Desmos Calculator Project
by
Heather Sanderson
A Calculator Project Submitted In Partial Fulfillment Of The Requirements For
Teaching Math and Science with Technology (656)
Instructor: Dr. Hari P. Koirala
Department of Education
Eastern Connecticut State University
July 22, 2018
Introduction: Standards, Goals, and Objectives
In my science classroom, I always have calculators available for my students. Calculators are available because I conduct a laboratory based class that often requires students to calculate the averages in trials and/or the percent changes in experiments. The calculators are necessary due to time constraints, and my students in seventh grade are expected to already know how to add, subtract, multiply, and divide. In science class, calculations are about using the right formulas and plugging them into the calculators to find accurate answers. I have used calculators in my own learning through my math and science classes in high school and college. I have found calculators to be beneficial because they allow complicated problems to be solved faster with more accuracy. I do not feel calculators have in any way hindered my learning of mathematics; in fact they have only enhanced it.
As I have mentioned, I keep a box of calculators in my classroom and allow my students to use them at any time. When I tell my students this at the beginning of the year, they are a little shocked because their only real exposure to calculators as 7th graders is in their math classes and calculator use is often restricted there. I tell them that my class involves application of math instead of assessment of their basic math skills. While I support calculator use in secondary grades, I believe elementary school math classes should not use calculators regularly. Those formative years are when students need to gain a solid understanding of addition, subtraction, multiplication, and division, as well as fractions. Calculator use too early may hinder students’ ability to grasp basic math concepts. In fact, one of the articles I reviewed, Pedagogical instruction with calculators, states that “educators have explained the inappropriateness of allowing students to use calculators when the main objective of an activity is the development of computational skills” (Lucas & Cady, 2012, p.389). Most elementary math work involves some sort of computation assessment, and therefore calculators should not be used. Though I did find it interesting in another article called Calculators as learning tools for young children’s exploration of numbers that Shuard (1992) and Groves and Stacey (1998) found “young children’s use of calculators led them to encounter and become interested in topics that were not traditionally part of their mathematics curricula, such as large numbers, negative numbers, decimals, and square roots” (Huinker, 2002, p.321). While calculators should not be used on formative or summative assessments for elementary school children, it may be a good idea to include a few activities throughout the year that explore calculator use with this age group to expand the way they think about math. The Common Core Standards for Mathematics (CCSS), National Council of Teachers of Mathematics (NCTM), as well as the K-12 Science Framework mention the importance of calculators. Calculator use is included in the eight standards of mathematical practice in the common core. Standard number five is “use appropriate tools strategically” and more specifically states a calculator as one of those tools and goes on to use an example of a high school student using a graphing calculator to “analyze graphs of functions and solutions” for how tools should be used (Common Core State Standards Initiative (CCSS), 2010, p. 7). The CCSS states that students “use technological tools to explore and deepen their understanding of concepts” (CCSS, 2010. P.7). Calculators are again brought up in the high school number and quantity section of the Common Core standards as a way “for students to become better acquainted with these new number systems and their notation” and goes on to say “they can be used to generate data for numerical experiments, to help understand the workings of matrix, vector, and complex number algebra, and to experiment with non-integer exponents” (CCSS, 2010, p. 58). One of the principles in the National Council of Teachers of Mathematics Principles to Actions Executive Summary is to integrate “the use of mathematical tools and technology as essential resources to help students learn,” and for the action part it instructs teachers to “incorporate mathematical tools and technology as an everyday part of the mathematics classroom” (National Council of Teachers of Mathematics (NCTM), 2014). Use of tools for mathematics is even brought up in the K-12 Science framework where it states “Mathematics (including statistics) and computational tools are essential for data analysis, especially for large data sets” (National Research Council, 2012, p.64). Standards for both math and science stress the importance of calculator use for student success in these subjects. One issue of concern with calculator use is that as calculators become more sophisticated, many teachers do not know how to properly use them. In the article Calculators in K-5 textbooks the authors discuss how calculator use has become more accepted and shows up in many state curriculum, but they also stress “as calculator technology changes, teachers need opportunities to learn not only how to use the tools well but also how to teach with them effectively” (Chval & Hicks, 2009, p.436). Another article, Technology in Mathematics Education: Preparing Teachers for the Future, also recognizes the importance of “preparing preservice teachers to utilize instructional tools such as graphing calculators” as a way “to close the gap and bring mathematics education into the 21st century” (Powers & Blubaugh, 2005, p. 255). As technology changes, school districts need to use professional time to train teachers in the technology they will be using in their subjects.
