Apps To Help With Distance Learning

With the world the way it is, most school districts will be switching from totally open to suddenly teaching via distance.  It will come with little warning due to the increased numbers of infected people.  We have one school in the district that is red and will be for a couple of weeks.  There are other districts who have to shut down for a week here and there. 

Many districts rely on Zoom or Google Hangouts to conduct class but it is good to know which apps work well with this type of class ahead of time.  These apps allow the teacher to recored lessons and collect work from students who are not physically in class. Fortunately, there are apps one can use in class to make it better.  Most students have a cell phone that allows them to download apps to use.

For math, I highly recommend Desmos for so many reasons.  It is wonderful for graphing equations without having to rewrite them into the y = something format first.  It also has activities for all sorts of maths and tutorials on different aspects of math.  In addition, most cell phones allow people to snap a picture of their screen so students can create graphs, snap a picture, and send it off. 

Another app I like to use are the hand writing recognition calculators.  These are ones students can use a finger or style to write a problem and the app turns the handwriting into a print format and does the math.  When I found one for my iPad, I showed it to a couple of scientists, both with Phd's and they had so much fun playing with it.  They wanted to try it out much like someone taking a lambergini out for a test drive.  They both downloaded it to their phones.

Flipgrid is a great app because it allows students to film themselves as they answer questions, present information.  It is free and it allows teachers to get a free account and then set up classes just like you do with google classroom.  Teachers can also assign "work" requiring students to create videos on a topic to turn in.  This app is great for helping student learn to communicate their mathematical thinking.  

Then there is google forms to use in google classroom.  I use forms to create short quizzes for my students.  I usually create multiple choice quizzes so students have the opportunity to practice for standardized tests.  I love the fact the quiz feature allows me to set it up so students are unable to open up new tabs in the browser to look for answers.  Google forms can also be used to create surveys, and pre-assessments.  It also integrates beautifully into google classroom.

I also love and recommend google classroom because I can post everything from warm-ups to exit tickets, teacher created videos, links, files in google drive, and so many other things to create a one stop place for class.  It allows me to create work at home if school suddenly goes red and a way to communicate with students in a way other than Zoom or Google Meets.

One way to help monitor student understanding is to have students contribute to creating a book on various topics using google slides, pages, or book creator.  It is easy to divide students into groups and have each group work on a book.  Google slides and book creator allows students to collaborate from a distance or in class.  It provides options to the teacher.

Finally, some of the online games such as Kahoot have created options to help with distance learning.  In addition, to the playing live as before, they also offer a work at your own pace options which is a nice option because it means all students have an opportunity to do their best.

I realize there are more out there that can be used to help improve distance learning.  Unfortunately, it is still something many of us are facing and we face the possible move from in class to distance and back.  All of these apps work with the move back and forth.  Let me know what you think, I'd love to hear.  Have a great day.

More Stressed Out Than Normal.

This past Friday, several of us were talking and we all agreed that we are so much more stressed than usual and it can all be attributed to the coronavirus.  Due to the size of our district and the way the villages tend to be accessible only by boat or air, each school makes the decision of how the school operates.

Originally, all schools were going to open late in a hybrid model with half the students attending Monday and Tuesday and the other half on Wednesday and Thursday with Friday off to deep clean. So we all planned accordingly.

Then just a couple days before the opening of school, we were told that our school meets all the criteria to open with all the students attending five days a week. Thanks to the principal, we managed to have hybrid the first week with students attending only four days a week on a reduced schedule of 9 to 1:30 for the next two weeks.  Then unless things change, we go back to five days a week fully the week of October 5th.

We've discovered we need all the extra time we have right now to prepare lessons so they can be given in class, or via distance because many of our students go in and out of quarantine due to members of their family who travel or due to the student heading out for some reason.  There is also the possibility that we could suddenly go red if we get a few people who are infected with the virus.  

We just got told on Friday that anyone listed as distance learning is probably at home under quarantine so we need to check every morning and send work home each day they are out unless a parent calls to request material for a full week.

In addition, it appears the administration is going to be going through the normal evaluation process where we have to be observed five times each semester.  They are also talking about having students take all the normal standardized tests from state to district mandated ones.  This is hard since students have been out about six months and are trying to readjust to school.

