I. Curricular Framework

Concept:

Ratios

Essential Question:

How does the concept of direct proportion relate to the study of density?

Bridge:

Sinking/Floating

Content:

Density

Outcomes:

II. Standards Aligned

III. Instruction and Assessment

1. Connect: Connecting to the Concept Experientially

Objective: To allow students to experience a situation where densities are compared and where knowledge of densities is useful.

Activity: To build an elevator using liquids. Students are to use various liquids, e.g., water, concentrated sugar solution, mineral oil, ethel alcohol in graduated cylinders (soup cans would work equally well) so that the elevator cage (a wooden block) will sink in one liquid and rise in another. Students work in groups of four.

Assessment: Quality of the elevator.

2. Attend: Attending to the Connection

Objective: To enhance students' ability to describe observations and draw conclusions. To arouse curiosity as to how densities can be determined.

Activity: Discussion of the experience. Groups are now asked to answer the following questions: 1. How many liquids did you need? 2. How did you decide which liquids to use? 3. How could you make your choice of liquids easier to begin with? Is there some knowledge beforehand that would help in making the decision? Answers to questions must be written in the group and turned into the teacher.

Assessment: Quality of written answers.

Assessment, Phase One, Level of Engagement, Fascination:

3. Image: Creating a Mental Picture

Objective: To connect the elevator experience to a generalization about density and sinking/floating.

Activity: Have the students look at a list of densities. Ask them to try and find out how the densities of the liquids that behaved similarly are related. Then have them look at the density of the wooden block (the elevator cage) compared with those of the liquids used. Ask the students to draw a conclusion concerning densities. Then have students observe two substances of the same mass with different volumes and decide which is more dense. Repeat with substances of the same volume, different mass.

Assessment: Validity of conclusions and reasoning.

Assessment, Phase Two, Seeing the Big Picture:

4. Inform: Receiving Facts & Knowledge

Objective: To enhance student understanding of ratios, of solving equations, and of the use of lab equipment.

Activity: Explain definition of density as ratio of mass/volume, and discuss units used. Present equation D=M/V and how to measure quantities and solve equations.

Assessment: Short objective quiz.

Assessment, Phase Three, Success with Acquiring Knowledge:

5. Practice: Developing Skills

Objective: To give practice on concepts and assist problem solving techniques.

Activity: Give students worksheets including: 1. Comparison of ratios. 2. D=M/V equations to solve. 3. A list of densities and two objects of equal mass, wherein students will be asked to predict which volume will be the greatest. Do the same with equal volumes in terms of predicting masses.

Assessment: Quality of worksheets.

Assessment, Phase Four, Success with Acquiring Skills:

6. Extend: Extending Learning to the Outside World

Objective: To give students the opportunity to personalize learning.

Activity: Students are asked to choose one of the following: 1. Draw a picture showing two objects of different density. Make sure the picture is detailed enough to show why the densities are different. 2. Find out two other concepts (in science or otherwise) that can be expressed as ratios. Report on those equations. 3. Determine the density of two solid objects that you own. Explain how you determine the density.

Assessment: Quality of the above.

7. Refine: Refining the Extension

Objective: To enhance students' ability to decide on options useful to their experience.

Activity: Choose an option and write an essay on why that option was chosen. Options: Plan how to measure the density of a gas in a step-by-step process. List three real situations where knowing the density of objects would be most useful. Explain how your knowledge of density would be useful. Find objects with the lowest and highest densities possible. What are they? How are those substances used? Are they rare? Where do they come from? Find out about densities and "black holes." Explain what would happen if a spaceship (with you in it) approached a black hole. Redo the elevator problem to find the best combination of liquids (slow, steady ride.) Document how you came to your combination.

Assessment: Quality of essays in terms of materials needed, resources, etc.

8. Perform: Creative Manifestation of Material Learned

Objective: To enhance student ability to follow through on a plan. To give students the opportunity to direct learning activities to more personalized objectives.

Activity: The students carry out their options chosen in step number 7. They share their results with their classmates.

Assessment: Quality of projects, personal involvement, and class sharing.

Assessment, Phase Five,Performance, Creative Use of Material Learned: