SWBAT create step-by-step instructions explaining how to find the density of an irregular object.

Apply what we have learned so far about density, mass, volume and displacement to create and communicate instructions for a new lab.

The strategy focus for this lesson is to activate and apply what students now know about density so that they can create their own procedures to find the density of an irregular object. In the next lesson students will write their own procedures, communicating in precise scientific language, a way to find the density of an irregular shape.

Students have experienced concrete examples of density. We changed the density of liquids and film canisters by adding mass and the density of raisins and popcorn kernels by adding volume. We found density of water and learned that centimeter cubes displace 1 milliliter of water. Now students will design and conduct procedures to find the density of irregular objects using their own experiences as their sources.

It is critical that you first determine where student understanding is prior to teaching density. The Investigation below takes a step-by-step approach to determine what students already know.

10 minutes

*Investigation Summary and Standards*

The Next Generation Science Standards Practice 3 (Planning and Carrying Out Investigations) calls for students to have a variety of opportunities to plan and carry out several different types of investigations. In this lesson students work collaboratively with their lab partner to plan and carry out a procedure to determine the density of irregular objects. Students collect quantitative data and apply math geometry skills as a communication tool. Students will see math applied in the science classroom as an opportunity for real-world application of math. Using the correct tools and taking precise measurements are important to the success of students in the lesson.

Students develop the procedure to find the density of irregular objects, using the concrete experiences with density from previous labs.

*Activating Relevant Prior Knowledge*

I will begin this class by review with students what they have learned so far about density.

- How did we change the density of the colored water to make the density towers? (Liquid Density Towers)
- How did we change the density of the film canisters? (Float, Suspend, Sink)
- How did we calculate the density of the film canisters? (Float, Suspend, Sink)
- What did we use to calculate the volume? (Float, Suspend, Sink)
- How did we find mass? (Float, Suspend, Sink)
- How did we calculate the density of water? (Density of Water)
- Why were we able to change the units for the density of water from 1 g / 1 ml to 1 g / 1cm
^{3}? - What is displacement? (Density of Water)
- How did we make the raisins and popcorn kernels float? (Raisins and Popcorn Kernels)

These questions are to help students recall prior knowledge that will help them create their own step-by-step instructions for finding the density of irregular objects. This strategy encourages metacognitive thinking by the students as they reflect on what they know and how they know it.

*The Challenge*

Next I will introduce the challenge. I will share several irregular shaped objects, including clay shaped in unusual ways, jacks and rocks. I will students reminding them that we used a ruler to find the volume of the film canister but how would we use a ruler to find the volume of an irregular object? How is it possible to account for the measurement of every nook and cranny?

*I will continue with a short introduction to Archimedes and his dilemma. King Hieron II of Syracuse in Sicily gave a jeweler gold to make a new crown. When the crown was returned it was beautiful in its fine detail but the king suspected that the jeweler had used silver in place of some of the gold. Archimedes was summoned by the king and told to find a way to prove that the king was cheated. Archimedes knows that density is a property that helps us identify materials. All pure gold has the same density as does pure silver and even clay. If Archimedes could find the density of the crown, he could compare it to the density of gold and prove that the jeweler did indeed cheat the king. But how could he find the density of the crown. It would be impossible to measure accurately.*

*Density Of Irregular Objects: Samples*

I explain the graphic organizer and vocabulary expectations to students. They should use the organizer to write instructions as they complete each task in their lab. Students should use the vocabulary listed on the organizer after all they are scientists explaining their procedures to other scientists. The organizer has blocks for a hook, topic, sentence, detail steps and a conclusion. Students often see writing as something you do only in the ELA classroom. This organizer is designed to support students as they write in science so they are not distracted from the primary goal of formally reporting their findings as scientists by the mechanics of writing a paragraph.

30 minutes

I ask students to turn and talk to their lab partner.

*Thinking about what we have done so far in our quest to learn more about density, what ideas do you have for finding the density of an irregular object?*

As I walk around the room, I listen in on student conversations. I will intercede if I hear them headed off entirely in the wrong direction. If I hear a misstatement, I use questioning to help them to clarify their own thinking. Here are some open-ended questions that are meant to keep the thinking where it belongs - by the students.

- What would happen if...?
- How would you test?
- Can you predict what would happen if....?

After 2-3 minutes, I ask the student partner groups to share their ideas with the table. Turn and talk allows students to participate in discussion and share their ideas and develop them further by talking to their peers.

Depending on what I hear, I may ask students more questions about what they know or set them to work by reminding them to use the graphic organizer to record their instructions.

I will circulate around the room listening to student discussion and prompting by asking again the questions we discussed at the beginning of the class if necessary. I want to make sure that students are using the vocabulary

When I created the irregular shaped clay samples for students to use, I cut the original shapes to match 3 centimeter cubes, 4 centimeter cubes and 5 centimeter cubes. As students record their displacement, I will bring with me centimeter cubes and reshape the clay to show the students that their procedure for finding the volume using displacement was spot on.

Creating Irregular Shapes

10 minutes

I ask students to share their mass, volume and density data using a Google Docs spreadsheet. I use Google Docs so that I can display the spreadsheet, using a projector, so all students can see the input.

Depending on the class, I may have students take a minute to look at the data and then ask, *"What do you notice? What questions do you have?"* But early in the year I may have to take the "wondering role" first, and model it. So I might ask students, *"I wonder why two entries with the same volume have different masses?"* I'm hoping to hear students suggest that the TBB may have been a bit off, or their reading of the measurement be off a bit, or some other possible reason for data anomalies.

We discuss the fact that all the mass entries are not exactly the same even though the volume is the same. *How did this happen? Is there a tolerance we can use to say that the results are the same? What plus or minus value is acceptable? *This will help us compare the values.

Sharing results shows the students that discrepancies in data collection are a normal part of the scientific process. I ask students what could have caused the results to be very similar but not exactly the same. Students are pretty good about citing measurement reading or calculation errors. We talk about the equipment we are using and how the balances may not be zeroed out perfectly.

This short discussion has a lot of value with students. When you accept answers based on an error tolerance, you are validating the process students used and their success even if all students do not have exactly the same answer.

Once all the data has been entered I challenge students to answer:

*How is it that two pieces of clay can have the same density; one with a volume of 3cm ^{3 }and another with the volume of 5cm^{3? }*

The final takeaway for students will be that density is a property of a substance. It is their "AHA" moment. Regardless of the sample size, the density will always be the same. They have the evidence!