## The Milky Way and Lentil Beans

Astronomers estimate that there are anywhere from 100 billion to 400 billion stars in our galaxy. It is a challenge, however, for our students to conceptualize extremely large numbers. An easy and effective way to help students visualize 200 billion and how that number relates to our Sun and galaxy is to use lentil beans to represent the stars in our galaxy. Students begin to grasp just how vast the universe is as well as how relatively small our solar system, and thereby Earth, is in comparison. During this process, students gain a better understanding of our Sun being one of 200 billion stars in our galaxy. This activity addresses the crosscutting concept of Scale, Proportion, and Quantity.

### Engage

I begin by first addressing a misconception about Earth’s place in the universe that students often possess. Many students greatly underestimate the vastness of the universe and our solar system’s smallness (and Earth’s smallness in comparison), believing that our solar system is a major part of the galaxy. To address the misconception, I show students a picture of spiral galaxy Messier 81 and ask them if the picture is of our galaxy. Many students will believe it is, and that one of NASA’s probes was able to go far enough to take the picture. I then reveal the actual galaxy in the picture. The NASA website has some great pictures of spiral galaxies taken by the Hubble Space Telescope (see Resources). NASA explains that a picture of our galaxy is not technically possible due to the size of our galaxy (see “NASA’s Educators’ Corner” in Resources). It is estimated that NASA’s newest probe, the Parker Solar Probe, may reach a speed of 692,300 km/hr (430,000 mph). That is fast enough to get from Philadelphia to Washington, D.C. in one second. At that speed, it would still take over 50 billion years to be far enough away in order to snap a complete picture of the Milky Way. This can be a good place to show The Power of Ten video to introduce students to astronomical distances (see Resources).

### Explore

#### Day 1

Each student receives one lentil bean, which they color yellow with a crayon or marker to represent our Sun. I have students tape the bean to a piece of paper in their notebook. I ask students to take guesses on what metric volume 200 billion lentil beans will take up, using 200 billion as an estimate of the number of stars in the Milky Way. I offer choices for volumes by showing them a bucket, the classroom trash can, the room, etc. As a class, we then go over the objective, which is to come up with a computational method to determine the volume 200 billion lentil beans would fill and then match that volume to that of a known object such as classroom(s), bedrooms, and so on.

It is important for students to understand that stars are not all one size like the lentil beans are; we are just using lentil beans to better understand such a large number. Throughout the activity, students should be reminded to reference back to the yellow lentil bean representing our Sun, which is essential for modeling the scale of an unobservable quantity.

I have students form self-selected groups of two or three students. Alternately, you can group your students according to specific student attributes such as reading level, interest level, or learning style. The class is told that by the end of the period, all groups must create a procedure for estimating the metric volume of 200 billion lentil beans. They must also produce a list of the materials they will need for conducting their procedure. I tell the class that each group will be given one three-ounce cup of lentil beans. To allow students time to exercise their creativity, I do not make other materials available at this time; I want them to come up with the materials they will need to develop a method for determining the metric volume of 200 billion lentil beans. Materials that work best include graduated cylinders, calculators, metric rulers, metersticks, or metric measuring tape. Groups may request other materials, but most often they realize the materials listed work best.

We begin with a brainstorming session where students write in their notebooks to develop at least one idea/step on how to proceed. I direct students to write in bullet points, rather than complete sentences, which allows students to practice organizing their thoughts in a clear, concise manner and is less time consuming. Then, each group receives a large, poster-size sheet of paper (bulletin board paper works well) so each group member can write their idea(s)/plan simultaneously on one corner of the sheet; all members’ ideas are visible for the group to consider. If groups are having trouble deciding, it is sometimes necessary for me to help guide them by asking questions such as “Do any of the plans have things in common?”

Once the group decides on a method, they show me their procedure. For each step, students show their work with a brief explanation. For example, for step 1 students might say, “We used a graduated cylinder and counted how many lentil beans fill 1 ml.” For step 2 they might say, “We need to work with cubic meters for volume, so we found that it takes 1,000,000 cubic centimeters to equal one cubic meter.” Work that they would be expected to show would be something like 100 cm × 100 cm × 100 cm.

Groups may come up several times to show me their procedure. This gives me a chance to formatively assess their understanding of volume. Often students have the idea to begin with counting the lentil beans in the cup and then keep multiplying to see how many cups it would take to equal 200 billion, at which point I remind them that the time constraint for the project is three days. Most groups soon realize that they can find the volume by beginning with how many lentil beans fit in one cubic centimeter and then use that to calculate the total volume of 200 lentil beans.

