Manipulatives Can Still Be Used In A Virtual Classroom.

 

Teachers often use manipulatives in class to help students move from concrete to abstract or vice versa but with many school districts moving to a virtual classroom, one has to have virtual manipulatives to use in class. Fortunately, there are quite a few sites out there that are available and many of them are free.

My experience is that some sites do not work as well with iPads because they require flash but others work well.  I'll let you know which ones seem to work on mac's and iPads so you'll know ahead of time.

Didax has a page of virtual manipulatives including algebra tiles that work on the Mac and iPad.  The nice thing about the algebra tiles aside from adding or subtraction, multiplying or dividing is that they can be used to show binomial multiplication and trinomial factoring.  It offers so many possibilities.  In addition, there are fraction strips with a number line, two color counters for basic math and other possibilities.

Math Playground has quite a few virtual manipulatives including a geoboard complete with rubber bands and a choice of grid lines or no gridlines for students to work on area, perimeter, or transformation.  It's a good way to visualize an open ended question like what are the measurements of a rectangle with an area of 32 square units.  In addition, there are apps designed for ratios, fractions, decimals, and measuring angles.  A few of their virtual manipulatives require flash but most don't so you can use them on your iPad or Mac.

I have an activity I use in Geometry which uses tangrams to create certain shapes based on specific pieces.  Some shapes are concave while others are convex and this site has tangrams one can use in whatever activity you want rather than requiring people to try to reproduce a specific picture.  This also allows a person to use pieces of the tangram to work on transformations, or rotations.  This is nice and works on Macs. 

The National Council of Mathematics has some nice virtual manipulatives in Illuminations. Their Algebra Tiles manipulative allows students to solve simple equations, substitute values into equations, practice binomial multiplication and factoring trinomials or binomials.  This one includes instructions for using the virtual manipulatives where other Algebra Tiles ones do not.

Hooda Math has a nice algebra balance activity which allows students to solve problems step by step once they've set the balance up with the original equation.  This set of virtual manipulatives allow students to set up the equation they want to solve or they can use one the program selects but it does not do anything more than a simple equation with a variable on both sides.  They also offer students the chance to work with Algebra Tiles which is actually a nice one to work with as it allows y^2 and a few other choices I've not seen before.

Although the National Library of Virtual Manipulatives (NLVM) is still out there and has so many manipulatives, I've never had it work on a Mac or iPad due to the language it is written in. I've never been able to download the app they offer but I have had it work on a windows based machine so it might work on chrome books.  This site, if you can get access to it has some great manipulatives that cannot be found anywhere else.

I hope these help with teaching during the pandemic.  Let me know what you think, I'd love to hear.  Have a great day.

Designing A Lesson For Any Situation.

I was so happy to stumble across the outline of a lesson plan that is designed for in class, hybrid, or remote and it doesn't have to be changed up should your school move from one to the other without hesitation. 

Although my school is face to face and has been since opening in September, we face the possibility of going hybrid or totally online at any time.  In addition, I have students who are out on a regular basis due to having to go out of town for medical or someone in their family travelled so they end up on quarantine for one to two weeks.

The general lesson plan covers everything from start to finish.  One should always open class with some sort of bell work such as a joke, a picture or, a cute meme.  For online lessons, this is the section where students are logging on or getting set up in class. 

Next it is important to go over rules and norms.  This is where you'd include information on expectations for behavior or expected interactions.  I'm taking two distance classes and both instructors include this information just after they welcome us to class and have given us something to work on to warm-up.  

This is followed by sharing time or a chance to connect with everyone. This might be a time to share a birthday, recognize someone who might have done something cool, or answer questions about work.  Then it is important to look at learning goals both as the learning goal and with the success criteria so students have a way to determine if they've learned what they need to learn.  It is important to address the learning goals every single class. I take time to post the learning goals on google classroom and have my students comment on the goals either with a question, or how they feel they are doing on learning the material.  

Once everyone is settled down, had time to connect, check to the learning goals, and looked at things students have done, it is time for a warm-up where you might have an open ended question, vocabulary, a previous problem, a problem that works on a skill, or even a three act task spread out over three days.

