nih.gov/ supplements/technology/student. Students should then click on the link to “Lesson 2—Solution to Probing for Answers.” This brings up the unit’s desktop, from which students can access this activity.
  2. Students can enter their data by first selecting a level (1 to 6) and then clicking on the squares they determined to be shaded. The reconstructed object will appear as data are entered.

It may be easier and less time consuming for the teacher to enter the data provided by the students.

National Science Education Standards icon

Content Standard E:
Identify a problem or design an opportunity.

For those using the print versionof this activity, proceed as follows:

  1. Show students a transparency of Master 2.9, Solution to Probing for Answers. Were they able to arrive at this solution? What might have made their task easier?

Some students do well thinking in three dimensions, and others do not. Many may recognize the need for additional technology, such as a computer and appropriate software, to make the job of reconstruction easier. Even a simple technology, such as wooden blocks or Legos, could have been used to construct a three-dimensional model of the intact object.

Discussion Question

assessment icon
Assessment:
This question allows students to integrate the information they have learned in the first two lessons and refine their understanding of what technology is.

  1. As a follow-up, ask students, “Have these activities expanded your understanding of technology? If they have, how?”

Activity 1 demonstrates the use of multiple probes to achieve different levels of resolution. It also demonstrates that the right tool, in this case a probe of appropriate size, must be selected to solve a problem (resolving the structure of an unknown object). Therefore, students should realize that there is an appropriate technology for a given problem (that is, the right tool for the job). Activity 2 demonstrates that solutions to a problem may involve more than one technology (the use of slices to determine the structure of a three-dimensional object and technologies to collect and analyze the data).

Web activity icon Lesson 2 Organizer: Web Version
Activity 1: Probing for Answers
What the Teacher Does Procedure Reference
State or write on the board, “Technology is a means of extending human potential or of extending human senses.”
  • Ask students if they agree with this statement.
  • Ask students to provide justification for their responses. Can they relate specific technologies to the extension of specific human attributes or senses?
  • Ask students to consider technologies that haveincreased our understanding of living systems.
    • Do they extend any human attributes?
    • If they do, which attributes are extended?
Steps 1–3
Ask students to focus on technologies (the eye, microscopes, X-ray techniques) that allow us to see biological objects. Ask,
  • “What technologies would you use to study a whole organism and why?”
  • “What technologies would you use to study cells and why?”
  • “What techniques would you use to study molecules and why?”
  • “Why can't a single technology provide information at all levels of organization of biological organisms?”

Introduce the concept of resolution. Ask students what resolution means.

Steps 4–6
Tell students that they will investigate resolution. Organize the class into groups of two and then pair two groups.
  • Arrange seating so that one group sits opposite the other.
  • Explain that the activity resembles the game Battleship.
  • Each group's task is to locate and define the shape of an object or objects on the master held by the opposinggroup.
  • Give each group a copy of Master 2.1, Probing for Answers Score Sheet.
  • Use a transparency of this master to demonstrate how the activity is done.

master icon

transparency icon

Steps 7–11

Begin the activity.
  • Give each group one master selected from Masters 2.3 to 2.8, Probing for Answers—Levels 1–6.
  • Give each group a 3 × 3 probe from Master 2.2, Probes. Instruct students to use this probe to locate areas 3 squares by 3 squares that contain the opposing group's shaded object(s).
  • After five minutes, ask students if they have enough information to specify the exact shape(s) and location(s) of the opposing group's shaded object(s).
  • Ask students what would help them define the shape and location of the opposing group's shaded object(s).
  • Give each group a 2 × 2 probe and ask them to refine their search with this probe.
  • After several minutes, ask students if they believe they now have enough information to specify the exact shape(s) and location(s) of the opposing group's shaded object(s).
  • Give each group a 1 × 1 probe and ask them to refine their search with this probe.
  • After several minutes, ask students if they believe they now have enough information to specify the exact shape(s) and location(s) of the opposing group's shaded object(s). Do they need another probe to complete their task?
  • Have opposing groups confirm that after using the series of three probes, they were able to determine the correct pattern on one another's master. Proceed to discussion questions.
master icon

