Teacher Resources

Surface Area and Volume Project

Surface Area and Volume Project

SURFACE AREA

You have been given all the resources required to build the pool of your dreams. Use your imagination, it could be in ground, above ground or a combination of both! It could be made of steel, plastic or concrete.

The only requirements are that it is a composite shape comprised of at least three different sections and it must fit into your backyard which measures 40 ft by 20 ft.

Now it’s your turn. Use the attached grid paper to design your pool. Make sure to include all measurements. You will need to include a top down drawing (looking at your pool as if you were in a helicopter above), and it must include all needed measurements for building.

You will need to include a side view of the pool to show the depth below or above ground (or both). Remember to also include all measurements required here as well.

On the page following the grid paper, you will need to calculate the interior surface area of your pool so that the contractor will know what amount of supplies are needed. Make sure to show all your work and label all calculations clearly.

Teacher Notes:

Curricular Competencies Covered

Here we are looking for student creativity to come up with a design for their own pool. If this project is completed in groups we suggest increasing the number of sections required in the pool design for more complex computations. Remember to check to make sure their pool fits in the required allowed area!

• Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving

• Visualize to explore mathematical concepts • Use mathematical vocabulary and language to contribute to mathematical discussions• Represent mathematical ideas in concrete, pictorial, and symbolic forms

Teacher Notes:

Look for a reasonable representation of their pool. Are the measurements representative of what is shown in their diagrams? Is the ratio of the sides to scale and at a good proportion?

Attached is an example sketch of the top view and the side view of a proposed pool. Please use this as an example of what to look for from your students. Also following that is the calculations for the surface area of our example pool. Make sure to check student calculations for accuracy and make sure they have units included in their work.

The student workbook includes graph paper for the students to complete their drawings on and a paper outlined with space for their calculations. We recommend you require submission of these three pages as an initial step to the project, or have them include it in the final submission of their entire project. The three pages are titled ‘Top View of Your Pool’, ‘Side View of Your Pool’ and ‘Surface Area Calculations’.

Top View of Your Pool

Side View of Your Pool

Surface Area CalculationsRemember to show all your work, and don’t forget the units!

VOLUME

We will return to your pool in a little while.

But first, we are going to ask, what is the volume of your body? Is this something that is easily calculated? No, not really. But we are going to do it!

You will need a few materials for this portion of the project:

1. Access to a measuring tape. Not a construction measuring tape, but a cloth one used in sewing. If you don’t have access to this you can use a piece of string and a ruler.

2. A bath tub.

First things first. Let’s draw a rough sketch of your body. Provided for you is a page with room for you to sketch yourself.

Once you’ve completed your sketch there are a few questions for you to respond to. Please take the time to answer honestly and think about your methods.

Curricular Competencies Covered

• Use reasoning and logic to explore, analyze and apply mathematical ideas• Estimate reasonably• Demonstrate and apply mental math strategies• Use tools or technology to explore and create patterns and relationships, and test conjectures• Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem

solving • Use mathematical vocabulary and language to contribute to mathematical discussions• Explain and justify mathematical ideas and decisions• Communicate mathematical thinking in many ways• Represent mathematical ideas in concrete, pictorial, and symbolic forms

Not every student is an artist! Here we are looking for the general shape of the human body, head, legs, arms and torso. It just needs to be a sketch.

In the area above we’ve included a sample sketch. We’ve also include some answers to the questions required. Keep in mind that these are not an exhaustive list but are just some of the more straight forward answers we would expect that students would be able to come up with. If students do come up with different solutions, they should be able to defend their choice if asked.

As part of the submission process, we suggest you require students to submit both the sketch and their answers to the questions. The page is titled ‘Sketch Yourself #1’ in the student workbook and the questions immediately follow.

Sketch Yourself #1

Teacher Notes:

1. If you had to pick 1 shape to represent your body, what would it be?

Rectangular Prism, Cylinder

Students should be able to defend their decision of shape choice and explain why or why not it is a fitting representation of their body.

2. Using your measuring tape, take the necessary measurements of that shape in relation to your body and calculate the volume:

3. Is this an accurate representation of the volume of your body? Why or why not? Explain.

For the Rectangular Prism:

LengthWidthHeight

For the Cylinder:Radius or DiameterHeight

For the Rectangular Prism:

V=lwh

For the Cylinder:V=πr2 h

Make sure they have included units in their calculations and measurements!

