assessing understanding → assessments → informal assessments → density

Drawing Models of Cylinders with Different Weights and Discussion

Activities: Unpacking Current Ideas: Comparing Two Cylinders with the Same Volume but Different Mass. Discussing and Analyzing Students' Current Models (See page 19 of the Density Curriculum for Lesson Plan)

As-You-Go Assessment Questions: At what level are students reasoning? Do they focus on crowdedness of particles or do they use a more macro-explanation (such as one cylinder being made of more than one material, being hollow, and/or having air in it)? Have students represented mass and volume? How do they represent each one? Do students think about the amount of matter that is in a given amount of space? i.e. the relationship between the mass and the volume? (They might do this by making the cylinders the same size and showing one having more particles than the other or by making boxes inside and showing a certain number of dots in each.) Are students thinking about details that aren't directly related to the cylinders? Are students drawing "scientific" models or "artistic" models? (Artistic drawings include features which are not directly related to what is happening with the cylinders, such as the table the cylinders are sitting on, the students sitting nearby, etc.) How do students think about what is in between the "particles" in the cylinders? Do they talk about space, air, something else? Are students clear on the meaning of "mass" and "weight"? (interchangeably or to differentiate between the amount of matter and a measure of that matter on Earth given the level of gravitational attraction.) How do students think of something that is lightweight? (e.g. that it is hollow, particles are spaced out, etc.)

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Exploring the Wooden Balls and Marbles Model of Cylinders

Activities: Exploring Models of Density: Introducing the Wooden Balls and Marbles Model. Critiquing the Wooden Balls and Marbles Model (See page 26 of the Density Curriculum for Lesson Plan)

As-You-Go Assessment Questions: Do students relate the balls or marbles to different types of particles and in the most sophisticated sense, that different atoms in different materials have different atomic mass? Do students realize that the model doesn't really capture differences in space between molecules? How do students think about what is in between the "particles"? (Do they think of it as air or space?) Are students clear on the difference between "more dense" and "less dense"? Are students reasoning about the mass of the particles as well as the mass of the cylinder?

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Exploring the Dots-Per-Box Model of Cylinders

Activities: Exploring Models of Density: Introducing the Dots-Per-Box Model. Critiquing the Dots-Per-Box Model. (See page 26 of the Density Curriculum for Lesson Plan)

As-You-Go Assessment Questions: Do students focus on how the model captures how much stuff is in how much space? Do they keep the amount of area in a box consistent? Do they know how to interpret a box with more dots compared to one with less dots (as more dense rather than less dense) and vice versa? How do students talk about what is in between the "particles"? Are students clear on the difference between "more dense" and "less dense"?

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Exploring the Bread Model of Cylinders

Activities: Exploring Models of Density: Introducing the Bread Model. Critiquing the Bread Model. (See page 26 of the Density Curriculum for Lesson Plan)

As-You-Go Assessment Questions: Do students realize that squishing the bread increases its density? Do they talk about it in terms of more matter or stuff in less space? Are students clear on the meaning of "mass" and "volume"? Do students confuse the meaning of "mass" and "weight"? Do students realize that there is air being pushed out of the bread but that unless it is mixed density (with a gas and a solid) usually the space in between isn't large enough for air molecules and it is just space? Are students clear on the difference between "more dense" and "less dense"?

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Measuring and Graphing Mass and Volume

Activities: Finding the Relationship Between Mass and Volume of Pure Substances. Analyzing the Patterns Between Mass and Volume. (See page 41 of the Density Curriculum for Lesson Plan)

As-You-Go Assessment Questions: Do students realize that they have to treat the variables, mass and volume, in relation to each other—that they can't impact one without impacting the other? Do the students realize that they can't change density directly, that they need to manipulate mass or volume? What language do they use to talk about figuring out density? Do they realize that it has to be inferred, not measured directly? Are students clear on the meaning of "mass" and "volume"? Do students confuse the meaning of "mass" and "weight"? How do students think about the volume of irregular solids?

