How Big Is The 2010 Guatemalan Sinkhole?

Resource: A Lesson from Robert Kaplinsky

Overview

Brief Description of the Resource: If you want to combine math and science in your classroom, Robert Kaplinsky has crafted the perfect lesson for you. By setting up the challenge for students (the mysterious appearance of a real sinkhole in Guatemala in 2010), offering digital media links and excerpts from articles, Kaplinsky has introduced students to how both math and science can be used together in real life. In this lesson, you will challenge students to determine how much material is needed to fill the sinkhole, offering them the chance to learn about volume and calculate the cost of the needed materials. Further extensions could be added to explore the causes of the sinkhole and how it is a result, in part, of human activity.

Technical and Cost Considerations: This lesson is freely available at the link provided. The articles and videos Kaplinsky references are also freely available. One thing to keep in mind is that it is not a ready-made page for students. Teachers will need to take the resources provided and put the information into a format for use by their students

Evaluation

Description of the Learning Activity

This is a lesson which helps teachers introduce volumes of cylinders in a real-life context. As mentioned above, teachers would need to take the resources Kaplinsky has provided on this page and put them into a format accessible for students. However, as Kaplinsky has already done the hard work of dreaming up the idea and gathering the resources, this shouldn't be too challenging.
1. Learning Activity Types

• LA-Explore: This lesson helps students explore/investigate mathematical ideas, specifically the volume of a cylinder, the cost of responding to a natural disaster and (related to science) the impacts of human activity on our world.
• LA-Apply - Students will apply mathematics formulas to problems and situations.

2. What Mathematics Is Being Learned?

Standards

As identified by Kaplinsky, this lesson addresses:

• CCSS 8.G.9: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
• CCSS G-GMD.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
• CCSS G-MG.1: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).

In Grade 5 we typically focus on the volume of rectangular prisms. However, our volume standard also more broadly applies to this situation:

• CCSS.MATH.CONTENT.5.MD.C.5: Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

Directing students to calculate the cost of the concrete needed to fill this sinkhole would meet the following standards:

• CCSS.MATH.CONTENT.5.NBT.B.7: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

In terms of Next Generation Science Standards (NGSS), this activity meets:

• 5-ESS3 Earth and Human Activity
• 5-ESS3: Obtain and combine information about ways individual communities use science ideas to protect the Earth’s resources and environment.
• 5-ESS3.C: Human activities in agriculture, industry, and everyday life have had major effects on the land, vegetation, streams, ocean, air, and even outer space. But individuals and communities are doing things to help protect Earth's resources and environments.

Proficiency Strands

• Procedural Fluency: Students will need to be able to apply the formula for the volume of cylinder to this situation. They will need to be able to calculate the cost of the cement needed to fill the hole.
• Strategic Competence: Students will need to use logic when assessing which estimate of the sinkhole's size is most reasonable.

Additional comments on what is being learned

Despite the correlation to Grade 8 standards, I tagged this as a Grade 5 activity because I believe my advanced students especially would value from being stretched to also determine the volume of cylinders. The decimal operations involved also closely align with Grade 5.

3. How Is the Mathematics Represented?

Normally when I answer this question, I think about things like, "Is this information represented graphically or numerically or through manipulatives or symbolically?" However, in this case, while there is some numerical representation (e.g. formulas, listing of statistics from different news outlets), the most powerful representations here are the images. Students will be captivated by how the math they see in the classroom can actually show up in the real world. The images of the cylinder represent math at its finest -- applicable to our world. Paired with articles and videos, these images allow students to connect with math (and science!) in a way they may not have before. The real-world grittiness of this problem means that the exact dimensions of the sinkhole are not clear-cut, but the practicality of it more than makes up for this obscured aspect.

4. What Role Does Technology Play?

The advantages here are that students can access a real-world math and science problem that doesn't take place in their school or community. Because of the Internet, we have access to these resources, and this allows students to access mathematics in a way they never have before. The only possible disadvantage of this technology might be for the teacher as the lesson is not entirely "pre-made" or ready for student viewing.

Affordances of Technology for Supporting Learning

• Representing Ideas & Thinking: Students are able to see math ideas as they play out in the real world.
• Accessing Information: Students learn about a phenomenon that is happening worlds away from them but still can be related to them.
• Communicating & Collaborating: This affordance is represented on this site not so much in the learning as in the teaching. When I started out looking for ways to link math and science, I would have had to create my resources from scratch were it not for this possibility to view others' ideas. Also, Kaplinsky acknowledges that this lesson was a product of digital collaboration between him and two others.

5. How Does the Technology Fit or Interact with the Social Context of Learning?

Social interaction would work very well with this lesson as it could be posed to a whole-class or small groups. The digital resources offer "clues" to solving the problem, and teachers could offer them to students gradually. The way the information is currently presented is not conducive to student viewing, but teachers can easily modify the lesson to make it so.

The technology is also an example of how Personal Learning Networks (PLN), or collaboration between educators online, can help teachers improve their lessons and practice.


6. Additional Comments

Teachers would be well-served to check out the rest of Kaplinsky's site. Although not all of it involves math lessons where math and science effortlessly merge, there are good resources available for teachers who seek to help students understand that math is meant for use in the real-world.

This evaluation was developed in my work for the MSU Course, CEP 805: Spring 2017, and is also accessible on the private course wiki.