Image: By Wolfgang Strickling [CC BY-SA 2.5 (http://creativecommons.org/licenses/by-sa/2.5)%5D, via Wikimedia Commons
There’s a big event coming to the USA on August 21st of this year, and I’ve been looking forward to it for a decade – ever since I heard of it. We get a coast-to-coast total eclipse of the sun, and many, many people live within a day’s drive of the path of totality. One of my favorite places to get info about the event is http://www.eclipse2017.org/ largely because I love their Google Map of the path, provided by Xavier Jubier, here.
As soon as camping reservations opened up along the centerline, I pounced and made our reservations. Many people are just learning about the eclipse now, however. I have started educating my students about what an eclipse is and why they should get to the path of totality on eclipse day. Every so often, I see a news story on my social media about the eclipse. It will start to get big, and I am sure many people will decide last-minute to get to the path of totality to take it in.
Since Denver and the front-range cities are within a day’s drive of the path, I wanted to use this space to share what I’ve learned about accommodations for viewing the eclipse.
If you live in Denver or Northern Colorado, you’re most likely thinking of heading north along I-25 to Wyoming to view the eclipse. Totality will occur along I-25 starting at Wheatland, all the way through where the interstate bends west and goes through Casper, then about 30 miles north into the wide open country. Most of the eclipse path in Wyoming has excellent weather prospects, so we’re lucky to have prime viewing areas so close to us!
Although Wheatland is on the southern edge of the path, most of town will still see almost a minute of totality. Recently, there were still hotel rooms available in Wheatland (although a couple of the hotels were charging premium rates, roughly $500 per night).
Just northeast of Wheatland is Grayrocks Reservoir. There’s a map of the reservoir here. The reservoir has primitive camping, or you could bring your boat on the lake and watch the eclipse from the water – or just drive up for a daytrip as it’s less than 3 hours from Denver. It will probably be less crowded to be farther away from the interstate, and this short jog northeast brings the time of totality to almost 2 minutes.
If you keep going east past Grayrocks Reservoir, you reach Fort Laramie, and then Lingle and Torrington. Fort Laramie is a National Historic Site run by the National Park Service. Torrington has camping, hotels and restaurants. The corridor from Wheatland through Torrington can be reached in less than 3 hours from Denver, and being on the southern edge of totality, this area may see smaller crowds and give you better mobility than areas on the center line. Yet you’ll still see a total eclipse for 1-2 minutes.
Continuing north on I-25 past Wheatland, you get to the Guernsey exit. Guernsey is about 15 miles east of I-25 and is home to a state park on a reservoir and historic Oregon Trail wagon wheel ruts left in the sandstone. The camping at Guernsey State Park is booked, but there is a golf course RV campground and a couple of motels. The Wyoming State Park system is offering day passes on its website. You can use one of the day passes to get in to any state park on the path of totality – Guernsey, Glendo State Park a little farther north, Edness K Wilkins State Park in Casper, and Boysen State Park near Shoshoni. This would give you guaranteed parking wherever your eclipse-day plans end up taking you, and you’d have access to the state park programs such as ranger talks.
Further north on I-25, you arrive at Glendo. Glendo is home to another state park on a reservoir, with the same day-pass program as Guernsey. Camping there has been booked for some time. Glendo is where the centerline of the path of totality intersects a major interstate highway going north from Denver. It’s still less than 3 hours away from Denver, and as such I expect this will be a very popular location as long as the weather looks good! Glendo is doing a lot of preparation for the eclipse. The town only has a population of 200 people – but it will likely swell to tens of thousands on eclipse day. Is it possible it could be hundreds of thousands? The state park will be busy, with hikes and ranger talks, boating and camping, and the main attractions will be at the Glendo Airport right next to the interstate. This will be the main viewing area along with vendors and exhibits. The school will also have eclipse exhibits.
If you decide to keep going on I-25, you get to the Orin exit, which has a rest area but limited facilities otherwise. If you go east from here and leave the interstate, there will be roadside stops but no actual towns – and you get to experience the vast openness and nothingness that is most of Wyoming. The first town of any size is Lusk – although in the northern part of the path of totality, Lusk will still see almost 2 minutes of the total eclipse. The town website for Lusk doesn’t indicate any eclipse events yet, so I don’t think they are doing a ton of planning or expecting big crowds. The biggest groups they may see will be people migrating south from the Black Hills area of South Dakota.
Continuing on I-25 from Orin, the interstate bends west and follows the path of totality through to Casper. Douglas and Glenrock are towns along this route, with lodging, viewing areas, and eclipse-related events planned. One charming stop might be Ayres Natural Bridge, a rock formation in a county park south of the interstate.
