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My name is Devlin Daley. You might know me as the co-founder of Instructure and creator of Canvas. While I’m not with Instructure day-to-day, I am a huge fan of all users and people in the Canvas Community.

 

When we designed Canvas, our philosophy was to provide an intuitive and broad set of features that easily integrated with external tools that would provide even more depth when needed.

 

But I have discovered that products providing deep math functionality are severely lacking. I've started a new endeavor, Derivita, to address this specific gap, and I wanted to let you all know about it.

 

Derivita is an online math homework system, and we are aiming to replace all the publisher systems like MyMathLab and WebAssign. We do this by using modern technology and presenting a unique market approach:

  1. We unbundle the publisher textbook bundle. Publisher math homework systems are tied to the book they are bundled with. Derivita courseware can integrate with any textbook, even OER, which lets teachers choose the best book for their needs and use it with the best technology for their students. Students can buy a used book or rent it, giving them serious cost savings.

  2. We’ve built a computer algebra system specifically for teaching math and science. Derivita can actually do symbolic math. This fixes all the poor student experiences interacting with math homework, while also allowing for completely open-ended questions that can still be auto-graded (“Give an example of an odd function,” “Rewrite this expression in any equivalent form,” and more).

 

I approached this product the same way that I approached building a new LMS: talking with educators, schools, and students from all over the country. We’ve discussed their pain points and where technology is letting them down. Then I brought the same technical experience in building large-scale systems that are easy to use and solve real problems, to create a product that works. And of course it integrates seamlessly with Canvas :)

 

I’d appreciate it if you could pass this along to your math and science faculty friends. We are new, have a quickly growing question bank, some gosh darn awesome technology, and the best integration with Canvas you’ll see.

 

Here are some videos that show Derivita in action:

 

Webinar recording of Introduction to Derivita https://youtu.be/_JLsBm2NoDs

Subject specific features for trigonometry https://youtu.be/82qhml16Hqg

 

xoxo

— Devlin

 

devlin@derivita.com

www.derivita.com

I have been pondering how to use Canvas and other online resources in the maths classroom and have come up with a few ideas - I would love to hear from others:

Maths Journals - set up a group discussions with only one student per group.  This can then be used as an individual journal space - students can add photos of work , reflect on ideas and the teacher can respond with individual feedback

Collaborations - In Office 365 or GoogleDocs - give studenta a problem with deliberate errors and ask them to work as a group and investigate, - use it as a text based online whiteboard - provide real life projects to investigate. - include interesting images, puzzles or patterns for students to explore together.

Peer Review - use the peer review function for students to provide feedback on thinking and problem solving techniques.

Maths Displays - use apps like Padlet or Sway (office365), photostory and many others to showcase student work, problem solving skills and thinking.  - Create an eBook on topics being covered and include student solutions.

Manipulatives - embed manipulatives in Canvas pages to encourage students to explore, find patterns and try out new ideas. - try polyup or mathslearningcentre.

Word Collections - use Answer Garden, Padlet, Office365 or GoogleDocs etc to collect interesting Maths words  and definitions. - Use discussions to ask students to define a word  or find more examples  - Ask them to post images of Maths words found in everyday life.

Real Time data - Investigate real time data feeds - population, weather, energy use, disasters, traffic (search for open data) then interpret that real time data and graphs.

Flip the Classroom - provide students with the means to learn new topics before coming to class, or review topics covered.  Make this homework and use class time for collaboration and deeper understanding.

Station Rotation - Tech time, Project time, Teacher time - set up stations students cycle through to enable you to spend time 1:1 with students.

Bump it up - Place anonymous work at different levels in a discussion (small group discussions might work best here) and ask students to discuss problem solving techniques and rate the work according to a scale you can define - ask them to compare their work and consider what they need to do to "Bump it up".

Real life maths - Make your own recording of activities that need some maths - eg Choosing what to buy at the supermarket (eg what is the best value cheese), How much paint will I need? - I am building a fence - What will it cost? - many ideas here.  Students view the problem and work out how to solve it.  