Another problem is that the rules are constantly changing.  We get told one thing one day and the next day it changes.  In fact, things can change twice in one day.  As teachers, we feel as if we are waiting for the other shoe to fall especially since one of the villages with a population of 700 has had 14 cases identified in under a week and has had to go red with everyone including teachers under quarantine.

It is the stress of not knowing what is going on and what may happen.  We are all under extra stress with having to provide extra materials from videos to worksheets with being evaluated and trying to keep our sanity throughout it.  I am exercising, dancing, and cooking to help relieve stress but I can't get rid of all of it.

I'm sure we aren't the only ones who are trying to survive the uncertainty of the situation.  I think districts are trying to get back to normal as soon as possible so it looks as if nothing is wrong but I suspect, if we rush back to operating "normally" too fast, we'll have to move several steps backward instead of moving forward.

Let me now what you think, I'd love to hear.  Have a great day.

Warm-up

If Lake Heron is 177 miles wide and you are able to paddle at 4mph, how long will it take you to cross the lake? 

Warm-up

If you get a good wind and are flying along at 37 mph, how long will it take you to travel the 277 mile length of the Grand Canyon? 

Visualizing Algebraic Transformations.

I just taught algebraic transformations in class and I did it a bit differently than I've usually done.  Usually, I just emphasize the equations and if you see this here, then the graph does this.  I changed things up this time because I've attended several webinars that encourage providing a visual element to go with the equations.

All along, I've encouraged students to graph the parent equation on Desmos and the new equation so they can see where the new graph is.  This made it easier for them to count the units left or right, up or down.  It was fun watching them involved in tracking how the new one moved and changed.

When we started the section that had the graph starting at a location other than at 0,0, and asking student to write a new equation for the transformed graph.  I asked students to attempt to write the new equation to match the transformation and then graph it to see if it matched the required movement.  It was interesting to watch students look at the new graph, change various numbers until it worked.  I admit, I gave them the official information but let them do more exploration rather than making them follow all the official rules.

After they had a chance to explore things, I showed them how to use the information given to rewrite the equations using the official rules. Many of my students "saw" the relationship between the equations and the movements.  Even the students who got the hang of using the equations with the new movement, graphed both equations to verify they were correct.  

In the process, I also discovered that about half the students didn't pay attention to the numbering on the axis lines.  Several ended up with an incorrect equation because they didn't see that the graph was labeled by two's rather than one's.  I suggested they take time to read the markings before they began looking for the new equation.

I noticed that students had a bit of difficulty with a reflection over the y - axis because for most of the functions they used, it didn't change anything.  They also had difficulty with horizontal and vertical shrink and stretch because they almost look the same and the difference is based on nuances.  Honestly, I teach all of this but it's hard to discuss when they will ever have to identify the shrinks and stretches. 

I think the next time I teach this, I'll incorporate more activities found on Desmos to give students a better grasp of transformations.  I think most people are comfortable just graphing things using some sort of graphing calculator and don't think they need to know any of this but I think they need to be aware of things.  This way they can look at the equation they graphed to see if it looks correct.

With all these new graphing calculator, it is not as necessary to know how to read an equation and graph it from the information in an equation. Let me know what you think, I'd love to hear.  Have a great day.

He Was Right!

The other day, I listened to a talk by Robert Kaplinsky in which he commented that if you gave kids a problem they had to solve using steps, about 80 percent could do it but if you gave them a problem with lots of blanks to fill in and come up with a certain type of problem only about 50% out of the 80% could do it while the 30% couldn't.

I took a simple problem from his Open Middle site.  It had two blank squares + x = two blank squares. The idea was to use digits one to nine only once to come up with the largest value for x.  It was the "Solving one step equations with the greatest solution."

I gave it to all my students from Algebra I to Pre-calculus and about half struggled with the problem and the other half managed to figure something out.  Some students decided their first answer had to be right and looked at me strangely at the idea that a problem could have more than one answer or at least the correct answer might not be the one they got.

I started with this one because it is a standard equation that all students should be able to solve. Honestly, I expected the students in my higher level classes to have no trouble but some did.  The ones who finally got the hang of it, did quite well and came up with some interesting solutions.  I downloaded the sheet from Robert's site that allows students to try multiple times while taking time to explain what they learned from their try.  

I think that some were happy to get an answer and they felt they had an answer so it must be correct.  I had others who made several attempts trying to find the largest value of x while others seemed to aim for the smallest as if they didn't quite understand the objective.  I even ad a couple who got the correct answer after multiple tries who showed me the different possibilities they thought of.