This past year I noticed a trio of Desmos calculator apps popped up on my students’, as well as my, iPad. There is the Desmos 4 Function, Desmos Scientific, and Desmos Graphing Calculator. Our school does not allow the students to access the app store, so apps students might need for school are placed right onto their iPads, often without any explanation. Neither I nor my students had any familiarity with these calculators, but I have learned these calculators are the ones that are approved for state standardized testing. I thought it would be a good idea to create an activity that teaches my students how to use these calculators while teaching them about the concept of density. Density is part of our 7th grade science curriculum and is covered under NGSS Standard “PS1.A: Structure and Properties of Matter” (NGSS, 2013, p.56).
Overview of Calculator Project
The purpose of this project is to explore the use of Desmos4 Function, Desmos Scientific, and Desmos Graphing Calculators with my seventh grade science classes in order to assist them in solving density equations, as well as interpreting density relationships through graphing. The project is one I came up with myself, but I included Desmos tutorial videos I found online and adapted a density graphing scenario based on a Pearson Laboratory I found on a chemistry website. This project is intended for all students. This project is significant because my students have access to using the Desmos calculators for all classes, for standardized testing, and for at home use. It is essential that my students learn when to use which calculator and how to access the different functions on each one. It will also be helpful to have all of my students using the same calculator when working in lab groups because “differences in the way that various calculators handle very large and very small numbers…can lead to discrepancies when students compare their results to those obtained by other students” (Krumpe & Keiser, 2003, p. 138). The students will save time because any disagreements on results due to the slight variation in how a calculator handles numbers will lessen when all my students are using the Desmos calculator. Tying the use of the Desmos calculator to my unit on density works best because it is when we use calculators the most, and there is also an opportunity to explore the graphing calculator. I am excited to explore the Desmos graphing calculator with my students since this is the first time they all have one. It has never been a requirement to buy a graphing calculator in seventh grade. The article Graphing calculator as tools states that “graphing calculators are particularly notable for their portability, ease of use, relatively low cost, and extreme functionality” (Browning & Garza-Kling, 2010, p. 481). The article goes on to say that they hope their “colleagues who do not currently use or have access to graphing calculators that it is worth the time and energy to explore available training and grant opportunities to make using such tools a norm at their schools” (Browning & Garza-Kling, 2010, 485). Now that all my students have a free graphing calculator on their iPads, it is the perfect time to start using it in my science class.
Project Activities
All of my activity worksheets and assessment questions, as well as the rubric are attached at the end of my paper.
My first activity is called Introduction on how to use Desmos Calculators.
Step 1: The students will open up the Desmos 4 Function Calculator app on their iPads. I attached a picture of what it should look like. I explain when this calculator should be used and specific keys they should be aware of for use. I also have a few density calculations for them to solve on the calculator.
Step 2: The students open up the Desmos Scientific Calculator. This is the first time many of my students will be using a scientific calculator so I provide a link for them to watch a tutorial video which is https://vimeo.com/210280260. I go over when they should use this scientific calculator and have them answer a few density questions with this calculator.
Step 3: The students open up the Desmos Graphing Calculator and I provide them with a link to a tutorial video on how to use the Desmos Graphing Calculator which is https://www.youtube.com/watch?v=hBpdSeJlMyA. I then explain how to create a table and how to label the x and y axis on the graphing calculator since this is what we will be using the graphing calculator for in science class. I then have them create a table, enter data, and graph their data. While my students are exploring the three Desmos calculators I will walk around and assess their progress and assist any students who are having difficulty.
My second assignment is called Solving Density Word Problems using Desmos Scientific Calculator. This assignment provides my students with an opportunity to solve a variety of different types of density problems using their Desmos Scientific Calculator. The students will explore using pi and exponents in some of the problems for the first time. This assignment contains a variety of word problems that solve for density, mass, and volume in a variety of ways to get my students familiar with various equations and calculator functions.
The third assignment is called Using the Desmos Graphing Calculator to Compare the Density of Different Metals. I adapted this activity from a Pearson Education Experiment.