Steps 12–20

Activity 2: More Than Meets the Eye
What the Teacher Does Procedure Reference
Hold a bread roll into which you have inserted food dye up to the class.
  • Ask students to describe what they see.
  • Is there anything about the roll they do not know from just looking at it?
  • Focus discussion on what is inside the roll and ask students how they would get that information.
  • Slice the roll to reveal the dye.
  • Ask students if they feel that they now have complete information about the object.
  • What additional questions do they have and how could they get the answers?
  • How many slices are required to define the dyed region(s) in the roll's interior? Focus discussion on resolution.
Steps 1–6
Ask students to have their Master 2.3 to 2.8 available.
  • Explain that the “level” designation on the master indicates the location of a slice through an object (1 at the top to 6 at the bottom).
  • Ask students to visualize their pattern in three dimensions by imagining that their shaded pattern represents the top of a stack of grey blocks. Their level is a slice two blocks thick.
  • Ask the groups to share their data (that is, the location of the shaded regions) and try to reconstruct the three-dimensional object that has been cut into six slices.
  • Ask if students were able to arrive at a solution. What might have made their task easier?
Steps 7–10
Have students click on “Lesson 2—Solution to Probing for Answers” and then click on the link to “Solution to Probing for Answers.” Have students enter their data to reconstruct the object.
Web activity icon

Steps 11–12

master icon= Involves copying a master. Web activity icon= Involves using the Internet.

transparency icon= Involves using a transparency.

 

 

print activity icon Lesson 2 Organizer: Print Version
Activity 1: Probing for Answers
What the Teacher Does Procedure Reference

State or write on the board, “Technology is a means of extending human potential or of extending human senses.”

  • Ask students if they agree with this statement.
  • Ask students to provide justification for their responses. Can they relate specific technologies to the extension of specific human attributes or senses?
  • Ask students to consider technologies that have increased our understanding of living systems.
    • Do they extend any human attributes?
    • If they do, which attributes are extended?
Steps 1–3

Ask students to focus on technologies (the eye, microscopes, X-ray techniques) that allow us to see biological objects. Ask,

  • “What technologies would you use to study a whole organism and why?”
  • “What technologies would you use to study cells and why?”
  • “What techniques would you use to study molecules and why?”
  • “Why can't a single technology provide information at all levels of organization of biological organisms?”

Introduce the concept of resolution, Ask students what resolution means.

Steps 4–6

Tell students that they will investigate resolution. Organize the class into groups of two and then pair two groups.

  • Arrange seating so that one group sits opposite the other.
  • Explain that the activity resembles the game Battleship.
  • Each group's task is to locate and define the shape of an object or objects on the master held by the opposing group.
  • Give each group a copy of Master 2.1, Probing for Answers Score Sheet.
  • Use a transparency of this master to demonstrate how the activity is done.

master icon

transparency icon

Steps 7–1

Begin the activity.

  • Give each group one master selected from Masters 2.3 to 2.8, Probing for Answers—Levels 1–6.
  • Give each group a 3 × 3 probe from Master 2.2, Probes. Instruct students to use this probe to locate areas 3 squares by 3 squares that contain the opposing group's shaded object(s).
  • After five minutes, ask students if they have enough information to specify the exact shape(s) and location(s) of the opposing group's shaded object(s).
  • Ask students what would help them define the shape and location of the opposing group's shaded object(s).
  • Give each group a 2 × 2 probe and ask them to refine their search with this probe.
  • After several minutes, ask students if they believe they now have enough information to specify the exact shape(s) and location(s) of the opposing group's shaded object(s).
  • Give each group a 1 × 1 probe and ask them to refine their search with this probe.
  • After several minutes, ask students if they believe they now have enough information to specify the exact shape(s) and location(s) of the opposing group's shaded object(s). Do they need another probe to complete their task?
  • Have opposing groups confirm that after using the series of three probes, they were able to determine the correct pattern on one another's master. Proceed to discussion questions.
master icon

Steps 12–20

 

Activity 2: More Than Meets the Eye
What the Teacher Does Procedure Reference
Hold a bread roll into which you have inserted food dye up to the class.
  • Ask students to describe what they see.
  • Is there anything about the roll they do not know from just looking at it?
  • Focus discussion on what is inside the roll and ask students how they would get that information.
  • Slice the roll to reveal the dye.
  • Ask students if they feel that they now have complete information about the object.
  • What additional questions do they have and how could they get the answers?
  • How many slices are required to define the dyed region(s) in the roll's interior? Focus discussion on resolution.
Steps 1–6
Ask students to have their Master 2.3 to 2.8 available.
  • Explain that the “level” designation on the master indicates the location of a slice through an object (1 at the top to 6 at the bottom).
  • Ask students to visualize their pattern in three dimensions by imagining that their shaded pattern represents the top of a stack of grey blocks. Their level is a slice two blocks thick.
  • Ask the groups to share their data (that is, the location of the shaded regions) and try to reconstruct the three-dimensional object that has been cut into six slices.
  • Show students a transparency of Master 2.9, Solution to Probing for Answers.
  • Ask if students were able to arrive at this solution. What might have made their task easier?

master icon

transparency icon

Steps 7–10

master icon = Involves copying a master. transparency icon = Involves using a transparency.  

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