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Exploring Relational Causality

Activity: Introducing Relational Causality. (See page 26 of the Density Curriculum for Lesson Plan)

As-You-Go Assessment Questions: Do students see that changing one part of a relationship changes the outcome? Do students recognize the role of comparison in a relationship? Do students realize that the relationship between the two variables causes the outcome, not one variable alone?

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Practicing the Formulas Related to Density

Activities: Calculating Density from Mass and Volume. Introducing Formulas for Calculating Density. Demonstrating the Formulas. Practice Using the Relationship between Mass, Volume, and Density to Calculate the Unknown Variable. (See page 49 of the Density Curriculum for Lesson Plan)

As-You-Go Assessment: Are students trying to memorize the formulas? Are students reasoning about the concepts then remembering formulas? Are students beginning to think about density as a relationship between mass and volume?

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Exploring if Cutting an Object in Half Affects Its Density

Activities: Does Cutting an Object in Half Affect its Density? Testing Predictions. (See page 57 of the Density Curriculum for Lesson Plan)

As-You-Go Assessment: Are students surprised that half of a cylinder is not half the density? Do they reason about what happens using the relationship of amount of matter in a given amount of space or focus only on absolute amounts of volume or mass?

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Finding the Density of Water and Other Liquids

Activities: Demonstrating How to Find the Density of a Liquid: Water. Finding the Density of Other Common Liquids. (See page 61 of the Density Curriculum for Lesson Plan)

As-You-Go Assessment: Are students clear on the meaning of "mass" and "volume"? Do students confuse the meaning of "mass" and "weight"? Are students clear on the difference between "more dense" and "less dense"? Are students surprised that the liquids have different masses? ...different densities?

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Considering the Mass, Volume, and Density of Gas

Activity: Analyzing Current Thinking. (See page 66 of the Density Curriculum for Lesson Plan)

As-You-Go Assessment: Do students think air takes up space? Do students think air has mass? How do students think about whether or not gas is matter? Are they able to think of evidence or ways to demonstrate that gas is matter?

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Exploring Atomic Mass

Activity: Introducing Atomic Mass (See page 97 of the Density Curriculum for Lesson Plan)

As-You-Go Assessment: Are students clear that protons and neutrons are more massive than electrons? Do students focus on the protons and neutrons as the main contribution to an atom's mass? Do students recognize that an atom of one element will have a different number of protons and neutrons from an atom of another element? Do students recognize that an atom of one element will have a different mass than an atom of another element? How do students talk about what is in between the protons, neutrons, and electrons? Do they talk about space, air or something else?

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Exploring Atomic Mass as a Cause of Density

Activities: The Role of Atomic Mass in Density. Exploring the Implications of Atomic Mass. (See page 97 of the Density Curriculum for Lesson Plan)

As-You-Go Assessment: Do students recognize that an atom of one element will have a different number of protons and neutrons from an atom of another element? Do students recognize that an atom of one element will have a different mass than an atom of another element? How do students talk about what is in between the protons, neutrons, and electrons? Do they talk about space, air, or something else? Do students recognize that atoms have about the same volume? Are students beginning to see how the mass of different atoms would affect the density of the atoms? Do they relate the atomic mass to the mass of the particles that they drew in their diagrams of the cylinders in earlier lessons? Do they realize that it contributes to the amount of matter in a given amount of space? Are students clear on the difference between "more dense" and "less dense"?

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Exploring Whether "Air Molecules" Can Fit Inside Atoms

Activity: Can an "Air Molecule" Fit Inside an Atom? (See page 97 of the Density Curriculum for Lesson Plan)

As-You-Go Assessment: Are students clear that an "air molecule" really refers to the different molecules that make up the air (i.e. nitrogen, carbon dioxide, oxygen, etc.)? Do students understand that a molecule is made of atoms? Do students recognize that all atoms are made of protons, neutrons, and electrons? Do they understand that an atom of an "air molecule" - for example, the carbon in carbon dioxide - has a certain number of protons and neutrons and that an atoms of - for example - aluminum also has a certain but different number of protons and neutrons? Do students recognize that all atoms have empty space between their nucleus and electrons? Do they understand that an atom of an "air molecule" - for example, the carbon in carbon dioxide - has empty space between its nucleus and electrons, and that an atom of - for example - aluminum also has empty space between its nucleus and electrons? Do students recognize the difference in size between a single atom of aluminum or copper and a molecule found in the air?