Casper will be an eclipse hotspot, as the first really sizable town north from Denver, with great weather prospects and the presence of the AstroCon convention. It takes about 4 hours to get to Casper from Denver, making it still doable for a daytrip for people who leave really early. Lodging in Casper has been booked for quite some time.
Finally, an additional option for people heading up for a daytrip from Denver would be to stop in southwestern Nebraska. Scottsbluff is on the southern edge of the totality path, but Scotts Bluff National Monument will still see 1 1/2 minutes of totality. The communities of Scottsbluff and Gering, along with the National Park Service, have set up viewing events and plenty of parking and free eclipse glasses. There is also a beer and wine festival in downtown Scottsbluff. This area promises to have a fun, community-wide celebration with easy in-and-out access to Denver and Colorado’s front range. In addition, Agate Fossil Beds National Monument is located in a more remote location north of Scottsbluff but will see a longer eclipse. Finally, the area around Alliance, home of Carhenge, the quirky replica of Stonehenge made from cars, will have about 2 1/2 minutes of totality and has plenty of community events planned. Intriguingly, there’s a music festival named Toadstock: Party on the Prairie. Still tickets available and free camping, and close to the centerline of the eclipse. I found a couple of other lodging options but don’t know how full they are. Viewing areas in Alliance will be available in several locations. Scottsbluff is almost exactly a 3 hour drive from Denver, and Alliance is 45 minutes northeast of there.
I made a Google Map with the information I know about eclipse viewing, lodging and events in southeastern Wyoming and southwestern Nebraska. I did not include Casper in the event map, but focused on everything within a 4-hour drive of Denver. This is my first total eclipse, but I can tell I am going to want to make it to another. If you possibly can, get out there.
Get solar glasses and eclipse viewing tips here:
Eclipse Chaser blogs:
And if you’re a teacher, start talking to your students, your district and your parent community about this as soon as you can. The eclipse will be seen throughout the entire USA and you’ll want to make sure all of your students have a chance to view it, get glasses and/or make pinhole viewers. The students may or may not be in school when the event happens, so encourage your school district to make plans now.
For my computer science class, Unit 1 is going to be about how computers work and how they use data. I first gave a poorly-written pre-test. It contains bits of recall and procedural knowledge and is not a test of critical thinking or problem solving. But I gave it because writing the assessment helped guide me in understanding the scope of Unit 1, and it will give me at least some evidence of what kids learned during the unit… important stuff in a world of data-driven teacher evaluations. Plus, it’s easy to grade, important stuff in a world of 160+ students.
I made a decision to start by introducing binary code and the rationale behind it: that it’s easy for a computer to “tell” if electricity is flowing or not flowing, and harder to decode an analog value – so a code based on switches that turn on and off makes a computer’s job easy.
I showed the kids a ribbon cable.
There are a few dozen wires running parallel to each other. Each one can have an electrical pulse that is either on or off – a 1 or a 0. A code made up of 1’s and 0’s goes through this ribbon cable. You can send any information you want if you can write a code for it made of 1’s and 0’s.
I held up a card, blue on one side and white on the other. I asked the kids if I could answer a yes/no question with it. They agreed pretty quickly that blue might be yes and white might be no (or vice-versa).
Next I asked them how many cards I would need to answer a question that I could respond with yes/no/IDK. At first the group thought I would need three cards, but when they thought about it, a group of kids persuaded everyone that 2 cards would do:
Yes = BB
No = WW
IDK = BW (or WB)
So you can represent three different codes with 2 cards. Next I offered a challenge. I asked the kids if they could come up with a code for the digits 0-9 using the cards. They would have to use all of the cards for every code (after all, a computer can’t choose how wide the ribbon cable is). They partnered up, and I said when they had a strategy, they could come to me and tell me how many cards they would need. Some groups said they needed 3 cards. Some said they needed 4 or 5 or 6. One group said they needed 10 cards.
Me: 10 cards? You don’t think you could come up with 10 unique codes with less than that?
Student: Well, ok. 5 cards then.
Me: Here’s 5 cards.
After a few minutes, some groups who had originally taken 3 cards approached me and said they needed another card.
Me: You need one more?
Student: I can only get 8 codes with 3 cards.
Me: How many codes can you create with 4 cards?
Me: Let me know when you find out. Here’s another card.
I found out that I hate the layout of my room for group work. I’m in a computer lab with fixed workstations that I can’t move. All the stations face the front of the room. Just awful for putting your heads together over writing or for walking around between groups. I was able to converse with some groups, but I wasn’t even able to see how many groups were disengaged or doing other things, let alone intervene with them – I need to think hard about how group work is going to work in there.
Here were some of the conversations I did have with kids.