Required Measurements: Calculation of Volume:

Let’s do it again!

This time we want you to sketch yourself again but we are going to change the method to which we cal-culate the volume of your body. Now, we want you to break your body up into three to five different 3d geometric shapes (ones that you know how to calculate the volume of, rectangular prisms, cylinders etc).

Once you have completed your drawing, calculate the volume of the shapes you suggested by taking the required measurements and using your math skills to determine the total volume of your body.

Then answers the reflection questions that follow.

Sketch Yourself #2

1. On the above diagram, draw in the different shapes you would choose to represent your body. Mark them in a different color so we can see them clearly.

Here we are looking for the general shape of the human body, head, legs, arms and torso. It just needs to be a sketch. On the sketch we are looking for the student to break the human body into 3 to 5 different shapes of which they will be able to calculate the volume of. They should clearly denote the different shapes on the diagram.

In the area above we’ve included a few different sample sketches. We’ve also include some answers to the questions required. Keep in mind that these are not an exhaustive list but are just some of the more straight forward answers we would expect that students would be able to come up with. If students do come up with different solutions, they should be able to defend their choice if asked.

Some students might go above and beyond and figure out different shapes that are applicable and research different formulas for these shapes. For example, using the sphere to model the head. They haven’t been taught this explicitly but are free to explore other ideas apart from what is required by the Math 7 and 8 content outcomes.

As part of the submission process, we suggest you require students to submit both the sketch and their answers to the questions. The page is titled ‘Sketch Yourself #2’ in the student workbook and the questions that immediately follow.

Teacher Notes:

2. Using your measuring tape, take the necessary measurements of that shape in relation to your body and the regions you’ve determined above and calculate the volume:

The student answers will vary here as their shapes may all be different.

Check to make sure they sum up all the different volumes they’ve calculated. Watch for the units!

Depending on the shapes the students choose to represent their bodies, they will need to use the different formulas for calculation of volume of those shapes. Make sure that they have included units in their calculations and measurements!

Required Measurements:

Calculate the total volume of your body:

Calculation of Volume:

3. Is this an accurate representation of the volume of your body? Why or why not? Explain.

4. Do you think this is a better or worse representation than the first time you sketched and estimated your volume? Why?

Students should be able to defend their decision of the different shape choices and explain why or why not it is a fitting representation of their body.

While we think that most students should be able to deduce that this is a better representation some will not. Look for a clear explanation as to why they think one way or the other.

Third time’s a charm, right?

This time we want you to sketch yourself one more time, but we are going to change the amount of regions from three to at least ten different geometric shapes. That is, we want you to divide yourself into at least 10 different 3d geometric shapes and calculate the volume of those regions. Make sure you use shapes that you know how to calculate the volume of.

Once you have completed your drawing, calculate the volume of the shapes you suggested by taking the required measurements and using your math skills to determine the total volume of your body.

Then answer the reflection questions that follow.

Here we are looking for the general shape of the human body, head, legs, arms and torso. It just needs to be a sketch. On the sketch we are looking for the student to break the human body into at least 10 different shapes of which they will be able to calculate the volume of. They should clearly denote the different shapes on the diagram.

In the area above we’ve included a sample sketch. We’ve also include some answers to the questions required. Keep in mind that these are not an exhaustive list but are just some of the more straight forward answers we would expect that students would be able to come up with. If students do come up with different solutions, they should be able to defend their choice if asked.

As part of the submission process, we suggest you require students to submit both the sketch and their answers to the questions. The page is titled ‘Sketch Yourself #3’ in the student workbook and the questions that immediately follow.

Sketch Yourself #3

1. On the above diagram, draw in the ten different shapes you would choose to represent your body. Mark them in a different color so we can see them clearly.

Teacher Notes:

2. Using your measuring tape, take the necessary measurements of that shape in relation to your body and the regions you’ve determined above and calculate the volume:

The student answers will vary here as their shapes may all be different. They should include measurements for at least 10 different shapes.

Check to make sure they sum up all the different volumes they’ve calculated. Watch for the units!