This is a website I'll be using at least once a week to help students learn more about solving problems with one answer but with multiple possibilities of getting their.  Students are so focused on a problem that has all the numbers that lead to the answer that they either have forgotten that there are many ways to get to a single answer.

The great thing about the problems is that they include hints and answers so you know what the answer should be as students work their way towards the solution.  There are problems for grades K on up to high school.  I started with one from 6th grade because I wanted my students to be able to do it without too much frustration.  The ones for Kindergarten require things like completing number sequences with caterpillars while some in high school such as having students create an absolute value equation where      x = -2 is an extraneous solution.

If you haven't used it, check it out.  It is designed to help students understand concepts better so they don't just solve a problem by going through the steps.  Let me know what you think, I'd love to hear.  Have a great day.

The Writing Process Applied To Math.

 I came across an interesting idea to use in math that makes total sense.  Let's look at the writing process used in English.  In theory, one brainstorms ideas on a topic.  The ideas are used to create the first draft before going over it and revising it multiple times till the final product.  Although many students think they can write the perfect paper on the first try, the reality is that it takes multiple revisions.  English teachers encourage or require multiple rewrites with peer reviews or teacher review.

In math, most of the time, students operate under the assumption that the should be able to get the problem solved in one try and if they can't something is wrong but what if we applied the language of a writing to solving problems.

The first step is to brainstorm ideas and thoughts for a paper but in math the equivalent would be to brainstorm the strategy one uses to solve the problem.  In English, the writer assembles the ideas into the first draft so in math we should think that the first attempt at solving the problem as the first draft.  When a person makes a second attempt at solving the problem it is like writing a second draft.  

I tutored someone in writing papers in college.  I spend a lot of time explaining that once you make a change anywhere in the paper, the rest of it has to be adjusted. The same applies to solving a problem.  If a student makes a arithmetic mistake, going back and correction the calculation is not going to make a change in the solution unless making the appropriate changes that result from the correction.  It is neat to think of every attempt as a rough draft and the final paper is completed when the correct solution is reached.  

So how can one present this to students so it becomes a part of their lives. By this I mean, so they are willing to redo a problem as many times as they need to come up with the correct answer.  One way, is to have students work open ended questions on a form with multiple compartments.  Students make their first try in the first box and when they make a mistake, rather than erasing their work, they stop and make their second attempt in the second box.  When they finally reach a solution, they have a record of the different ways they tried.

This record allows students to review what they tried, think of new ways to try and they have a record of their learning because as they get better at solving a specific type of problem, they can see it because it will take fewer tries to solve.  

A teacher could have students use this type of paper to show their work for each problem on an assignment. The work is shown on the paper while the answer is placed on the assigned sheet.  The record also allows the teacher to assess their understanding of the concept and the process.  I found a great worksheet for having students show their attempt on the OpenMiddle website.  Although it is designed to go with those problems, it is the perfect sheet for students to do all work on because it asks them to verbalize what they learned at the end of each attempt.  

I love this concept because it helps students see that it is ok to take several tries to find the solution to a problem and that each time the student makes an attempt, they learn something.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

The height of the cup is 4 inches while the diameter is 1.5 inches.  What is the volume of the cup?

 

Warm-up

 

The semi-circle has a diameter of 10 feet.  What is the area of the window?

Cool Series

I seldom write about books, especially fictional books but I stumbled across a series I fell in love with.  The author, Julie Moffett created a heroine I can absolutely relate to.  She wrote the Lexi Carmichael Mystery Series.   

Lexi Carmichael is twenty five years old with a degree in mathematics and computer science.  She works for the NSA but prior to that she did some hacking until she got caught.

When it comes to social situations, she has no idea how to relate.  She'd rather be on her computer, doing her thing than try to interact with normal people.  She has three best friends, one is female who helps her navigate normal society while the other two are guys who used to work for the NSA but left to work in the private sector and are more geeky and hacker like than her.

Lexi ends up involved in mysteries where she has no idea what is going on at the beginning but ends up using her math and computer skills to solve it.  Being into math myself, I follow the logic and knowing something about computers, I understand the talk.  I feel as if she is someone I could be friends with and hang out with.  