Goal setting and reflection - use quizzes and unmarked surveys for students as exit cards and reflection triggers.

 

Would love to hear some more ideas on adding value to maths lessons with Canvas.

 

Isobel

   Are you ever at a loss as to how to make quizzes quickly and painlessly?  One of my favorite ways to create math quizzes or assignments in Canvas is to use Problem-Attic.  It is quick and easy to use, allows teachers to choose questions by standard, and exports as a QTI zip file to put straight into Canvas.

   Problem-Attic.com isn't pretty, but it is easy to use.  You will need to get a subscription to download to Canvas, but our district (Charlotte- Mecklenburg Schools) bought a licenses for all math teachers.  Once you are logged in, you can choose which question bank you would like to use.  I usually choose the "Common Core" bank.  Within it, you can choose your standard to see all the questions for that standard.  

   After you choose all the questions you like, you can export the file as a QTI.  Once you download the fie, you import it through settings into your course.  All the answer choices and formatting is brought with the quiz. You can even choose not to make it multiple choice and use numeric response.  

Hello All, 

 

This is my second blog post pertaining to Canvas in the Math Classroom.  If you missed it, check out the first post Canvas In the Math Classroom, which focused on using Canvas tools to save time in the classroom.  Much of a Math classroom's time is spent reviewing homework and so I provided some ways I had used Canvas to increase my time on new content while still providing that very important homework reflection opportunities to students.  

 

This posting is directed toward error analysis activities.  People with that 'Math Brain', actively think about their work and answers asking themselves; Does this make sense?  If I do the problem in a different way will I get the same answer?  Does my final answer match my estimated answer?  As a math teacher, you probably think in this manner as well and it is organic for you.  For students who struggle with math do not typically run through these questions when tackling math equations.  So, it is our job as educators to help train their brain to do so and that is where error_analysis activities are so important.

 

 

After an initial introduction to a new topic, I loved to set up a gallery walk of common errors.  I also put in some correctly completed work so that students did not already know everything posted was wrong.  After a couple of years in the classroom, you have an arsenal of common mistakes that students seem to always make.  Instead of waiting to see if this group will do the same thing.  Immediately address it before students try their hand at the math problems.  During the gallery walk, have students participate in a real time using  canvas chat tool.  If your institution has not turned on this tool, the discussion tool will do as well.  For a distance course, create a content page with the images of  a gallery walk included.  You can also choose to have students edit the content page and place feedback directly on the page.

 

I have also used the canvas_chat tool allowing students to share predictions about the most common mistakes made in calculations pertaining to the content I am teaching during the lecture.  Yes, during the lecture.  Allowing students to actively participate in the lecture without slowing your flow of teaching.  

 

Finally, utilize arc video to create a correctly performed calculation but one that is not the most efficiently performed.  Allow students to add comments during points in the video that would make the solution more efficient.  This is a great activity for groups as many times students are tentative to throw their hat into the ring.  They tend to share with their peers to confirm their thinking and then will be more likely to share.  If your institution is not currently using Arc, create the video in a Discussion post.

 

I hope these ideas will help you infuse some error analysis activities into your instruction.  I would love to hear how you are using Canvas in error analysis activities so go ahead and comment here to share tips.

As a Canvas trainer, I often do not get enough time to reach out to the math teachers / professors in the room during trainings.  Anyone who has experience teaching math (at any level) feels the pain when a group of colleagues breath that heavy sigh when the topic turn to math concepts.  As with most educational tools, math seems to demand more and the application of Canvas in the math classroom is no different.  However, Canvas has met that challenge and continues to improve upon the offerings to support math teaching and learning.  

 

I thought I would share some ways that Canvas supported my instructional practices in math classes and share the tips I learn from others as I travel and collaborate with other teachers during my trainings.