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Exploring Atomic and Molecular Bonds as a Cause of Density

Activity: Introducing the Role of Atomic and Molecular Bonds (See page 104 of the Density Curriculum for Lesson Plan)

As-You-Go Assessment: Are students clear that a molecule is made of atoms? Do students understand that bonds exist, even if they are not sure how to explain them? Do they understand that bonds refer how atoms and molecules stay together? Are students clear that bonds are not matter, so they do not have mass? Do students recognize how the strength of a bond affects how close the atoms are to each other? Do students recognize that bonds affect how atoms and molecules come together and are organized? Are students beginning to see how the atomic and molecular bonds would affect the density of a substance? Do they see how stronger, tighter bonds would lead to more atoms fitting in a certain amount of space?

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Exploring Whether "Air Molecules" Can Fit Between Bonds

Activity: Is There Air in Between the Bonds? (See page 104 of the Density Curriculum for Lesson Plan)

As-You-Go Assessment: Are students clear that an "air molecule" really refers to the different molecules that make up the air (i.e. nitrogen, carbon dioxide, oxygen, etc.)? Do students understand that a molecule is made of atoms? Do students recognize that the bonds between atoms lead to certain configurations and orientations of atoms? Are students beginning to see that because the bonds between atoms and molecules only allow for certain configurations and a certain amount of space, "air molecules" cannot fit in the space between atoms in an average molecule? Do students recognize that all atoms have empty space between their nucleus and electrons? Do they understand that an atom of an air molecule—for example, the carbon in carbon dioxide—has empty space between its nucleus and electrons, and that an atom of—for example—aluminum also has empty space between its nucleus and electrons? Do students recognize the relative sizes of a single atom of aluminum or copper and a molecule found in the air?

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Thinking About Two Causes of Density: Atomic Mass and Bonds

Activity: When One Cause Overrides Another Cause (See page 104 of the Density Curriculum for Lesson Plan)

As-You-Go Assessment: How do students talk about the causes of density? Do they talk about the amount of mass within a given amount of space? Do students talk about the mass of the particles or atoms? Do students talk about the distances separating particles or atoms? Do students talk about the strength of the bonds connecting the particles or atoms? Do they talk about the orientation of atoms and/or molecules? How do students talk about what is between particles or atoms? Do they talk about space, air, or something else?

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Exploring Mixed Density as a Cause of Overall Density

Activity: Exploring How Mixed Density Affects Overall Density (See page 110 of the Density Curriculum for Lesson Plan)

As-You-Go Assessment: Are students clear that one substance can have a different density than another substance? Are students beginning to see how the density of individual substances can contribute to the overall density of the combined substances? (For instance, that objects with air inside tend to have a lower overall density than those without because the density of the air is added to that of the material to get the overall density.)

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Modeling the Multiple Causes of Density

Activity: Drawing Models of Multiple Causes of Density (See page 115 of the Density Curriculum for Lesson Plan)

As-You-Go Assessment: Are students beginning to see how the mass of different atoms would affect the density of the atoms? Are students clear that a molecule is made of atoms? Do students recognize that bonds affect how atoms and molecules come together and are organized? Are students beginning to see how the atomic and molecular bonds would affect the density of a substance? Do they see how stronger, tighter bonds would lead to more atoms fitting in a certain amount of space? Are students beginning to see how the density of individual substances can contribute to the overall density of the combined substances? Are students able to reason about the multiple causes of density? Are they beginning to recognize how the specific causes of density are important in different situations?