Aside from the three best friends, she ends up working for a former MI-6 agent who left there to start his own company with one of the original hackers after working for the NSA.  When things get dicey and she needs additional help, she brings in the other two guys because they are considered the absolute best of the best when it comes to hacking.  These guys are twins and they work may be a bit more socially inept than her.  The last main character is an Italian guy, Slash,  who works for NSA and apparently used to work for the Vatican in computers.  He is also a hacker, carries a gun, and ends up protecting her.

There are currently 12 books in the series.  I am on book number three where she ends up helping Slash find out who broke into the Vatican coffers to steal a bunch of money and frame his uncle.  Unfortunately, the person who installed the gate way is found dead, someone tries to sedate and kidnap Lexi, and Lexi managed to find three encrypted files that lead them to the instigator and the actual crime. 

I'm always on the lookout for books I can recommend to my female students to read.  Books the have a female protagonist rather than a male. Books that might encourage them to think of going into math, science, or computers.  Honestly, I relate to Lexi when it comes to preferring to hang out on computers rather than trying to read those signals put out by society.  

I also admit to enjoying it when the character begins to think about statistics, number patterns, and such.  It's also nice when Lexi's best friend often asks everyone to speak in English because she doesn't understand Geek Speak.  I felt that way in high school when I was around other girls.  I didn't relate to the whole dating thing.  I didn't know how to wear make-up, fix my hair, or even manage to look totally put together.  Reading that Lexi feels weird when dressed up and doesn't feel outside of her normal jeans and t-shirt, makes me feel like I'm not that weird. 

Amazon had the first volume with the first four books on sale and I purchased them.  I started reading and I'm hooked.  I will probably work my way through all 12 volumes because I want to see what the next situation she'll end up in and what skills both math and computer she'll use.  Check it out, enjoy, and next week, I'll be back to normal topics.  Thank you for letting me share a series with you.  Let me now what you think, I'd love to hear.  

I Did It!

Due to the uncertain times, I'm having to create lesson plans for everything from being totally open with all students in the classroom to being on red and having to teach via distance.   Everything I plan, I do it with the possibility of circumstances changing over night.

Right now, we are on a modified schedule of half the school attends Monday and Tuesday, while the other half comes on Wednesday and Thursday.  Friday is our day for deep cleaning but next week, all students will come to school from 9:00 am to 1:30 pm so we have time at the end of the day to deep clean.  The first week in October, we'll be going full days with all the students but that could change if we get any more cases in town.

With everything the way it is, I've put some serious consideration into how I'm going to do things this year.  I've set up google classroom for all my classes and the one thing I've done for the first time, is to begin creating my own videos for students.  I am not recording the whole lecture.  Instead, I am making short to the point videos lasting no more than 10 minutes.

The other night, I made three, one for Algebra I, one for Algebra II, and one for my Pre-calculus class. Each video covers the material so they can see how to do the work.  They were really easy to make.  I used my iPad Pro, Apple Pencil, and my copy of Stage Pro.   Stage Pro is an app put out by Belkin and it turns your iPad into a document camera or allows you to record videos. 

I will tell you that it costs to buy but they do have a free version.  I have both but use the pro version because it has everything.  It allows me to set a plan background and record myself as if I am doing a lecture on a white board or I can put plane graph paper or graph paper with the traditional X, Y coordinate system.  In addition, I can bring in a photo of a problem I've done a head of time and write over it like I might do if I were showing students how to find an error.  I also have my choice of fine line aka college ruled or large ruled paper to use as a background if I have trouble writing in straight lines.  There are maps offered but I focused on the things I prefer using.

The app offers a choice of 8 ink colors tow write with and a pen with a choice of four thicknesses that resembler everything from a pen or pencil to a thick marker and three choices of an eraser.  If you are not great at basic shapes such as triangles, squares, or circles, the app offers you these shapes. You can enlarge the shapes to create a colored background.  I can type information or add sticky notes or labels to the product so as to show what is important or show steps.  There is even a choice for making your own labels. 

I had fun using the app to create videos.  It was easy to start and pause the recording as I filmed myself.  I could stop the video, change the background such as going from a graph to a whiteboard and then start recording again.  The button showing the time, is the pause button while the original record button starts and stops the buttons.

Although it saves the videos on the iPad, it was easy to upload them to google drive and from there one can place the videos into google classroom.  I can also provide each student with a link so they can download all videos from google drive.  Furthermore, the district is working on arranging for students to be able to take computers home so they can download all information and work to the computers so they do not have to rely on internet.  