Step 1: The students open up their Desmos Graphing Calculator app and I give them mass and volume data for two unknown metals collected from 9 labs groups.
Step 2: The students create a table on their graphing calculator and input the data given to them
Step 3: The students create a labeled graph on their graphing calculator of their data.
Step 4: The students answer a few questions about density relationships and identify what the two unknown metals are.
I expect most of my lower level students will be able to be successful in these assignments since a calculator “off-loads computation so that students can focus on analyzing relationships and patterns” and “provides visuals and interactive modeling of problems” (Suh, 2010, p. 443). If there are modifications needed, I can give my struggling students the formulas for solving for density, volume, or mass. I can also provide a list of units to use for mass volume and density. For my higher achieving students, I can have them explore lines of best fit on their Desmos Graphing Calculator which is a topic that our science curriculum does not begin to cover until 8th grade. I will grade all three activities of this project as one assessment and I have attached a rubric. I will also include different density problems and they can use their Desmos calculators on their final unit assessment which will give me more opportunities to check for understanding.
Final Thoughts
While I have taught my density unit in the past, I have not done it with the new Desmos calculator apps my students now have available to them. I also have never gone over how to properly use a calculator with my students even though they have many questions every year on basic calculator skills. I also have not shown density relationships through graphing before. I think this project is worthwhile because my students will be using the Desmos calculators on standardized tests, on classroom assignments, as well as homework and they need to be familiar with how they work. Also density is a topic that comes up many times throughout my chemistry and earth science curriculum and my students need a solid understanding of the relationship between mass, volume, and density all year. The concerns I have is that I myself have not used these Desmos calculators before and have been trying to familiarize myself with them this summer. I also do not remember using a graphing calculator in the past, though I did my undergraduate studies 20 years ago and may have just forgotten. I have been doing my best to watch the tutorial videos and I have solved various equations on the calculators to gain a better understanding. Overall I feel this project will familiarized my students with all three Desmos calculators and teach them about density at the same time.
My First Assignment
Name ___________________________________ Date _______________________ Class ___________
Introduction on How to Use Desmos Calculators
You may have noticed that your iPad has come with three Desmos calculator apps. We will be exploring when to use which calculator app and the functions available on each one. The three calculator apps are called Desmos 4 Function, Desmos Scientific, and Desmos Graphing.
First we will explore the Desmos 4 Function.
Open the Desmos 4 Function app on your iPad
This is what you should see:
Back and forward arrows
New equation arrow
This calculator will be used for basic math functions. This calculator allows you to calculate multiple equations all on the same screen. Just make sure to press the curved arrow in the bottom right corner when you move to a new equation. If you want to go back or forward a step, use the 2 small arrows on the top left. This calculator also automatically shows the answer on the screen without pressing = which is different than other calculators you may have used in the past.
Explore using the calculator by solving the following density problems. Practice keeping each equation on the screen. Remember to use units.
An object has a mass of 45 g and volume of 9cm3, what is its density? _____________________
A cube has a mass of 345g and is 5 cm on each side, what is its density? ____________________
A liquid has a mass of 177g and fills a graduated cylinder to 55mL, what is its density? ______________
Next we will explore the Desmos Scientific Calculator.
I would like you to first watch the following tutorial on the Desmos Scientific Calculator:
Next open the Desmos Scientific Calculator on you iPad.
This is what you should see.
Exponents
Pie
Notice the expanded options on this calculator. In this class we will mainly be using the exponents and pie features but in future classes you will be using many other functions. If you click on abc you will have access to the alphabet for algebraic equations. If you click on the func key you will have access to advanced math functions. HINT
Try the following density problem on the scientific calculator.
A cylinder has a mass of 95g, a radius of 7cm, and a height of 15cm, what is its density?
_______________________
Next we will explore the Desmos Graphing Calculator.
Watch the following tutorial on the Desmos Graphing Calculator first.
https://www.youtube.com/watch?v=hBpdSeJlMyA
Open the Desmos Scientific Calculator on your iPad.
This is what it should look like.
To make table Click here to label axis
This graphing calculator will allow you to quickly create a table and input you data. To do this you just click the + button on the top left and click on table. You then can put in your data for you independent and dependent variables. To label your axis you click on the tool button on the upper right side. This graphing calculator will allow you to see the relationship between the independent and dependent variables.
