Making Worksheets More Student Friendly.

 

Over the years, I've tried getting rid of worksheets but I end up using them when I have a sub, when I know the class is going to be shorter due to an assembly or because it is the only way available to find the type of problems I want to use.  Unfortunately most worksheets end up requiring the students to fill them out and turn them in but that isn't necessarily the most student friendly way of doing things. Just recently, I sat down to really think about how to make worksheets more student friendly and more interactive so they can complete them without getting frustrated.  

The other day, a few things came together in my mind and I think I figured out a way to make digital copies of worksheets that can be posted with help, hints, places for answers, or for showing how to do problems. It relies on using interactive images at genially.  I have several ways of making the worksheets more interactive and helpful.  

The first step is to create a jpeg of the worksheet.  This is easily done by finding a digital copy of the worksheet and bringing it up in a PDF reader like preview on the Mac.  Export the pdf as a jpeg so it is in image form. Once it is in this form, on your desktop, you can then import it into the interactive image frame. 

I chose to do a worksheet on domain and range with mapping so students get to decide if it is a function.  It is a nice visual worksheet so students can easily see the arrows.  Once you've uploaded the worksheet, you can put buttons in it, like the one you see in the corner.  The button is an eye and I set it up as a link to a short YouTube video on the subject and I've got it opening in another tab so the student can still see the work.

As a clue I can link the problems to a second page with a picture and a bit of text showing a function visually with a couple of notes so they can compare.  I can also add a page with text saying the same thing if I want.  I can also add a page with a link to the answers if I want or to a google form so students can post answers with descriptions of why they are a function or not a function.

Another way to make the work more student friendly is to take a screenshot of one of the problems off a worksheet and import it into the interactive image window.  One can link to a short video that shows how to solve this type of problem.  The nice thing about videos is they can rewatch it as needed.

For this worksheet, I would give the students the actual worksheet but I would have several problems posted individually online so they can use the interactivity to help learn to solve the problem. 

The button with the eye has a link to a short video showing how to solve one step equations and the other is page showing how to solve it step by step with explanation.  On another problem, later on, I would only list the first two steps and for the third, I would only do the instructions for the third step.  A couple problems, I'd only list the first step fully, and have the written instructions for the second two steps.  For the final few problems, I'd just list the starting step as a prompt.

The window or page provides support for those who need the extra bit but it is also a great way of providing guided practice at the same time.  If you prefer, you can put all the buttons on the digital copy of the whole worksheet but you also have the option to break it down.  If you desire, you can add a link to a google form with a few problems that students do on their own just to check their understanding.

It is so easy to add video, assessments, explanations, and examples so students get immediate help rather than struggling through the assignment.  You can also have them do the actual work on a physical worksheet and turn that in or have them place the work on a google form.  It is all up to you.  Let me know what you think, I'd love to hear. Have a great day.

Math For Thanksgiving

It's that time of year again when you only have a couple of days to teach this week because it is the week of Thanksgiving.  I love having the students do Thanksgiving themed math activities this week because they are in no mood to do regular work.  Unfortunately, most of the things labeled Thanksgiving math are the standard worksheets that substitute turkeys for chocolate or add cute Thanksgiving pictures to the worksheet.  This is where Yummy math comes to the rescue.

The link will take you to enough activities to last the whole week and give you lots of choice.  The activities span grades from upper elementary through all of middle school but some are quite easy to adjust to use in high school. There is one for planning the turkey for Thanksgiving Dinner and deciding which method - bake, fry, or smoke - is the best based on cost.  The worksheet takes students step by step through it including having them read the chart that suggests how long it takes to cook different sized turkeys. 

Another activity helps students learn to adjust the recipe for mashed potatoes for 4, 8, 10, and 12 people at first and then up to 32 servings.  It also asks students to explain how they found their answers. There is also an activity that has students calculating the amount of ingredients needed for like 23 people.  A very real life activity unless you have family members bring dishes.  Yummy math didn't forget the cranberry sauce in that they have another activity for this. 

There are three activities dealing with football since for many people, those games are extremely important. One has students reading various graphs to make predictions on the next move if it is the fourth down.  Another one has students use the pythagorean theorem to determine how far someone ran and the final has students interpreting data on an infographic in regard to NFL home advantage versus away games. 

For those not into football, there are two activities that have students analyze Macy's Thanksgiving Day Parade.  One activity has students analyzing the route from 5 years ago to determine if it is the best one and how long it will take folks to cover the route.  The other looks at two new balloons and looking at their dimensions in comparison to humans, bicycles, etc to give a better idea of size.  