At this point, you get to the lesson and in math it is more important to let the students do the problem first so as to encourage productive struggle rather than demonstrating the problem first, having them do it with you and then letting them do it by themselves.  It has been shown that by having students try the problem first before doing it with the teacher, they receive more benefit from the lesson, and the teacher part of the lesson should be last.  

When letting students try a problem by themselves, it is good to encourage discussion either in small groups in class or via breakout rooms or via chat.  For the we do, where the teacher works with the students, it can be done with the teacher having students suggest steps, or if online, let them share it via jam board, or in chat. The last step should be the teacher lecturing on the topic but it should include interactive elements otherwise students won't pay enough attention.

The final step should be some sort of exit ticket where teachers share a joke, ask students to complete something to show what they learned or include a question showing that students listened to the lesson if it is online or if they were absent.

The framework is here with all the information you need to create the lesson.  I love it because I can use it to create a lesson for any circumstances without making a lot of changes.  That is important for all of us, especially since the numbers of infections are increasing across the nation. I am happy to have the information because it is stressful to create lessons with an audience that can go from in person to distance at the drop of a hat.  Let me know what you think, I'd love to hear.  Have a great day.  

Paying For Education During the Coronavirus.

 

I stumbled across an article on the news about a hospitality college in Indonesia who is working hard to stay open during the coronavirus.  The Venus One Tourism Academy in Bali, Indonesia has taken the step of accepting alternative payment for tuition since people do not have as much money.

The school will accept coconuts, moringa leaves, or gotu kola plants.  The school uses the coconuts to produce virgin coconut oil which can be sold as a way of making money.  The moringa leaves and gotu kola plants are used in herbal soaps which are sold.  In addition, both moringa leaves and gotu plants are said to have medicinal properties.

The school changed it's tuition policy back in March when the virus hit by allowing students to split tuition into three payments but as the coronavirus continued, they moved to accept produce so they can stay in business and provide other skills for these hospitality graduates.  In addition, the owners of the school claims this helps students learn to entrepreneurs so one day they might start their own businesses.  

The way the scheme works is the student brings in fresh picked coconuts and the school accepts them at the current market price which is around 35 cents.  The amount is totaled up and applied against their tuition.  In addition, they do the same thing for the moringa leaves and gotu plants so a student has an alternative way to pay for education even if their parents have lost their jobs.

In the United States there are at least four colleges who prior to the pandemic allowed students to exchange work for their college education.  Two of the colleges are in Kentucky, one in Missouri, and one in Nevada.  Most of these colleges require their students to work 10 to 20 hours per week to pay off tuition, they are expected to still pay for the other costs such as books, room, and board.  When students do not have to pay tuition, it makes the cost of going to college much easier.

Unfortunately due to the coronavirus, many of these opportunities may not be available but as a math teacher, one can still use these examples to help students determine the amount actually saved by going to one of these colleges.  I found a list of 16 places of learning but many of these restrict their offers to residents of the state or a certain area, to people who want to learn a certain trade, or of certain religious beliefs.  

Many of these colleges do pay a minimum wage to help students pay for the rest of their costs.  Many schools ask seniors to compare the costs of colleges so students know how much they need to find scholarships and loans for.  If you have students do a comparison on if the work programs will pay for all the additional costs or if they'll have to take out a loan to cover the extra amount.

This makes for a wonderful compare and contrast activity for college or trade school. I've learned that many of my students pick out a college based on where their family went but they never think about how to pay for the experience.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

The smaller elephant is about five and a half feet tall. Estimate the height of the tree in inches.

Warm-up

How high do you think the arch is in dolphins?  How wide is the base?

Place Based Math

 

The other day, I attended the third webinar in a series on teaching math via distance or hybrid because there is always the possibility that our school district could end up going red. The class addressed turning math problems into open ended problems but at the very end, the instructor mentioned place based math.

By definition, place based math activities are activities that use local history, culture, economy, arts, or literature to help students learn more about math.

The instructor indicated that one needs to create situations that are based on local knowledge and understanding.  For instance, here in Alaska, I might post a picture of someone standing under a pair of bones that form a parabolic shape.  Based on what they see, you might ask students to estimate the height of the bones, or ask them to create a quadratic equation for the parabolic shape.  