Out in rural Alaska, internet is not the most reliable thing and many families cannot afford it due to the cost so allowing students to download videos and assignments means they can work at home but if we go to red, the school has ordered a bunch of thumb drives that teachers can download the info to and the thumb drives can be picked up by the student or their parents when they pick up lunch.  

I am proud of myself because I finally started making videos.  I plan to make videos for every lesson so students can keep up.  This all works for students whose families end up on quarantine on a regular basis.  Before you assume, we have parents and students who have to travel due to their jobs or due to medical so when they return, they and the whole family have to undergo a 14 day quarantine.  These videos allow students to stay up with all work while being quarantined.  

Let me know what you think, I'd love to hear.  

Conversation Response Starters.

 

It is easy to find conversation starters but not as easy to find responses.  In addition, many students have difficulty responding to a conversation starter.  Often students need help learning both to start and respond to create a better conversation. I say better conversation because many students have the "I got 3x +2." and "I got that too." so they've had it and it's over.  In reality this does not help students learn to talk about math to any depth.

There are certain techniques to help students learn to carry out better conversations.  What ever techniques a teacher decides to use, it is important that it include something for the other student to use to help respond with something other than  yes or no. 

I once participated in training to do improvisational theater.  The biggest rule for improvisational is to never, never, never do anything to get a "no" because the no stops everything cold.  One thing we did was a "Yes and......." where we said "Yes and..........." and filled in something so the other person could say yes and something.  This could be used in math like this:

Student 1 - "I got the answer 14."  Student 2 - "Yes I got that and I did it by adding 3 to both sides." Student 1 - "Yes I did that too and when I did it, I eliminated the constant" etc.  This is not something you want to start out with.

One way to encourage this is to pass out partner discussion cards in which there is a starter prompt and a response prompt to get the full conversation going.  These cards all have a starter question with a response prompt and are based more on general strategies rather such as "What strategy could you use to solve the problem?" and "I could have used......" or "How do you know your answer is reasonable?"  I know it is reasonable because......."

Although there are several sites with cards ready for purchase, it isn't that difficult to surf the internet finding examples for you to make your own.  If you want to make your own, remember to think about asking students to discuss strategies or give explanations so the discussion begins with a "What", "Why", or "How."  Just remember that these cards fall into one of four categories.  The first is "Making sense of problems and persevere" with questions such as "What strategy did you use?" or "How would you explain your strategy to others?".

The second is "Reason, Explain, and Critique" which asks things like "How did you get your answer?" or "How can you be sure your answer is right?".  Next is "Reflect and connect" with questions like "What is the relationship between ________ and _________", or "What skills or concepts did you use?".  Finally is the "Sentence Starters" such as "The strategy that makes the most sense to me is........" or "I was really surprised when........".

The nice thing about these partner discussion cards is that they can be used via distance learning through the use of breakout rooms or in math journals.  This type of activity does not have to be used only in a regular class. Furthermore, why not have some of these questions on a Poster that is hung on the wall so students can easily look up and check for a conversation starter starter or response. 

In regard to posters, I found this on the internet with some great suggestions for conversation starters and responses that go with four main areas.  One is "Clarify the problem and ideas for solving it." which asks "What are we trying to do?" or "In future problems like this we need to remember to ......".  Another is "Discuss representations and models" with questions like "How can we explain this to others?" or "Another way to show this is.........".  Next is "Explain and support reasoning." asking "What does that mean?" or "In math we always need to ........".  Last is "Use multiple methods of solving." with questions like "How can we solve it with symbols?" or "I think these two methods relate because......."  

The poster with these questions can easily be printed out and hung on the wall where students can refer to it or check it out or make copies for every student so they can put it in their notebook to refer to during conversations.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

If four coconuts produce 50 ml of oil, how many coconuts do you need for 625 ml of oil.

Warm-up

If it takes 20 avocados to produce 250 ml of oil, how many avocados do you need to produce 825 ml of oil?

Encouraging Conversations In Math Class.

One of the most important things in math involves conversation between students.  Unfortunately, many students arrive in high school without having the basic skills needed to share ideas or explanations of how or why they completed a certain problem.  In fact, the principal discussed that one thing they have to look for evaluations is a certain level of talk carried out during class.  