The activities are not only focused on Thanksgiving itself but there are two dealing with Black Friday deals. One worksheet asks students things like how much do they save if they buy the item on sale, translating it into percent off, and completing a chart, similar to data charts in science. The other is the same type of activity but it uses different items including large screen tv sets and games.  The final financial activity has students interpreting data off of graphs in regard to consumer spending over a 5 year period.

There are enough activities that you can have different groups work on different activities so everyone's interest is met.  You could even cluster the turkey, mashed potatoes, and pumpkin pie ones as planning a meal, the football and Macy's ones as entertainment over the weekend and the financial ones for the traditional Black Friday sales.  Let me know what you think, I'd love to hear.  Have a great day.  On Wednesday, there is information on creating interactive worksheets that help the student.

Warm-up

 If you are planning breakfast for 892 people and you decide each person should be served half a fruit but you know only 33% will want grapefruit, how many grapefruit should you buy for the breakfast?

Warm-up

 If there one grapefruit tree produces 1400 pounds of fruit in a year, and there are two grapefruit per pound, how many grapefruit does the tree produce each year?

Making Videos Active.

 

I try not to assign videos to my students unless there is some sort of interactive element.  If students have to interact with the video, they are more likely to pay attention and really watch it rather than just being distracted and not getting anything from the material. 

One of the places I've used in the past is Edupuzzle because it allowed me to add questions to the video so it would automatically pause.  In addition, they offer a free plan with up to 20 videos in ones account.  I do not know if you can delete the ones you've already used so you can designate more to your account.  

The nice thing about Edupuzzle is that you can use premade videos or you can make one yourself.  When you look on a premade video you can check it out and it tells you where the activities are in the video and what type of activity are inserted.  In addition, they list the other videos based on the one you are looking at.  If you don't like one, you can make one of your own.  You choose the video from one of many sources from Youtube to National Geographic to TED talks and more.  Then you insert the type of activity which could be multiple choice, open ended, or a note and you can use all of the video, or only a small part of it so you have a ton of versatility.  Finally, you can use your google ID to log in and you can set up classes so you can assign the videos to each student but there are permissions involved so Edupuzzle offers letters you can send home explaining it all.

If this site is not for you, you can use google suite to create interactive videos.  This site has a lovely hour long video showing how to create interactive video lessons using G suite with a focus on distance learning but the material is still valid for creating interactive videos and you can select just a specific topic rather than planning for a full class period. I love videos because I can watch, stop it, and try each step myself.  I've found when I can see what is supposed to happen is much more helpful than just reading the steps.  The real information on the video starts around 13 minutes in since this is actually a presentation.  It takes you from start to finish and begins with google hangout which will be google chat after January 1, 2023. I mention this because the person has you begin with meeting yourself on google hangout but google chats will still allow you to have video meetings.

When you meet with yourself, you record your whole presentation just like you would do if this were a real meeting.  She talks about how one would include handwritten examples which is awesome in math. She walks you through the process step by step to make your own document camera so you can do it on a paper if you don't want to use google jam board. 

I like that the instructor takes you step by step through planning a lesson with all the things you need to think about and shows you everything in detail. I like the information and directions included so I can make the videos with examples and assessments.  She talks about including assessments by using google forms or a rubric via google classroom. If you want a set of interactive videos available to help students, check the site out and have fun.

So you have Edpuzzle which uses regular videos from other content creators with questions and notes and gsuite that will allow you to make your own lessons.   Let me know what you think, I'd love to hear.  Have a great weekend.

The Geometry Of Gerrymandering.

 

The midterm elections are mostly over and a couple of cases on voting seem to head to the state court systems or the Supreme Court.  Often, the cases that make it to court deal with the way the area is divided up for voting.  States often want to redraw districts to favor the party in charge but did you realize how much of a role geometry plays in this whole situation?

It turns out that geometry provides a powerful tool for establishing the best division of area into voting districts for places that have at least two parties.  According to the constitution, the candidate who gets the most electoral votes wins but the way the districts are designed can have a huge impact on how the votes are distributed.

When governments rearrange the shapes of each district, they can encourage a favored candidate to win to keep them in power and to provide representation that may not be really representative of the district.  We'll use a small example of 50 voters who live in a 5 by 10 area, one person per square.  The voter distribution is 20 are red and 30 are blue, so if you divide the area into 5 districts, you have several possible results.  If you have two rows of red and 3 rows of blue and divide it so you have two districts of red and three districts of blue, the blue will provide more votes for their candidate so if this were the house, you'd have two red and three blue but what if you want the blue to win all the seats?  You would redesign the 5 districts so all 5 districts are set up so there are four red voters to every 6 blue voters and the blue would take all the seats but what if you wanted red to win the majority of seats.  You would have to redraw the districts so three of the districts had more red than blue and the red would get three votes.  The first few scenarios can be accomplished using regular districts but the last situation requires districts to be done in irregular shapes rather than standard shapes.