 

In this first posting, I want to share ways Canvas can help save time in the math classroom.  According to NCTM, 20 - 30% of the week is spent reviewing math homework assignments but yet only 65% of students complete the assignments (I know shocking).  Canvas has some excellent tools that can be leveraged to cut the homework review time in half and even require more student participation when reviewing these assignments.

 

Here are three ways to reduce time spent reviewing homeowork:

1.  Use Quizzes:  Quiz tools are not just for assessment.  Leverage the quiz tool to determine the most missed homework questions.  Simply create a quiz where the question is simply "Answer to Question 1" for example and the answer choices are "Correct / Incorrect".  As the Do Now, show the answers on the overhead and have students identify the questions that they did not get right.  Then, review only those questions with the class.  This saved me an enormous amount of time.  I also had a quick view of those students why simply were just lost and was able to meet with them in small groups.

 

2.  Flip an Assignment.  Give the answers!!  Create an assignment that provides an image of the answers to the work.  I have also used a 3rd party tool called Thing Link where I have created hot spots that would display the answers on the worksheet.  Then, the assignment submission from the students is their error analysis or reflection on their performance. 

 

3.  Use the Peer Review Tool to have partners check each other's work.  Have students submit pictures of their math work and then discuss the questions where their answers differed from each other.  Many students quickly found mistakes using this method and received tips from another in a different context that can help improve student comprehension.

 

I would love to hear of some other unique uses of saving homework review time by using Canvas tools.  Share them if you've got them.

 

Susan Jones

Another beta day

Posted by Susan Jones Jan 24, 2017

It's another day when I"m spending lots of time repeating clicking tasks.   I want a quiz with images and a quiz without images.   I have to individually click "move/copy this question" and then click to move it (thankfully once I've chosen a destination, that's the default), and move the 26 questions to another bank to edit them.   

    If I *could* do what it looks like I could do -- click off multiple questions, see their cute little check marks, click "save a copy here, too!"  and then click "do!"   it would save a ton of time, especially since if I'm interrupted in the task I can see which boxes are ticked.   When I'm doing the questions individually, I can't see which questions I've moved. 

   When I want a cumulative quiz, I can't nest randomization.  I'm trying to make an "addition facts practice" so that you master one, learn the next, then blend them together.  I can't set up a quiz and guarantee at least N questions from this category (say, the five times tables) and M questions from another, and then randomize them.   

     So... I'm going to make an 'easy blend' and a 'harder blend' and yes, make yet *another* bank and randomize them.   No, I can't put banks in folders to organize them -- so I'm trying to name them so that alphabetization does that.   Fortunately renaming is an option  

    Still, I at least want "learn your addition facts" to be a complete thing before I see how it works in other options... and then there's the challenge to *get* my persistent finger-counters to move away from that to imagining and getting things more quickly! 

Susan Jones

Math OER online

Posted by Susan Jones Dec 27, 2016

Not sure making this a "status update" will show up in the right places so I'm making this a "blog post."   Math Worksheets, Tables, Charts and Tutoring Help from HelpingWithMath.com      has a really nice mess of OER for math that I haven't even begun to explore.   It's targeted at parents and everything's Creative Commons licensed.   I found a really nice number line generator that I want to send students to so they can see what happens when they move things around.  

   We have some exercises in our book that have students write different number lines but this would be a nice accommodation for folks whose motor skills interfere.  

Synopsis

This blog post will show how to look up values in a formula question that can't be generated directly. In particular, it will show how to look up critical values from a student's T distribution to generate a confidence interval. It is extendable to other situations.

 

Introduction

I was trying to create a formula question that would ask students for a confidence interval about a single mean. Recently, I've been generating multiple drop-down questions that asked a series of questions about single proportions and hypothesis testing in general, but this time I wanted the students to actually compute the values, not just select them from multiple choice list.

 

The first problem is that Canvas will only allow a single value for a formula question. Not a big deal, I can ask for either the upper limit or the lower limit and if they get one of them, then they probably know what they're doing.