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Modeling Changing Density: Ball and Ring Demonstration

Activity: Drawing Models of the Ball and Ring Demonstration (See page 120 of the Density Curriculum for Lesson Plan)

As-You-Go Assessment: How are students thinking about density? Are they reasoning about the three causes? Are students thinking about the process of heating the ball? How are they representing the increase in temperature? Do they show the bonds as being affected by the heat? Do they realize that density can change? Are students focusing on amounts of matter in a given amount of space? Are students keeping the same amount of matter in their models?

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Modeling Changing Density: Heating Liquids and Gases

Activity: Drawing Models of What Happens When Liquids and Gases Are Heated. (See page 120 of the Density Curriculum for Lesson Plan)

As-You-Go Assessment: How are students thinking about density? Are they reasoning about the three causes? How are students thinking about the process of heating? How are they representing the increase in temperature? Do they show the bonds as being affected by the heat? Do they realize that density can change? Are students focusing on amounts of matter in a given amount of space? Are students keeping the same amount of matter in their models (for example, the same amount of mass before and after heating)?

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Modeling What Causes Something to Sink or Float

Activity: What Causes Something to Sink or Float? (See page 154 of the Density Curriculum for Lesson Plan)

As-You-Go Assessment: How are students thinking about what causes something to sink or float? Are they thinking about density, weight, buoyancy, or something else? If students are thinking about density, how are they thinking about it? Are they reasoning abut the three causes? Are students thinking about the liquid and the object, or are they focusing only on the object? If students are thinking about weight, how are they thinking about it? Are they thinking in a linear causal way, that the weight of an object is what causes the object to sink or float? Or if students are thinking about both the liquid and the object, how are they thinking about them? Are they thinking in a relational causal way, that the relationship between the liquid and object causes something to sink or float?

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Exploring Sinking and Floating Fluids

Activity: RECAST Activity: What do Liquid Layers Tell Us About Density? (See page 160 of the Density Curriculum for Lesson Plan)

As-You-Go Assessment: How are students thinking about what causes something to sink or float? Are they thinking about density, weight, buoyancy, or something else? Are students talking about the "weight" of the liquids, or the "density" of the liquids which make the liquids sink or float? Whichever terminology they use, are they reasoning about both mass and volume in relation to each other or absolute amounts of mass or volume? Are students reasoning linearly about the sinking and floating of the liquids? Are they talking about the "weight" of the liquids making the liquid sink or float? Are students beginning to reason relationally about the sinking and floating of the liquids? Are they talking about the "density" of the liquids making the liquid sink or float?

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Exploring Relational Causality: Sinking and Floating Fluids

Activity: Applying Relational Causality to Liquid Layers (See page 160 of the Density Curriculum for Lesson Plan)

As-You-Go Assessment: Are students talking about the "weight" of the liquids, or the "density" of the liquids which make the liquids sink or float? Are students reasoning linearly about the sinking and floating of the liquids? Are they talking about the "weight" of the liquids making the liquid sink or float? Are students beginning to reason relationally about the sinking and floating of the liquids? Are they talking about the relationship between "density" of the different liquids, which makes the different liquids sink or float? Are they able to see the relationship within a relationship—that the mass/volume relationship of one substance is compared to the mass/volume relationship of another substance to determine the outcome of sinking or floating? How are students thinking about the three causes of density? Do they focus on one cause or another? Do they draw the causes to appropriately represent the different densities? Are students beginning to see that something which is more dense than the substance it is in will sink, and something which is less dense than the substance it is in will float?

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Thinking About What is Happening in Galileo's Thermometer

Activity: Analyzing an Analogy (See page 164 of the Density Curriculum for Lesson Plan)

As-You-Go Assessment: Are students thinking about the "weights" of the glass balls or the overall "density" of the balls (the liquid and air inside the glass of the ball and the metal tag underneath)? Are students reasoning relationally about the sinking and floating of the glass balls? (that changing the density of the liquid in the tube or the overall density of the glass ball (by impacting the density of any or all of the components—the liquid and air inside, the glass of the ball and the metal tag underneath) impacts the relationship between them?) Are students reasoning about the three causes of density in their explanations?

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