When she read out every thing the third party evaluation said students should be doing, I was surprised. We didn't get to that level of discussion in my college math classes.

In today's world it is important to encourage frequent mathematical conversations in class because it helps them deepen their own understanding while clarifying their own thoughts.  In addition, it helps turn students into a community of learners. 

Before beginning the discussion, it is important for the teacher to define exactly what they want to accomplish at the end.  With the goal in mind, the teacher has somethings to think about.  Before the discussion begins, the teacher should choose a problem which guides students towards the goal, and think about possible student responses so as to be prepared for misconceptions that might need to be addressed.

During the discussion, the teacher should monitor student responses, listening for misconceptions, and areas of concern.  Think about which students have a solution that meets the teachers original goal so the students can share with the rest of the class.  Furthermore, take time to decide what order the solutions will be presented in.  One might consider arranging the solutions from the most widely used method to one that is unique.  Finally connect solutions so students are able to discuss similarities and difference.

Finally, after the discussion, teachers need to go back through the solutions to look for misconceptions or areas requiring clarification.  As students to review their solutions to see if they seem reasonable or select a solution and have students find a method to determine if the answer is reasonable.  In addition, students should be able to justify the method they used to arrive at a solution.  Finally, take time to have students examine errors to discover where they went wrong and what they need to correct the problem. They should be given time to rework the problem until it is correct.

There are seven techniques teachers can use with students to help them learn. These can easily be used in the classroom.

1.  Revoicing or repeating - The teacher can do this or have another student do it.  The person repeats what the student said and asks if this is what the student said.  This technique can help clarify a student's thoughts or emphasize the thought.  When this technique is used frequently in class, it can help students recognize the important elements of a conversation and select these to remember.

2. Repeating - this is different than revoicing in that a student repeats or paraphrases the important ideas stated by another student.  This one helps students identify important ideas and slows down the conversation so students have time to process the information.

3. Reasoning - in this activity, the teacher asks one student to compare their reasoning with that of another student.  Students have to analyze the other student's reasoning before they can begin to compare the other student's logic with theirs.  Students end up diving deep into things, while making sense of the other person's thinking patterns.

4. Adding on - this is where once a student has finished sharing their thoughts, the teacher asks others to add on to what was said.  This encourages students to participate and is best used when only a few students are involved in the discussion.

5. Wait time - This is hard for many instructors because we don't like silence and even waiting 10 seconds is so hard as it feels like we are waiting forever.  Many students need just a bit extra time to assemble their thoughts.  When we don't give enough wait time, we discourage some students from sharing.  

6.  Turn and talk - is more of a think-pair-share. This technique allows students to talk in pairs, where they are able to express ideas in a more secure situation.  It also gives the teacher a chance to listen in to discover misconceptions, ideas that need clarification, or students who need just a bit more to be there.  This is a great assessment tool.

7. Revise - this is where students revise their thinking as a result of all this talk.  Students are able to explain how their thinking changed from where they were in understanding to where they are now.  In addition, they can explain why their thinking changed.

These are techniques to help encourage conversation in class.  Unfortunately, you cannot just implement all seven in one day.  It is important to introduce one technique to the students and have them practice it over a period of time until they have it down.  When practiced enough, students will do these automatically and their ability to discuss the material will increase accordingly.

On Monday, I'll share some conversation starters and response starters to help students who might have trouble getting started.  Let me know what you think, I'd love to hear. Have a great day.

Guided Practice

Many teachers are facing the challenge of teaching either via distance or in a hybrid model which does not allow as much time for helping students individually as much as we did before.  I worry about being able to provide enough guided practice in class so my students really learn the material.

As any teacher knows, practice is needed for students to learn to do anything, be it sports or math.  It does not mean getting them to do it perfectly the first time because more learning goes on when they make mistakes and have to correct them.

Guided practice is a way to help students practice learning a new skill or old skill at their developmental level with increasing levels of difficulty. In class, it is easy to plan for guided practice but it is not as easy when you have less time with the students in class.  Normally, it would be possible to divide students up into groups to work but with Covid-19, it is not as easy.

Fortunately, there are some methods of guided practice we can use in this time of unique instruction.  One is called the "Gradual Release of Responsibility Method" which is also known as the "I do, We do, You do" model.  This method moves from teacher focused to student focused by transferring responsibility.