 

The second problem is that this type of question is generally pointless as any good statistical package (and some that aren't good) will compute confidence intervals for a user. Without work, there's little way to know that the student did it themselves or had technology do it for them. I much prefer using the 2 SD rule that plays off the 68-95-99.7 (Empirical) rule. In one of its forms, it says that the positive critical value for a 95% confidence interval (or a two-tailed significance level with α = 0.05) is about 2. We know a more accurate version for the normal distribution is about 1.96, but as rules of thumb go, 2 is a lot easier to multiply by than z=1.96. That also leads to another rule of thumb for estimating the maximum margin of error as 100%/sqrt(n), which is slightly easier to remember and work with than the 98%/sqrt(n) that you would get using z=1.96. But let's set the notion that it's a pointless question aside for a moment, because many textbooks and professors still ask this kind of question.

 

Desired Question

Here is the problem that I would like to ask:

 

McDonald's claims that their Big Mac sandwich contains 590 calories. The calories in random sample of [n] Big Macs followed a normal model with a mean of [mean] calories and a standard deviation of [sd] calories.

 

Find the [side] limit of a [level]% confidence interval for the number of calories in a McDonald's Big Mac.

 

We've already stated that you can't ask for both limits of the confidence interval at the same time. And while I would love to randomly choose "lower" or "upper" for the [side], you can only generate random numbers, not random words. So, I'm going to have to revise my question and replace the [side] by one of the two words.

 

Also, there are certain confidence levels I would like to use, like 90%, 95%, or 99%, but you can only generate random numbers between the specified minimum and maximum, not random numbers chosen from a list. So, for the time being, I'll just hard-code one of the values.

 

McDonald's claims that their Big Mac sandwich contains 590 calories. The calories in random sample of [n] Big Macs followed a normal model with a mean of [mean] calories and a standard deviation of [sd] calories.

 

Find the upper limit of a 95% confidence interval for the number of calories in a McDonald's Big Mac.

 

Here are the definitions used in the formula question

 

VariableMinMaxDecimal PlacesExample Value
n725012
mean6006501649.6
sd3075273.06

 

The upper limit of the confidence interval is the sample mean plus the critical value times the standard error of the mean, where the standard error of the mean is the sample standard deviation divided by the square root of the sample size and the critical value is looked up in a Student's T table with n-1 degrees of freedom.

 

As a formula, that would be upper=mean+cv*sd/sqrt(n) and if you wanted the lower limit, it would be lower=mean-cv*sd/sqrt(n)

 

What's missing is the critical value, cv, but that's kind of the point of this blog post.

 

Find the Critical Values with Excel

Microsoft Excel has functions for the statistical distributions we need. In particular, this one is for the Student's T distribution. Both of these are new to Excel 2010, the older version TINV() works like T.INV(), but it is recommended that you don't use it.

  • T.INV.2T(probability,df) returns the critical T value for a 2 tail test with probability area in both tails combined. That is, if you want the critical value for a 95% confidence level, you would ask for T.INV.2T(0.05,df)
  • T.INV(probability,df) returns the critical T value when the area to the left is given as the probability, so if you want the critical value for a 95% confidence level, you would ask for T.INV(0.975,df)

 

So, we create a table in Excel with the degrees of freedom that match the sample sizes [n] from the problem. Since [n] went from 7 to 25, I would need degrees of freedom ranging from 6 to 24.

 

Here's what my table looks like.

2015-10-25_22-04-19.png

The formula in cell B2 is =T.INV.2T(0.05,A2-1) and then I copied that down to cell B20. I also formatted the cells to have 3 decimal places since that's what is most common in the tables. I don't use tables myself, I have an online calculator that I wrote that gives 6 decimal places and have my students use that.