It is important to be sure groups are using correct computations such as using correct metric units (cubic centimeters and meters) and the correct formula for volume. Some groups may need to be asked some guiding questions pertaining to the metric volume in order to proceed. For groups who are struggling, I ask questions such as “What is the formula for finding volume of a cube or solid rectangle?” and “What solid volume is one milliliter equal to?” (The equivalency of one ml = 1 cm3 can be demonstrated by pouring 1 ml of sand into a 1 cubic centimeter cube, which can be made from paper.) Groups may need reminding that the volume of the cup is in ounces and they will need to find the volume of 200 billion lentil beans in a metric measurement. Once the procedure is approved, each group member must have the procedural steps written in their notebooks so the group can proceed if members are absent.

#### Day 2

At the beginning of class, I have students look at the yellow lentil bean taped in their notebooks. The class is reminded that this activity is to help them understand the perspective that our star, the Sun, is just one star amidst approximately 200 billion stars.

Once students believe they have an estimated volume that 200 billion lentil beans would take up, the next step is to come up with a comparable volume that they are familiar with. Students visualizing a volume larger than a classroom filled with lentil beans is a lot more meaningful than just determining a volume of (approximately) 8,350 cubic meters filled with lentil beans. I have supervised groups who have wanted to measure the hallway or gym, although this may not always be possible. When doing so, make sure that students keep the metersticks below waist level.

Students may choose to find the dimensions/volume of their room or rooms at home. For students who may not have access to a meterstick at home, a one-meter length of string with decimeters marked could be provided. This is also a great way to get families involved.

### Explain

#### Days 3 and 4

Each group must develop a poster to show evidence of a model that shows how they calculated the volume of 200 lentil beans. This must include their method, rationale, calculations, and results (see rubric in Figure 1). Many groups include pictures and drawings on their poster in order to visually depict their procedure. These posters are arranged around the classroom for a gallery walk during which students examine each other’s work. As the groups walk around the room, taking a few minutes at each poster, they make comments and evaluations of each poster in their notebooks for the follow-up discussion and summative assessment. Many students write what other groups did differently or the same as their group, which engages them in constructing viable arguments and critiquing the reasoning of others. Students may want to use sticky notes to put questions or comments on the posters. The sticky notes can also be used with the follow-up discussion.

### Elaborate

Finally, we discuss the results as a whole class with students sharing their comments from their walk. Most of the groups get very similar mathematical results even if arriving at the conclusion in a slightly different manner. I use this as an opportunity to talk about how important consensus is for scientists. This discussion is a chance for groups, which may have made some errors, to see the correct results as well as understand what they did wrong. During this discussion, once the class has talked about comparative volumes of 200 billion lentil beans, I challenge them to imagine what volume it would take to have the lentil beans represent all the stars in our universe. I show the class a picture called the Hubble Extreme Deep Field image (see Resources). I explain that this image shows many galaxies in just one small section (about that of a penny held at arm’s length) of our night sky. Astronomers have no actual count of how many galaxies there are in our universe, but they believe there are billions. Some students have come up with suggested answers by multiplying the volume they came up with (e.g., the classroom filled with lentils) by another 200 billion.

### Evaluate

To assess their understanding, I ask students to answer the following questions. Differentiation for some students may include allowing them to use their notebook for the written assessment or including prompts from the calculation worksheet.

### Questions

1. Thoroughly explain with supporting evidence the steps your group took to arrive at your final answer, including the final volume. If your group’s result was incorrect, explain your method or calculations and any errors, and how the errors could have been corrected (error analysis). The claim evidence reasoning format (CER) can be used here.
• The overall objective of this activity was to help you gain an understanding of our Sun as one of 200 billion stars in our Milky Way galaxy. Explain why it was important to keep referring back to the one yellow lentil bean that represented our Sun. (“The bigger the space filled with lentil beans, the more lost our Sun lentil bean seemed.”)
• Use the experience from this activity to explain how a search for other Earth-like planets around other stars (exo-planets) could (or could not) be justified.

This method of using lentil beans can also be used to help students understand any large number such as the chemical unit of a mole. If time does not allow for the complete activity, it can still be a powerful demonstration. Give each student a lentil bean (our Sun) and again ask what volume 200 billion beans would occupy. (The actual volume 200 billion lentil beans would occupy is approximately 8,000 cubic meters [32 × 25 × 10 m] or a building measuring 105 ft.(l) × 82 ft.(w) × 33 ft.(h), which is larger than a typical school gymnasium. This can help students understand the concept of our Sun as one in 200 billion.)

References

Baggaley K. October 2015. Why we can’t grasp very large numbers.

Freeman D. 2018. August 16. The big pull that will make the Parker Solar Probe the fastest human-made object. NBCNews.com.

Ghose T. 2013. Ginormous numbers could create a mental black hole.

Howell E. 2018. How many stars in the Milky Way? 2018.