Depending on the shapes the students choose to represent their bodies, they will need to use the different formulas for calculation of volume of those shapes.

Check to make sure they have completed at least 10 different calculations of the different shapes labelled above.

Make sure that they have included units in their calculations and measurements!

Required Measurements:

Calculate the total volume of your body:

Calculation of Volume:

3. Is this an accurate representation of the volume of your body? Why or why not? Explain.

4. Is this a better or worse representation than the first or second time you sketched and estimated your volume? Why?

Students should be able to defend their decision of the different shape choices and explain why or why not it is a fitting representation of their body.

While we think that most students should be able to deduce that this is a better representation than the first or second estimations of their body’s volume, some will not. Look for a clear explanation as to why they think one way or the other.

Okay! This part of the project needs to be completed where you have access to a bath tub.

Now for the fun! Time to get your bathing suit on.

Did you think we were joking? I’m serious, put it on!

We are going to use the bathtub in order to figure out the volume of your body, to the best of our ability. Here are the required steps:

1. On the attached pages, you will need to sketch your bathtub. Label the measurements required in order for you to calculate the volume.

2. Fill the bath tub about 2/3’s full.3. Measure the depth of the water.4. Calculate the current volume of the bath tub. 5. Jump in!6. Submerge yourself to the best of your ability, and with the assitance of goggles or another

person have them mark the depth the water is after you are submerged.7. Jump out! And dry off!8. Measure the depth the water was when you were submerged.9. Calculate the volume of the bath tub when you were submerged.10. Take the submerged volume and subtract from it the volume of just the water. And voila! You

have the volume of your body!

Curricular Competencies Covered

• Apply multiple strategies to solve problems in both abstract and contextualized situations • Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem

solving

The Bathtub

Sketch Your Tub:

You decide the views required, is one enough? Do you need more than one?

These views will vary from student to student. We highly suggest they submit two different views, or a 3d marked up drawing with all measurements.

We have left this section a little bit more on the inquiry side, giving students gentle hints along the way.

Look for concrete demonstration of the modeling of the tub, are all the measurements there, did they draw more than 1 view?

When it comes to the calculations of the water in the tub, did they remember to not just calculate the volume of the entire tub, but to take the measurement of the depth of the water and use that for the calcuations?

We suggest you collect the following pages from your students in the project submission: ‘Sketch Your Tub’, ‘Calculations for the Volume of the Bath Tub with just Water’, and ‘Calculations for the Volume of the Bathtub with You Submerged’.

Teacher Notes:

These calculations will vary from student to student and depend on the dimensions and shape of the tubs. Check calculations for validility and correct use of formula.

Calculations for the Volume of the Bath Tub with just Water

These calculations will vary from student to student and depend on the dimensions and shape of the tubs. Check calculations for validility and correct use of formula.

These calculations will vary from student to student and depend on the dimensions and shape of the tubs. Check calculations for validility and correct use of formula.

Calculations for the Volume of the Bathtub with You Submerged

Total Volume of Your Body:

Curricular Competencies Covered

• Apply multiple strategies to solve problems in both abstract and contextualized situations • Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem

solving • Explain and justify mathematical ideas and decisions• Represent mathematical ideas in concrete, pictorial, and symbolic forms

Now, if you had your pool that you previously designed, and it was filled three-quarters of the way full. How many of you could you fit into your pool before it overflows?

Think about all the nessecary calcuations you will need to perform before you start!

Explain your steps to your calculations and your final result. Feel free to use additional pages if nessecary. Following those calculations is a chance for you to be able to reflect on the discoveries you’ve made and what you have learned. Please take the time to answer the questions thoughtfully and honestly.

Students have not yet calculated the volume of their pool, so they will need to perform this calculation and then calculate what three-quarters of the volume of their pool is.

Then using that calcuation and the volume of their body, they should be able to determine how many of themselves would fit before the pool is overflowing. You will want to assess their calcu-lations. Did they round themselves up or down, or include part of a person?

Suggested submission for this portion of the project: ‘Calcuations – How Many of You Can You Fit?’, ‘Connecting and Reflecting Questions’

Teacher Notes:

Your Pool and You

Students will need to calculate the volume of their pool. This should be multiple calculations of volume as their pool is made up of a miniumum of three different sections.