 

The next part of the process requires some manual editing since Excel doesn't have an easy way to combine a range into a comma-separated list (without using Visual Basic for Applications). Copy the values in the cv column (B2:B20) and paste them special as plain or unformatted text into a text editor like NotePad, WordPad, or even Word. Ctrl-Alt-V should do the trick for most Microsoft programs. Then go through and replace each line break with a comma. If you're using Word, you can do a search/replace. Find ^p and replace with ,

 

Strip the trailing , so you have this:

     2.447,2.365,2.306,2.262,2.228,2.201,2.179,2.160,2.145,2.131,2.120,2.110,2.101,2.093,2.086,2.080,2.074,2.069,2.064

 

Those values are, respectively, the critical t values for 6 df through 24 df with a two-tail significance level of 0.05.

 

Google Sheets wins again

Note that if you use Google Sheets, the same T.INV.2T() function works, but you now have a =JOIN() command that will automatically put all those numbers into a comma separated list for you.

 

Go to an empty cell, say C1 and enter =JOIN(", ", B2:B20)

 

Notice that I put a space after the comma so the lines wrap better (the reason will be obvious later in the blog).

 

Getting the list into Canvas

The next challenge we face is to get the list into Canvas inside a formula question.

 

Once again, Canvas doesn't make this easy. There are two functions I can find that will take a list of comma separated values and put them into a list. Those are reverse() and sort().

 

You can put either of these statements into the formula definition. Save it with 3 decimal places since that's how many decimals are in the numbers.

  • cvlist=reverse(2.447,2.365,2.306,2.262,2.228,2.201,2.179,2.160,2.145,2.131,2.120,2.110,2.101,2.093,2.086,2.080,2.074,2.069,2.064)
  • cvlist=sort(2.447,2.365,2.306,2.262,2.228,2.201,2.179,2.160,2.145,2.131,2.120,2.110,2.101,2.093,2.086,2.080,2.074,2.069,2.064)

Both of those lists return the same thing. The reverse() merely reverses the order we had and the sort() arranges it from smallest to largest, but they both turn out the same.

 

The important thing to note is that now the degrees of freedom go from 24 to 6, rather than 6 to 24.

 

Picking the critical value based on [n]

 

The at(list,index) function will return the element in position index of the list. Note that the first position is actually position 0, so instead of the indices going from 1 ... 19, they go 0 ... 18.

 

So, to get the critical value when [n]=25, we need index 0, [n]=24 is in position 1, [n]=7 is at index 18. A little math shows us that we need index=25-n.

 

Add another definition statement to get the critical value. Again, save it with 3 decimal places.

  • cv=at(cvlist,25-n)

Finding the upper limit

Now we have everything that we need to make it work. cvlist and cv should have 3 decimals, upper should have 4.

  • cvlist=reverse(2.447,2.365,2.306,2.262,2.228,2.201,2.179,2.160,2.145,2.131,2.120,2.110,2.101,2.093,2.086,2.080,2.074,2.069,2.064)
  • cv=at(cvlist,25-n)
  • upper=mean+cv*sd/sqrt(n)

Now I generate a bunch of possible solutions with a tolerance of 0.005 for two decimal place accuracy or 0.0005 for three decimal place accuracy.

 

Here's what it looks like when done. Note that the really long line pushes the results off the screen to the right, so you may not be able to see the results without scrolling.

 

2015-10-25_22-31-32.png

But I really want a random confidence level!

 

Earlier, I made a note that for the time being you would have to hard code your confidence level. That's not entirely true if you're willing to accept values that aren't in a table, like 93%. If you're doing that, you're going to be using technology, so you're not limited to the 3 decimal places.

 

This time I extended my table to include all confidence levels between 90 and 99.

 

2015-10-25_22-36-14.png

The formula in cell F2 is =T.INV.2T(1-F$1/100,$E2-1) and then I copied it down to cell O20. I formatted each cell with 6 decimal places since that's what my online probability distribution calculator returns.