1. Create a plot of mass vs. volume using the following data:
Volume (mL)
Mass (g)
5.0
0.44
15.0
1.33
24.0
2.12
52.0
4.60
64.0
5.66
81.0
7.17
Make sure to label both of your axes.
My Second Assignment
Name __________________________________ Date __________________ Class ________
Solving Density Word Problems using Desmos Scientific Calculator
Now that you have become familiar with the Desmos calculators on your iPad we will practice using them. On this worksheet you will be using your Desmos scientific calculator to solve the following density word problems. While you are using the online Desmos calculator for computation, you still need to show how you set up your equation in the space provided. Also remember to use proper units in your answer. You may need to use chart below for some problems.
Common Densities Chart
Benzene 0.88b/mL
Gasoline 0.7g/mL
Ether 0.71g/mL
Brass 8.6g/cm3
Copper 8.9g/cm3
1. What is the density of a liquid with a mass of 120g and a volume of 7mL?
2. What is the volume of a 220g of an object with a density of 55 g/cm3?
3. We have an object with a density of 620 g/cm3 and a volume of 75 cm3. What is the mass of this object?
4. What would be the mass of #3 in kilograms?
5. A block of wood has a mass of 180 grams. It is 10.0cm long, 6.0cm wide and 4.0cm thick. What is its volume and density?
6. Find the volume 0f 20.0g of benzene. (use chart)
7. A cube measures 3.0m on each side and has a mass of 25g. What is the density of the cube?
8. Will the cube in #7 float in water? Will it float in benzene?
9. An irregularly shaped stone was lowered into a graduated cylinder holding a volume of water equal to 20.0mL. The height the water rose to was 30.2mL. If the mass of the stone was 25.0g, what was its density?
10. A solid object listed in the chart has a volume of 10.0cm3. It has a mass of 86g. What is its density? What material is the object made of?
11. If two objects have the same density and A has a higher mass than B, which object A or B has a larger volume?
12. If 5.0mL of ethanol has a mass of 3.9g and 5.0mL of benzene has a mass of 4.4g. Which liquid is denser?
13. A cup of gold colored metal beads was measured to have a mass 425 grams. By water displacement, the volume of the beads was calculated to be 48.0 cm3. Given the following densities, identify the metal.
Gold: 19.3 g/mL
Copper: 8.86 g/mL
Bronze: 9.87 g/mL
14. What is the mass of a cylinder of lead that is 2.50cm in diameter, and 5.50cm high. The density of lead is 11.4g/cm3 and the volume of a cylinder is V=πr2h.
15. A little aluminum boat (mass of 14.50 g) has a volume of 450.00 cm3. The boat is place in a small pool of water and carefully filled with pennies. If each penny has a mass of 2.50 g, how many pennies can be added to the boat before it sinks?
16. A solid ball has a mass of 50 grams and a volume of 20 cm3. What is the density?
17. A solid ball has a mass of 100 grams and a radius of 2 cm. What is the density?
18. A solid cylinder has a radius of 2 cm and a length of 7 cm. It has a density of 3.1 g/cm3. What is the mass of the cylinder?
My Third Assignment
Name ________________________________ Date _____________________ Class_____________
Using the Desmos Graphing Calculator to Compare the Densities of Different Metals
(Adapted from Pearson Education Mass, Volume, and Density Experiment)
You will be using the Desmos Graphing Calculator App on your iPad to compare the densities of two unknown metals. You then will identify each of the metals.
Step1: Open the Desmos Graphing Calculator on your iPad.
Scenario: Samples from two unknown metals A and B were given to 9 lab groups in class. They measured the samples mass and volume and recorded their data below.
Step 2: You will input the volume and mass data for the two different metals below into 2 tables using your Desmos graphing Calculator
Step 3: Make sure you label the x and y axis using the tool key in the upper right side
Metal A Metal B
Lab group
Volume (cm3)
Mass (g)
1
3.8
10.10
2
1.7
4.31
3
3.0
8.05
4
3.1
8.21
5
4.1
10.35
6
3.2
8.22
7
1.7
4.51
8
3.7
9.93
9
1.8
4.7
Lab group
Volume (cm3)
Mass (g)
1
3.8
33.41
2
3.9
34.62
3
3.1
27.63
4
2.4
21.00
5
2.5
20.92
6
3.2
26.92
7
3.6
34.00
8
2.5
21.22
9
3.2
27.15
Analyses and Conclusions:
1. What happens to the mass of an object as volume increases?
______________________________________________________________________________
2. What does slope of the line for each metal represent?
______________________________________________________________________________
3. Identify Metal A and Metal B using the chart of common metal densities below for reference. Remember the measurements were taken by 9 different lab groups so there may be slight error in the numbers.