Me: Were you able to make a code for 0-9?
Student: Yep. Here it is.
Me: I see. Very systematic approach. How many codes could you make total with 4 cards?
Me: Tell me why you think so.
Student: Because you do 2 for the first card, and then x2x2x2. It’s like that problem where you have to pick how many outfits you can make with the 3 sweaters and 4 pairs of socks and so on.
I also found some misconceptions, and I will need to check back in the coming days to see if they’ve been fixed. Why does this student think this?
Me: Why did you need 4 cards?
Student: Because I could only get 9 codes with the 3 cards.
Me: Tell me why it’s 9 codes.
Student: Because that’s 3×3 which is 9.
Me: Can you show me what all 9 codes are?
But then of course we ran out of time before he could show me.
Anyway, when we were done, as a whole class we shared a couple of solutions and processed how many codes a computer could make with 4 bits (16), 5 bits (32), 6 bits (64), 7 bits (128) and 8 bits (256). I asked the students if 256 seemed to be a common and popular number and if they were starting to understand why computers liked this so much. It’s the number of different codes you can make with 8 bits, which makes a byte. 4 bits has a cool name too – it’s a nibble.
I introduced binary place value to the kids using a place value chart. I wish I knew how to have them “discover” this on their own (is it important for them to?). I know I was taught directly, and I know my understanding of place value improved dramatically when I actually understood other number bases.
I showed them how to convert some decimal numbers to binary, like 3, 19, and 30. The kids were SO excited by this. I told them we were going to do a worksheet tomorrow and their eyes lit up. I’m not kidding. A student approached me after class and said “I think I get this and I was wondering if you could give me a little extra challenge tomorrow.” I said “Maybe another method like base 3? Where you have the digits 0, 1, and 2?” He said “Yeah, I’d like that!”
I had a great day and I love my job.
Number bases are not explicit in the Common Core standards, which is a shame in my humble opinion. You feel so smart when you get a different number base. But if you wanted to do a lesson like this one and attach it to CCSS, you could use this one.
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
I’ve attended a virtual conference before, and now I will be a first-time presenter!
My presentation is called Authentic Learning in Math through Computer Coding: Turning Consumers into Creators.
It will be Thursday, May 1, at 5:00pm Mountain Daylight Time, through the Reinventing the Classroom conference.
To tweet about it before, during, or after, use the hashtag #reinvent14.
I’m really excited! It’s a subject I’m really passionate about, and I am looking forward to connecting with other educators who are also interested in coding as part of the core curriculum.
Here is my slide set. It contains active links you can follow, to a bunch of documents and coding activities I am sharing.
My Twitter handle is @DuPriestMath. Please get in touch – I would enjoy the dialogue!
I hope to see you there.
In my seventh grade math classroom, the second unit we studied was on the power standard of “proportionality”. Students had learned about basic programming commands and how to use the coordinate grid. Their learning would be more powerful, I decided, if they had the opportunity to use the ideas of ratio and proportion with variables in a computer program. A common task is to scale quantities, or images, up or down to make sense of a situation. It’s a great fit for computer programming.
- CCSS.Math.Content.7.RP.A.2 Recognize and represent proportional relationships between quantities.
- CCSS.Math.Content.7.RP.A.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
- CCSS.Math.Content.7.RP.A.2c Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.
I really focused on the last standard, representing proportional relationships by equations. Variables are a new concept to middle-schoolers. It’s also one of the most important concepts in computer science, so there is great synergy there. I would focus on the use of variables and how you can use them to represent a proportional relationship. I wove these lessons in with our usual math lessons on proportionality.
1) Fractions, Ratios, and Rates starter: To give the students a chance to explore proportionality and how it can be represented graphically, I gave them three simple programming tasks: Draw 3/5 of a circle. Draw two rectangles in the ratio 1:2. Show with a diagram that I have taken 5 friends to a movie for a total cost of $75. The students needed to use the built-in documentation to learn how to draw arcs and rectangles, and work in workgroups to accomplish the task. It took about an entire 90-minute block, but almost everyone was successful.
2) Proportions and variables: Students had done a few activities involving variables and programming in the previous unit, so I wanted them to explore using variables in a proportional reasoning setting. I gave them the Population Program which is a troubleshooting activity. It shows two bars representing the populations of two cities, but one is clearly an incorrect length. I asked the students to fix the program so the bars correctly showed a comparison between the populations of the two towns.