 

The next trick is how to get Canvas to keep the order. If you use a sort() command, it will mix up the confidence levels and the degrees of freedom and the list will be useless. You could use reverse() to keep the order, but just reverse it. Copying and pasting isn't as straight forward this time because the values will copy across rather than down, so all the n=7 or df=6 values will occur first.

 

I make Canvas make each value unique by adding 10* the confidence level to each value.

2015-10-25_22-43-08.png

I did this in a separate portion of the spreadsheet, but you could have done it to each cell where you had it before. My formula in cell Q2 is =F$1*10+F2 and then I copied it down to cell Z20.

 

Now I copy the values into a text editor and replace every tab or newline character with a comma.

 

That ends up looking like this after adding the sort() and putting in spaces so it will line-wrap:

 

sort(901.943180, 912.019201, 922.104306, 932.201059, 942.313263, 952.446912, 962.612242, 972.828928, 983.142668, 993.707428, 901.894579, 911.966153, 922.046011, 932.136453, 942.240879, 952.364624, 962.516752, 972.714573, 982.997952, 993.499483, 901.859548, 911.927986, 922.004152, 932.090166, 942.189155, 952.306004, 962.448985, 972.633814, 982.896459, 993.355387, 901.833113, 911.899222, 921.972653, 932.055395, 942.150375, 952.262157, 962.398441, 972.573804, 982.821438, 993.249836, 901.812461, 911.876774, 921.948099, 932.028327, 942.120234, 952.228139, 962.359315, 972.527484, 982.763769, 993.169273, 901.795885, 911.858772, 921.928427, 932.006663, 942.096139, 952.200985, 962.328140, 972.490664, 982.718079, 993.105807, 901.782288, 911.844015, 921.912313, 931.988934, 942.076441, 952.178813, 962.302722, 972.460700, 982.680998, 993.054540, 901.770933, 911.831700, 921.898874, 931.974158, 942.060038, 952.160369, 962.281604, 972.435845, 982.650309, 993.012276, 901.761310, 911.821267, 921.887496, 931.961656, 942.046169, 952.144787, 962.263781, 972.414898, 982.624494, 992.976843, 901.753050, 911.812316, 921.877739, 931.950940, 942.034289, 952.131450, 962.248540, 972.397005, 982.602480, 992.946713, 901.745884, 911.804553, 921.869279, 931.941654, 942.024000, 952.119905, 962.235358, 972.381545, 982.583487, 992.920782, 901.739607, 911.797755, 921.861875, 931.933530, 942.015002, 952.109816, 962.223845, 972.368055, 982.566934, 992.898231, 901.734064, 911.791754, 921.855340, 931.926362, 942.007067, 952.100922, 962.213703, 972.356180, 982.552380, 992.878440, 901.729133, 911.786417, 921.849530, 931.919992, 942.000017, 952.093024, 962.204701, 972.345648, 982.539483, 992.860935, 901.724718, 911.781640, 921.844331, 931.914292, 941.993713, 952.085963, 962.196658, 972.336242, 982.527977, 992.845340, 901.720743, 911.777339, 921.839651, 931.909164, 941.988041, 952.079614, 962.189427, 972.327792, 982.517648, 992.831360, 901.717144, 911.773447, 921.835417, 931.904524, 941.982911, 952.073873, 962.182893, 972.320160, 982.508325, 992.818756, 901.713872, 911.769907, 921.831567, 931.900307, 941.978249, 952.068658, 962.176958, 972.313231, 982.499867, 992.807336, 901.710882, 911.766675, 921.828051, 931.896457, 941.973994, 952.063899, 962.171545, 972.306913, 982.492159, 992.796940)

 

Now it's time to pick out the one you want. There are 19 critical values for each confidence level, the maximum n was 25, and the minimum level was 90.

 

That means when the sample size is [n] and the confidence level is [level] that the zero-based index is 19*(level-90)+25-n

 

The addition of the 10*level means that we will need to subtract that after we look up the value.