Students will then need to calculate three-quarters the volume of their pool.

The difference between these two measurements is the volume they can fill the pool with before it overflows. So this value divided by the volume of their body will tell us how many of themselves they can fit into the pool.

Did they give you a solution with a decimal? Maybe we should let them know you can’t just put a piece of a person in the pool? Their solution should be rounded down to the nearest whole person.

Calcuations – How Many of You Can You Fit?

Suggested Improvements:

Curricular Competencies Covered

• Reflect upon mathematical thinking• Connect mathematical concepts to each other, and to other areas and personal interests • Use mathematical arguments to support personal choices

1. How accurate were your estimates compared to the actual volume of your body?

2. Obviously our measurements are not perfect. In what ways could we have improved the accuracy of the submersion technique? List at least three improvements you could make.

Students should compare their three different estimates of their volume to their actual calculated volume.

• Having someone else measure the depth of the water when you were submerged instead of yourself.

• Was the water completely still when measuring? If it’s rippling this will affect the height. • Tubs are not usually perfectly rectangular. We maybe should have used a shape that was a

perfect rectangular prism or cylinder. Something that would allow us to correctly calculate the volume.

• Was your body fully submerged? Did you wear goggles? Was there anything that could have caused your body to be increased in volume for any particular reason?

3. Given the three methods we used to estimate the volume of your body, what would you suggest to someone who needed to get an accurate value of their volume (given that they weren’t able to submerge themselves to find it)?

4. Why might you ever need to know the volume of your body?

5. Where else could you use the submersion technique?

6. What was something you liked about this project? What was something you’d like to see changed?

Student answers will vary, but we hope that they have discovered the more accurate your measurements are for certain areas, the more accurate the volume. So, breaking the body up into as many representable pieces as possible to get the most accurate volume.

Student answers will vary. Look for creativity in thinking this one through.

Again, student answers will vary. Hopefully students will come up with other applications of using the submersion technique. Like the displacement of water and ice, or using a measuring cup filled with water to actually figure out the measurement of butter.

Student answers will vary.

Attached is a rubric for assessing the student work throughout the project and a grade sheet you are able to return to the student. Part of the evaluation included is a self assesment designed for the student to complete and submit to the teacher based on the work they completed during the project, which is to be included in their grade.

By no means is this meant to restrict you in what you assess on this project but just a guide for the basic information to look for. If you wish to assess in more detail go right ahead. If you would like to create your own rubrics and guidelines for this project, or have alternative requirements that you’d like your students to complete, we’d be happy to share your additional resources on our blog for others to use if you’d like!

As always we can be reached at info@studyforge.net and are happy to help!

Teacher Notes:

Project Rubric:

CATEGORY 4 3 2 1 SCORE

Delivery

All information required is presented in a neat and orderly fashion.

Most of the information required is presented. Delivery is for the most part neat.

Delivery method is messy and thrown together. Some of the information required is presented.

Pieces of the information required is presented although not coherent and work shown is messy.

Originality

Product shows a large amount of original thought. Ideas are creative and inventive.

Product shows some original thought. Work shows new ideas and insights.

Uses other people’s ideas (giving them credit), but there is little evidence of original thinking.

Uses other people’s ideas, but does not give them credit.

Accuracy

Calculations of all volume and surface area are correct, use the correct formulas and all work is shown.

Calculations of all volume and surface area are mostly correct, use the correct formulas and all work is shown.

Calculations of all volume and surface area are somewhat correct, some formula errors and not all work is shown.

Calculations of all volume and surface area are not correct, some formula errors and not all work is shown.

Content

All required work is shown and knowledge about the topic is present. Questions are answered thoughtfully in respect to what is being asked.

Includes essential knowledge about the topic. Subject knowledge appears to be good. Questions asked in the outline are addressed.

An attempt is made to address some of the questions in the outline but significant thought is lacking.

Content is minimal OR there are several factual errors. No attempt is made to address the questions in the outline or support them.

SCORE /16

Students Name(s):

Assessment Schedule – Surface Area and Volume Project

Percentage Weight Score Percentage of Final Grade

Self - Evaluation Assessment 15% /32

Project Assessment 85% /16

Final Grade %