The activity had many correct ways of solving it, and a few incorrect ways that *looked* correct, which I didn’t anticipate at first! I found the populations of the two towns on Wikipedia, and conveniently, the population of Greeley is almost exactly 5/8 of the population of Fort Collins. The program starts with this code:
// the population of Fort Collins (Wikipedia)
var pop_ftc = 148612;
// the bar for Fort Collins goes all the way across the screen
var bar_ftc = 400;
// the population of Greeley (Wikipedia)
var pop_greeley = 92889;
// This looks wrong.How long should the bar be for Greeley?
var bar_greeley = 10;
In the picture, you can tell the bar for Greeley is way too short. The students started by adjusting the variable for “bar_greeley” until it looked about right. When looking at a visual, I was surprised at how good their estimation skills actually were when dealing with these numbers. Most students understood that Greeley’s population was more than half of Fort Collins’, but not more than 3/4, and they adjusted it approximately correctly. Some students just left it there and called it good.
One possible solution, which many students landed on, is to divide 148612 / 400 which tells you the scale factor from the bar to the population. In this case it’s about 371. They would then divide Greeley’s population by 371 and get about 250, which is a proportional length of the bar for Greeley.
Another possibility is to divide Greeley’s population by Fort Collins’ population, and notice that it gives you the ratio of 0.625. Greeley’s bar, then, must be 62.5% of the length of Fort Collins’ bar, so they could multiply 0.625 by 400 and get a correct length of 250 for Greeley’s bar.
A third possibility is to divide BOTH Fort Collins’ population and Greeley’s population by 400. This scales both populations down to number in the hundreds, and since you divided both populations by the same amount, the ratio remains the same (there’s a connection with equivalent fractions). Fort Collins’ bar changes to a length of 371 and Greeley’s is a length of 232.
So here’s the common mistake many students made which was devilish to sort out. They simply divided Greeley’s population by 400, because that number shows up in the program right above it. The result was 232. When you set the bar length for Greeley to 232, it *looks* correct. It’s more than half of Fort Collins’ bar, but not more than 3/4, and visually it seems just about right. But the ratio between the bars is now no longer the same as the ratio between the populations! The answer is close but the process is completely wrong. Helping students to sort out why this was a mistake was really tough when they’re still novices at abstract thinking.
Some students used variable expressions to solve it, but not many. It turned out mostly to be a calculator activity, which was fine because that’s where they were when we tried it. I LOVED that it tested their estimation skills and gave them instant visual feedback about whether they were on the right track. It taught me a lot about where they were with ratios and proportions. We had a great discussion.
3) Our final unit project was pretty open-ended, but I wanted it to be creative and fun. The students had to create some kind of diagram, based on real data, that would show proportionality. I showed them some examples and a rubric from a Google Doc, here.
The project had some requirements that were non-negotiable. It had to use variables to represent quantities. The ratios had to be calculated using variable expressions. It needed to represent the data in a way that was proportional to the collected data. They had to explain what math they did, what they learned about proportionality, and why their graph was proportional to their original data.
The kids got really excited and started doing research. For many, they created tally sheets and did class surveys on whatever they were interested in : favorite sport, favorite color, number of pets. Some made Google forms to collect data. Others did research online about what they were interested in: annual salaries for their favorite careers, populations of cities, or the number of domestic pets in the country. Still others collected data in other ways: a popular project was to open a bag of candy and count the different colors.
Creating the graph with variables was more challenging for some kids than others, but it was extremely cool to see that moment when the light bulb went on and they realized the power of variable expressions. If the number of skittles is “s”, and your bar has a length of “s * 12”, you can modify the number of skittles and the bar changes proportionally. The other bars change proportionally. It’s funny how very exciting that little insight was.
Some kids really challenged themselves to do hard math by creating pie charts which require pretty complicated variable expressions. They were awesome projects.
I gave the students a survey to find out what they thought of the Rates and Ratios project. 68 students answered the survey. The project was:
The most popular response was “fun” which about 2/3 of the students gave. I don’t have reference data to see what students think of non-programming math projects: are they fun? But I was encouraged by the results and really loved what this project did for my students when it came to proportional reasoning and variable expressions.
Welcome! I started this blog as a repository for teacher resources on programming in the math classroom. I’m a former software engineer – turned – teacher, and when my classroom became a 1:1 technology classroom, I made a decision that I was going to introduce every kid to programming and teach them how to become better mathematicians through programming. Not every lesson has been successful, but I have continued to try, and this year, some amazing things have been happening in my 7th grade math class. Kids create abstractions and models. They tinker. They visualize. They ask questions about how to go deeper into a math topic. They get frustrated, and they persist, and they try harder, and they eventually succeed and feel the true joy of accomplishment, and they want to share with others what they did. They can articulate what they learned, how they learned it, and what the math in the program does – because they created it.
I welcome your contributions, questions, and feedback. I hope you decide to come along on the journey. You won’t regret it!