 

But don't go jumping for joy yet. You can't call that cvlist, because when you put in definitions, you can only specify up to 3 decimal places. That means that you would lose the precision of looking up numbers using technology and you would need to tell your students to round to three decimals when they look up the number. Students would forget, they'd miss the problem, and be upset at you.

 

To avoid that bleak outcome, you need to include the at() command inside the main calculation and not as a separate calculation.

 

upper = mean + (at( sort(901.943180, 912.019201, 922.104306, 932.201059, 942.313263, 952.446912, 962.612242, 972.828928, 983.142668, 993.707428, 901.894579, 911.966153, 922.046011, 932.136453, 942.240879, 952.364624, 962.516752, 972.714573, 982.997952, 993.499483, 901.859548, 911.927986, 922.004152, 932.090166, 942.189155, 952.306004, 962.448985, 972.633814, 982.896459, 993.355387, 901.833113, 911.899222, 921.972653, 932.055395, 942.150375, 952.262157, 962.398441, 972.573804, 982.821438, 993.249836, 901.812461, 911.876774, 921.948099, 932.028327, 942.120234, 952.228139, 962.359315, 972.527484, 982.763769, 993.169273, 901.795885, 911.858772, 921.928427, 932.006663, 942.096139, 952.200985, 962.328140, 972.490664, 982.718079, 993.105807, 901.782288, 911.844015, 921.912313, 931.988934, 942.076441, 952.178813, 962.302722, 972.460700, 982.680998, 993.054540, 901.770933, 911.831700, 921.898874, 931.974158, 942.060038, 952.160369, 962.281604, 972.435845, 982.650309, 993.012276, 901.761310, 911.821267, 921.887496, 931.961656, 942.046169, 952.144787, 962.263781, 972.414898, 982.624494, 992.976843, 901.753050, 911.812316, 921.877739, 931.950940, 942.034289, 952.131450, 962.248540, 972.397005, 982.602480, 992.946713, 901.745884, 911.804553, 921.869279, 931.941654, 942.024000, 952.119905, 962.235358, 972.381545, 982.583487, 992.920782, 901.739607, 911.797755, 921.861875, 931.933530, 942.015002, 952.109816, 962.223845, 972.368055, 982.566934, 992.898231, 901.734064, 911.791754, 921.855340, 931.926362, 942.007067, 952.100922, 962.213703, 972.356180, 982.552380, 992.878440, 901.729133, 911.786417, 921.849530, 931.919992, 942.000017, 952.093024, 962.204701, 972.345648, 982.539483, 992.860935, 901.724718, 911.781640, 921.844331, 931.914292, 941.993713, 952.085963, 962.196658, 972.336242, 982.527977, 992.845340, 901.720743, 911.777339, 921.839651, 931.909164, 941.988041, 952.079614, 962.189427, 972.327792, 982.517648, 992.831360, 901.717144, 911.773447, 921.835417, 931.904524, 941.982911, 952.073873, 962.182893, 972.320160, 982.508325, 992.818756, 901.713872, 911.769907, 921.831567, 931.900307, 941.978249, 952.068658, 962.176958, 972.313231, 982.499867, 992.807336, 901.710882, 911.766675, 921.828051, 931.896457, 941.973994, 952.063899, 962.171545, 972.306913, 982.492159, 992.796940), 19*(level-90)+25-n)-10*level) * sd/sqrt(n)

 

Luckily, Canvas will accept spaces in a formula, so you can copy/paste what is above and it will wrap to fit within the box and your results won't be pushed off to the right.

 

Here is what the question and variable definitions look like:

 

McDonald's claims that their Big Mac sandwich contains 590 calories. The calories in random sample of [n] Big Macs followed a normal model with a mean of [mean] calories and a standard deviation of [sd] calories.

 

Find the upper limit of a [level]% confidence interval for the number of calories in a McDonald's Big Mac.

 

Here are the definitions used in the formula question

 

VariableMinMaxDecimal PlacesExample Value
n725012
mean6006501649.6
sd3075273.06
level9099095

 

But I really, really want to randomize upper/lower

 

Tough. You can't always get what you want.