Metal A is ______________________________________________
Metal B is ______________________________________________ Density of Metals Chart
Lead 11.3 g/cm3
Brass 8.7 g/cm3
Zinc 7.14 g/cm3
Steel 7.8 g/cm3
Aluminum 2.6g/cm3
Platinum 21.5 g/cm3
My Rubric
Skill
Needs Improvement (0)
Developing (2)
Proficient (4)
Score
Desmos 4 Function Use
Most questions with Desmos 4 Function Calculator are answered incorrectly
Most questions with Desmos 4 Function Calculator are answered correctly
All questions Desmos 4 Function Calculator are answered correctly
Desmos Scientific Calculator Use
Most questions with Desmos Scientific Calculator are answered incorrectly
Most questions with Desmos Scientific Calculator are answered correctly
All questions with Desmos Scientific Calculator are answered correctly
Desmos Graphing Calculator use
Most questions with Desmos Graphing Calculator are answered incorrectly
Most questions with Desmos Graphing Calculator are answered correctly
All questions with Desmos Graphing Calculator are answered correctly
Density work problem math calculation
Most density word problems are calculated incorrectly
Most of the density word problems are calculated correctly
All of the density word problems are calculated correctly
Density Word Problem Units
Most density word problems do not have unit or correct unit labeled
Most of the density word problem have the unit correctly labeled
All of the density word problems have the correct unit labeled
Understanding of mass volume density relationship
Most of the mass, volume, density relationships are incorrect
Most explanations of the mass, volume, density relationships are correct
All explanations of the mass, volume, density relationship are correct
Identification of unknown metals
No unknown metals are identified correctly
1 unknown metal is identified correctly
Both unknown metal are identified correctly
Total Points /28
References
Browning, C.A., & Garza-Kling, G. (2010). Graphing calculators as tools. Mathematics
Teaching in Middle School, 15(8), 481-485
Chval, K.B., & Hicks, S.J. (2009). Calculators in K-5 Textbooks. Teaching Children
Mathematics, 15(7), 430-437.
Common Core State Standards Initiative. (2010). Common core state standards for mathematics.
Retrieved from http://www.corestandards.org/assests/CCSSI_Math%20Standards.pdf
Huinker, D. (2002). Calculators as learning tools for young children’s explorations of number.
Teaching Children Mathematics, 8(6), 316-321.
Krumpe, N., & Keiser, J. (2003). Getting to know a calculator’s numerical limitations.
Mathematics Teacher, 96(2), 138-140.
Lucas, K. K., & Cady, J.A. (2012). Pedagogical instruction with calculators. Teaching Children
Mathematics, 18(6), 384-389.
Mr. Nona Physics. (2015, Sept 15). Using Desmos to create a best fit line. Retrieved from
https://www.youtube.com/watch?v=hBpdSeJlMyA
National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: Author. Executive summary retrieved from
https://www.nctm.org/uploadedFiles/Standards_and_Positions/PtAExecutiveSummary.pdf
National Research Council. (2012). A framework for K-12 science education: Practices,
Crosscutting concepts, and core ideas. Washington, DC: National Academy Press
Next Generation Science Standards (2013). Next Generation Science Standards: For states by states. Washington D.C.: Author. Retrieved from http://www.nextgenscience.org
Pearson Education Inc., (N.D.). Mass, Volume, And Density. Chemistry Laboratory Manual. Retrieved from http://saval- chemistry.weebly.com/uploads/2/4/7/8/24783238/chlmlabt4.pdf
Powers, R., & Blubaugh, W. (2005). Technology in mathematics education: Preparing teachers
for the future. Contemporary Issues in Technology and Teacher Education, 5(3/4), 254-
270.
Suh, J.M. (2010). Tech-Knowledgy & diverse learners. Mathematics Teaching in the Middle School, 15(8), 440-447.
Teacher 2 Open High School. (2017). Tutorial: Desmos Scientific Calculator. Retrieved from