These examples are not all theoretical.  Back in 2012 in New York State when 58 percent of the voters voted democratic but the democrats got 21 out of the 27 available seats. On the other side, 51 percent of the voters in Pennsylvania only won 5 of the 18 available seats in the same year.  The practice of redrawing districts to give a certain party the advantage is referred to as gerrymandering which comes from Elbridge Gerry who was governor of Massachusetts in the early 1800's.  His party was good at redoing districts into strange shapes to give his partner the advantage.  A cartoonist noted that the districting looked like a salamander so the term gerrymandering was born.

It appears local and state governments change the lines of districts about every 10 years when a new census comes out.  Over the 10 year period people move and the number of red and blue voters change so the lines have to be redrawn to help a political party stay in power. Although intentional gerrymandering is illegal, most people find it difficult to establish rules for fair districting, and this includes mathematicians.  Every state has their own rules which makes it even more difficult.

The most fair criteria for districting is that the number of red and blue voters should be about equal, each district should contain about the same number of total voters, should not discriminate against any ethnic group, not cross county lines, and follow natural boundaries but in reality, it is hard to do this.  In addition, if one wants to keep compact districts, it can't always be done and doesn't always produce fair voting results.

One study looked at the presidential election in Florida in 2000 because the number of republican voters equaled the number of democratic voters but the republicans had the edge in results.  The scientists redrew district lines to meet the definition of compact districts while meeting Florida state rules but the results showed the republicans had the advantage. The skewed results came from the fact that most of the democrats lived in urban areas while republicans lived in rural areas. This leads to the republicans winning more. Others did more research and discovered you cannot prove the districts were drawn to give one party the advantage by just looking at the lines.

One set of scientists discovered that one has to look at the efficiency gap. The efficiency gap is calculated by subtracting the "wasted" votes of the two parties from each other and then the answer is divided by the total number of votes.  A wasted vote is defined as a vote cast in the district where the other party won or is above the margin needed to win. The smaller the efficiency gap, the more impartial the results.  Sometimes the efficiency gap isn't the best choice when all the voters of a party live in the same place.  So another group wrote a computer program to determine possible ways to set the districts based on state requirements.  They applied this to the state of Maryland in 2011 and the computer came up with 250 million possibilities.  They found the results gave the democrats an advantage.  In fact, 99.79 percent of the 250 million results favored the democrats. 

Many states have moved to using independent commissions to set up the districts and these commissions use computer programs to find the fairest way to set up the voting districts so the results are more fair to all but some states are still trying to adjust districts to give them an advantage.  So this is where math comes into play.  Have a great day and let me know what you think, I'd love to hear.   

Creating Interactive Image

 

Every to often, I want to create interactive photos so that students can click on things to bring up information.  The two programs I've used in the past cost money and I don't always have the money available so I went looking for something free.  I found a program that is free and that allows the creation of interaction photos and other things.

Genially is a site that allows you to create a variety of interactive activities from presentations to gamification to so much more.  One can sign in using any google ID you already have and it allows educators to say they want to use it for class.  

After I set up an account, I then clicked on new project and discovered I could create a presentation, infographic, gamification, interactive image, video presentation, guide, etc.  You have a choice.

So I chose interactive image since that is what I wanted to focus on. As soon as I clicked on interactive image, it went to the page for creating an interactive image and there was a video right there I could play that took me step by step through the process.   That helped so much.  I would strongly recommend watching the video a couple of times to make sure you have an idea of how to do thing.  

Once I imported a photo, I had my choice of these types of interactivity to include with it.  I could do a tooltip which provides a short title or description when you run your curser over it.  A window which is a box that has text, images, video, or other content.  The ability to link a button to a page, audio, or adding a reveal.  So many possibilities.

When you actually get to the editing page, it is much like canva and other similar programs.  It gives you a ton of different buttons you can choose from and it is easy to resize the button.  It is also easy to create the interactivity to make the photo much more interesting.  When you are done, you can download the interactive photo or use it with google classroom.

 In addition, Genially also offers courses to help you learn to use the site for teaching.  At the moment, there is a course on gamification, a micro course on assessments, and a micro course on using it as an add-on for google classroom.  This site has lots of templates one can use for teaching and the site allows you to easily separate the educational templates from the rest.  The educational subtopics are educational presentations, unit plans, graphic organizers, timelines, informational organizers, flashcards, quizzes, planners, and assessments.  

I went looking for a place to create an interactive image and ended up with a place that will allow me to do so much.  Let me know what you think, I'd love to hear.  Have a great day.