 

The best you could do is to fake a word like this

 

McDonald's claims that their Big Mac sandwich contains 590 calories. The calories in random sample of [n] Big Macs followed a normal model with a mean of [mean] calories and a standard deviation of [sd] calories.

 

Find the [side] (0 means lower limit, 1 means upper limit) of a [level]% confidence interval for the number of calories in a McDonald's Big Mac.

 

Then you would add a definition for [side]

 

VariableMinMaxDecimal PlacesExample Value
n725012
mean6006501649.6
sd3075273.06
level9099095
side0101

 

and then add an if(side,1,-1) function to the big long one. JavaScript treats 0 as false and 1 as true, so the 1 gives a 1 and the 0 returns a -1.

 

limit = mean + if(side,1,-1) * (at( sort(901.943180, 912.019201, 922.104306, 932.201059, 942.313263, 952.446912, 962.612242, 972.828928, 983.142668, 993.707428, 901.894579, 911.966153, 922.046011, 932.136453, 942.240879, 952.364624, 962.516752, 972.714573, 982.997952, 993.499483, 901.859548, 911.927986, 922.004152, 932.090166, 942.189155, 952.306004, 962.448985, 972.633814, 982.896459, 993.355387, 901.833113, 911.899222, 921.972653, 932.055395, 942.150375, 952.262157, 962.398441, 972.573804, 982.821438, 993.249836, 901.812461, 911.876774, 921.948099, 932.028327, 942.120234, 952.228139, 962.359315, 972.527484, 982.763769, 993.169273, 901.795885, 911.858772, 921.928427, 932.006663, 942.096139, 952.200985, 962.328140, 972.490664, 982.718079, 993.105807, 901.782288, 911.844015, 921.912313, 931.988934, 942.076441, 952.178813, 962.302722, 972.460700, 982.680998, 993.054540, 901.770933, 911.831700, 921.898874, 931.974158, 942.060038, 952.160369, 962.281604, 972.435845, 982.650309, 993.012276, 901.761310, 911.821267, 921.887496, 931.961656, 942.046169, 952.144787, 962.263781, 972.414898, 982.624494, 992.976843, 901.753050, 911.812316, 921.877739, 931.950940, 942.034289, 952.131450, 962.248540, 972.397005, 982.602480, 992.946713, 901.745884, 911.804553, 921.869279, 931.941654, 942.024000, 952.119905, 962.235358, 972.381545, 982.583487, 992.920782, 901.739607, 911.797755, 921.861875, 931.933530, 942.015002, 952.109816, 962.223845, 972.368055, 982.566934, 992.898231, 901.734064, 911.791754, 921.855340, 931.926362, 942.007067, 952.100922, 962.213703, 972.356180, 982.552380, 992.878440, 901.729133, 911.786417, 921.849530, 931.919992, 942.000017, 952.093024, 962.204701, 972.345648, 982.539483, 992.860935, 901.724718, 911.781640, 921.844331, 931.914292, 941.993713, 952.085963, 962.196658, 972.336242, 982.527977, 992.845340, 901.720743, 911.777339, 921.839651, 931.909164, 941.988041, 952.079614, 962.189427, 972.327792, 982.517648, 992.831360, 901.717144, 911.773447, 921.835417, 931.904524, 941.982911, 952.073873, 962.182893, 972.320160, 982.508325, 992.818756, 901.713872, 911.769907, 921.831567, 931.900307, 941.978249, 952.068658, 962.176958, 972.313231, 982.499867, 992.807336, 901.710882, 911.766675, 921.828051, 931.896457, 941.973994, 952.063899, 962.171545, 972.306913, 982.492159, 992.796940), 19*(level-90)+25-n)-10*level) * sd/sqrt(n)

 

Okay, maybe you can have your cake and eat it too, but that last step of "0 for lower and 1 for upper" is likely to confuse the students.