When the teacher models the action, it is the "I do" part.  With the teacher modeling, students get a chance to see the task and how it is done.  It introduces them to it.  It is suggested that teachers break the material into small, clear, steps by using some sort of visual chart to help students understand the process.  Include mnemonic and acronyms to help facilitate student recall while encouraging students to take notes of things they might have trouble remembering in the future.  Furthermore, it is important to give students time to ask questions at the end of each step for clarification and to allow them time to process.

The next step is the "We do" stage where it is done together.  I've done this stage by having students do the same process I modeled in the "I do" stage.  This can also be done by working in small groups or in pairs. In terms of zoom, it would be done via the use of breakout room but it is much harder with the 6 foot distancing which is why one can create worksheets with missing information that students fill in.  

In addition, one might ask what the next step is?  This helps students work on recall to move the information from short term to long term memory.  One might also ask students to debate whether a certain step is better than another such as would you divide by the number outside the parenthesis in a distributive property problem rather than multiplying?

The "You do" stage is actually divided into two parts.   In the first part the teacher is facilitating responsibility from herself to the students and in the second stage, students are given full responsibility for completing the problems.  In the first part, students are encouraged to complete as much of the task as possible with the teacher stepping in to gently guide the student towards completion. In this stage, teachers should ask students to explain what they've done and why they did it that way.  Students should be encouraged to ask questions when they stall and teachers should provide direction via open-ended questions, prompts, or nudges to help the student remember the next step.

In the final stage for "You do", the student is expected to complete a task from start to finish and be assigned a number of problems to complete to reinforce learning.  One can also have students do similar problems that have a small twist or are just a bit different to help with transference of material. 

Sometimes having group or pair work is difficult in class due to the coronavirus. I've found that if I create a worksheet with an example complete with explanation and then write the following problems so students fill in the missing material, it can do the same thing.  What I mean about following problems is that I might have two or three that are missing the final step so students have to write that in.  Then I might cut out the final two steps so students have to fill those in to complete the problem.  Eventually, the only thing students have is the problem it's self.  This has been especially helpful for students who struggle with math.  

Let me know what you think, I'd love to hear.  Have a great day.

Happy Labor Day

Warm-up

I will tell you the number you get at the end of this problem.

Write a three-digit number (with three different digits).
Mix up the digits to get another three-digit number.
Subtract the smaller number from the larger.
Add the digits in the difference. (If you get a two-digit answer, add the two digits to get a single digit.)
Subtract 5 to get a final number.

Your answer is 412.

Warm-up

I will tell you your answer at the end of this math problem.

Think of a number between 1 and 100.
Multiply your number by 4.
Add 12.
Multiply this number by 2.
Add 16.
Divide this number by 8.
Subtract your original number.  

Your answer is 5!

Math Games for the Social Distanced Classroom Part 2.

There are more games and more games that can be modified to play in the classroom during times of social distancing.  Games we can play during social distancing, or via distance learning are important.  No more sending problems down the rows.  No more moving people up or down the rows.  So we have to make changes.

1.  Match Game - This is where students are given a worksheet with three columns.  The first column has the problems while the second column has the answer but they are not lined up correctly.  In other words the answer that is next to the problem do not match up.  In the third column, students work out the problems and once they have the answer, they write the letter of the answer next to the problem.  

This can be done with any math topic from solving simple equations to trigonometric functions to multiplying binomials.  It takes just a bit of work to prepare the sheets a head of time but well worth it.  Furthermore, this game could be done using cards on the desk with the problem worked out on the back of the card with the problem.  

2. Round Trip - Although this is normally done with students standing next to each other, it can be played with 6 feet of distance.  This can be played with students sitting at their desks while using white boards. First step is to designate the the first two players but have the other students ready to work the problem to check the two designated players work.  Show the first problem and let the two designated students work out the problem.  The first one with the correct answer as checked by the other students get to play against another student.  The idea is if one student can work their way around the room completely, they are the total winner otherwise, go with the one who answered the most problems.

Any math topic can be used for this game which makes is possible to use it in everything from basic math to calculus and anything in between.