In another place such as in Colorado, it might be looking at pictures of signs showing the grade of a mountain road with the numbers blacked out and asking students to come up with the grade or perhaps asking them to explain what a 6 percent grade represents in terms of the mountain.  Take it a step further by asking them to decide what grade is too steep for a fully loaded truck going uphill.

Something like that wouldn't work well where I live because the only local roads go a few miles inland and there are barely any speed limit signs and no grade signs for certain.  But if I asked my students to tell me how long it takes to get to the next town by boat or by snow machine which opens up the possibility of  having students create their own word problems.  

Another possibility down in the area of the Gulf would be showing a shrimping boat and asking students to estimate the amount of shrimp the boat could hold and what the load could sell for.  Up here, it would be taking a picture of a local fishing boat and asking students about the number of salmon it could hold in pounds.

One of my favorite activities for locally based math is to have students recreate a cross section of the local landforms from a topographic map so they can see an outline of something they are familiar with.  Once they have the cross-section completed, I ask them to calculate the slope or grade of a few different points on the cross-section.  

There are also wonderful mathematical exercises one can do with the differences in daily highs or daily lows over the period of a month for the area.  If it's in a colder place, some of the math would involve negatives from start to finish. There is also the possibility of having students calculate the daily average temperature for the month based on data collected by the students every day.

A couple of my freshmen argued they didn't need math at all.  I said they did and they should name something that didn't require any math.  They promptly suggested they didn't need to know math for when they went out hunting with their guns.  This lead to pointing out that they use an intuitive math they've developed over time based on the experience of learning to shoot.  I also took time to explain that the calculational math we do in class is what we use to explain how the bullet moves through the air, it's speed, it's trajectory.  In other words, we can use mathematical equations to explain the actual firing of a gun. 

Again it was something the boys could relate to and introduced the topic of mathematical modeling to explain how things work.   I'll take this a step further later but in the next week, I've got some ideas for locally based math to use as warm-ups. Let me know what you think, I'd love to hear.  Have a great day.

The Importance of Number Sense.

We talk about number sense in regard to our students but I can tell you with absolute certainty, that too many students arrive in high school with little to no number sense.  Unfortunately, the lack of number sense creates some problems of its own.  

Students who have a well developed number sense tend to do better in math because a good number sense encourages them to think flexibly while feeling more confident. 

In addition, if students do not develop a strong number sense early on, they will have difficulty developing the foundational knowledge to do even simple arithmetic and certainly will struggle with performing more complex mathematics. A study of seventh graders was conducted back in 2013 lead researchers to conclude that the students who struggled at this age were the same ones who had the least amount of number sense in first grade.

Students can develop number sense by visualizing numbers in a variety of different contexts, exploring numbers, and relating to numbers in different ways but it takes time.  One way to help students develop a better number sense is to show there are multiple ways to complete a problem.  Ask students for suggestions on how to solve it and write the suggestions on the board.  This gives students a chance to see different strategies.

Another suggestion is to ask students to calculate certain problems in their head because when students perform mental math it helps them build their knowledge of numbers and their relationships.  When the numbers get a bit too large or does not work with the memorized steps they need to learn to be flexible with ways to solve these problems.

In addition, teachers should have students participate in classroom discussions where they talk about different strategies that could be used to solve various problems.  This helps students clarify their thinking while developing the ability to critical think about other peoples strategies.  It is important to note the strategies on the board so students can see a relationship between their mathematical thinking and symbolic representation.

Take a moment to embed estimation and rounding activities into various situations as it is something that textbooks do not cover as well.  Furthermore, the teacher should ask them about their numerical thinking for both correct and incorrect answers because it shows you value their thinking and it has to make sense to them.  Finally, take time to pose questions which have more than one answer such as two numbers added together make 35.  What two numbers might they be? or Suggest three sets of numbers that add up to 35.

So it is important to work with students on developing number sense, even if they are in high school.  Let me know what you think, I'd love to hear.  I do plan to revisit this. Have a great day.