3.  Loopy numbers - This game has students follow a specific rule such as one follows for a function machine.  The rule is "Multiply the ones digit by four and add 1 to the product.  This rule is applied to the result of the previous calculation where you multiply the ones digit by four and add one to the product and continue.  An example might be begin with 15 so you do 4 x 5 + 1 = 21.  Then you take the 21 and multiply the 4 x 1 + 2  = 6. The next round would be 4 x 6 + 0 = 24.  Then 4 x 4 + 2 = 18 followed by 4 x 8 + 1 = 33.  Then we have 4 x 3 + 3 = 15.  At the end, the student should end up with the number they started with.  No matter what two digit number they choose, if they follow this rule, they will end up where they started.

4.  Coordinate Battle Ship - This is a version of battle ship that uses two squares of graph paper on one sheet.  The left side is filled with the players ships while the right one is where they mark down hits, etc.  To start, each player marks down their ships on their coordinate plane with one carrier, two destroyers and three submarines using dots. When both players have placed their ships, one person calls out a coordinate of where they think the other person has a ship.  The other person says hit or miss and then calls out a coordinate for them.  With social distancing, it is easy for people not to sneak a look, especially if you have students use a folder to create a wall.  If you'd like, this site has a sheet all ready to go along with the directions.  Students have a fun way to practice or review the use of coordinate planes. 

Here are four more games that can be played in a socially distanced classroom.  Let me know what you think, I'd love to hear.  Have a great day.

Math Games For The Social Distanced Class Room, Part 1.

 

My school year has started with about three weeks of inservice and at this moment the students are due to start on September 14th with masks and desks spread out as close to 6 feet apart as possible.  Furthermore, only half the students will be in class at anyone time.  I realize I could assign students to play games on digital devices but those do not usually allow as much interaction among class members so I decided to find games I could have students use in class.

I'll be sharing several in today's column and I'll share several more in Friday's column.  The games are fairly easy and won't need a ton of preparation.

1.  I have...... Who has....  game.  This game uses cards with an answer and a question but the answer does not go with the question on the card.  For instance the card might read "I have x = 3, who has the answer to x - 7 = 4."  The answer of x = 11 is on someone else's card with a new question.  To play, you make sure you have enough cards for one per student and that the answers and questions line up so the last person to have the answer is the same one who read the first question.  After I pass out the cards, I usually give students a chance to read their cards so they are ready for the game.

To start have the teacher or a student read the first question such as " Who has the answer to x - 7 = 4?" Give students a chance to find out the answer to it so they see if they have the answer.  If students are struggling , encourage students to talk about solving the problem so they can help each other.  Once the answer is figured out, let the students see who has the phrase " I have x = 11".  The student identifies themselves and reads the next "Who has problem?" It continues until everyone has had a chance to answer  a question and ask a question.  

This game is a great way to have students practice previous and new skills.  It can be used for any grade and almost any topic from basic addition, to multiplying binomials, to factoring, to practicing multiplication facts.  I've used it to help scaffold missing skills and used it to help students learn a new skill.  I also admit, I have messed things up so I didn't manage to go all around the classroom and I've also managed to accidentally come up with equations that ended up with the same number.  On the other hand, when I've gotten all the cards set up correctly, it has been lots of fun.

2.  Math Bingo.  I pass out empty Bingo cards to my students.  On the board, I have a huge number of possible answers.  I ask students to fill out their bingo cards with answers from the board.  For instance, if I wanted to have students practice order of operations, I might say, select any numbers between 1 and 99 and write them down on your card in any order.  

Once everyone had their cards filled out, I might write the first equation on the board such as 2 x 3 + sqrt 25 x sqrt100 =    .  I let the students figure out the answers by doing the calculations and usually someone calls out an answer but no one writes the answer down until a second or third student confirms the answer is correct and then students cross it out if they have it on their card.  I'll put another equation and wait till they come up with the answer.  Usually, students want to play blackout because they are having so much fun.

I've used math bingo with fractions, order of operations, one step, two step and multistep equations, factoring trinomials, area, perimeter, trig functions, and any other math topic I can think of.  Again, it allows students to practice their already learned skills and newly acquired skills.  

3. The Great Escape - normally requires students to line up but in the time of social distancing, it won't work.  Instead have students stay seated at their desk.  Go through and ask each student three questions.  If the student gets the first one right, ask the second, but if they don't get all three correct, move on.  If the student manages to get all three correct, they can leave a minute early from class, or get to do fewer homework problems that night.  The reward is up to the teacher.

On Friday I'll be sharing a few more games that can be done in a classroom where the desks are 6 feet apart due to social distancing.  Let me know what you think, I'd love to hear.  Have a great day.