TUVA Labs

 

As math teachers, we are always looking for data we can use in our classrooms that is authentic and interesting.  It has to be interesting to capture student attention and buy in.  This is where TUVA Labs come in.  The offer three types of information to use in the classroom for everything from bellringers/warmup to activities, to data stories.  Each one can be used for a specific purpose.

The material can be in data stories which allow students to generate their own questions, evaluate data found in different forms such as charts, tables, or graphs, or look for patterns and make observations.  Data stories are great for warm-ups, conversation starters, or an introductory activities.  These are short 10 to 20 minute activities.

They provide data sets complete with associated activities that are real-world, content rich, data sets obtained from sources such as NASA, the Census Bureau, NOAA, the CDC, and so many others.  The activities require that students analyze the data, and can be used as part of a classroom lesson. These are longer, taking from 20 minutes to a full class period. The final type is the task which has students applying what they've learned and can be used to challenge students or extend concepts.

They offer students the opportunity to create a dot plots, scatter plots, bar charts, histograms, and box plots, or construct their own mathematical models, while making predictions and interpreting data. In addition, they can look for patterns and apply mathematical or statistical concepts to situations that are real and authentic. They've got materials rated for grades 3 to 12.

Although, Tuvalabs offer both a free version and a paid version, the free version only allows you to access 10 free lessons, upload 5 data sets and set up basic student accounts.  The free lessons cover things such as dinosaurs, Atlantic hurricanes, devastating earthquakes,  the population of the Lynx and Snowshoe hares in Canada for science.  For math, there are lessons on comparing the profits between Pixar and Dreamworks, determining who is at the highest risk of getting measles, relationship between diameter and mass of M&M's and several others.

Each lesson can be accessed through google and each has an activity preview. The preview discusses learning goals while explaining the lesson step by step. In addition, you can look at all the case cards, see how many activities have been created, and how many students have used them. Now if your school lets you invest in the paid version, you end up getting access to every lesson, activity, data set, etc, all 267 of them.  There are unlimited uploads, premium student accounts, integration with google classroom and other LMS and other advantages.

The company does provide tutorials designed to help students learn how to do a variety of topics from how to do certain charts, to filtering data, to random sampling, and so many others.  Now I will say, this is something I would be more likely to do during an actual face to face class because I'd want to be there to monitor and answer questions rather than trying to run it virtually.  Next, I would strongly recommend you test drive this by signing up for the 10 free lessons to see if it would work well for your lessons.  let me know what you think, I'd love to hear.  Have a great day.

The Geometry Of Haircutting.

I never thought there would be geometry associated with haircuts until I got hooked on those hairdressers who look at "fails" and discuss what they did wrong and how to avoid it.  One of the guys mentioned geometry and haircutting in the same breath so of course my ears perked up. 

In general, geometry plays an important part in cutting hair since many cuts are based on geometric principles.  Take the wedge cut, bob, and bangs for instance. They are based on geometric angles.  In addition, a hairstylist has to know the angle they need to hold the scissors and comb to get the desired result.

Furthermore, a hairdresser has to know how to divide the head into various geometric shapes, as they divide the hair up into sections to cut the hair, dye it, highlight it. They have to know how cut layers so the layers look proper.  They don't want to do what has been advised on Tik-Tok because they will end up with chunks.  If you haven't seen it, the most common method is to either divide the hair into two pigtails which have elastic wrapped around the hair at the point they want to cut it and then they cut it.  This method results in a curved haircut which is shorter by the ears and longer in back with choppy edges.

The other method is to put your hair in a ponytail with the elastic band placed where you want to cut the hair.  Cut it just past the band and it is supposed to produce a layered look.  It sort of ends up that way but its in chunks so it doesn't look particularly great.  Hairstylists learn to cut hair so it doesn't chunk and ends up looking proper.

When hair is cut, stylists may use a beveled cut to accomplish the finished look.  Beveled cuts is a technique that uses diagonal cuts to make the stacked look in hair.  On the other hand,  they might cut hair in a convex line to create the U or V shape of the hairstyle or the concave to create a curved line like an arch. The concave lines are most often used at the back of the head or in bangs, or around the ears. 

The angle they actually use to cut the hair helps define the look of the hair.  If there is no angle or a zero degree angle is used for a one length cut as a horizontal line.  If hair is cut at a 45 degree, it produces a stack or a wedge, which is a triangular cut.  If the hair is cut at a 90 degree angle, its called a universal cut. but the 180 degree cut results in a layered cut.

In addition, math is used to mix the chemicals properly to straighten hair, perm it, bleach it, dye it, or highlight it.  Many hairstylists end up working as independent business people who rent a station in a beauty parlor and they have to figure out what to charge for their services so they can make money while still meeting all their bills.

So as you've seen, geometry plays a large part in cutting hair.  Let me know what you think, I'd love to hear.  Have a good day. 

Warm-up

 

If it takes 540 peanuts to make a 12 ounce jar of peanut butter, how many peanuts will it take to fill a 16 ounce jar?

Warm-up

 

If a peanut plant produces on average 42 peanuts per plant, how many peanuts would you have if you grew 1538 plants?

Is Online Instruction Effective?

 Many teachers are on their second year of virtual instruction being alternated with in person as the number of COVID cases increase and decrease.  Most of us were thrown into the deep end back in the spring of 2020, without any training, any direction. We are on the second year after that are we are still bouncing back and forth.  

In the meantime, people has had a chance to conduct research on this topic.  It is obvious that when class has to go virtual, students miss out on the interpersonal interactions they normally experience in person.  

In regard to most online courses for high/middle school, and elementary are designed to resemble the in class structure. The teacher usually has a warm-up, the lesson, and offers chances to interact virtually before homework is assigned.  The teacher tries to include time to work with individual students. Unfortunately, online classes are not as effective as in-person classes for most students.

In one study, students were placed in either online or in person classes when they had to repeat the second semester of Algebra I.  The results indicated that the students who took the class in person did much better than those in the online version. In addition, those who took the online class felt it was more difficult than taking the same class in person.

Although some students do well in virtual or online classes, the majority do not. Students who have a weaker academic background tend to so much worse in online classes. There is evidence to support the idea that students who do really well in person will do well online but for those who struggle to learn math in person will so significantly worse when enrolled in an online class.

It is possible to design an online class to help lower performing students.  An online class needs to have a strong curriculum with strong teaching practices in place. It needs to have activities and teaching methods designed to engage students because they face more distractions with less oversight so they may not have the same motivation. Teachers need to set expectations such as responding to a specific number of questions or interacting with other students during class time. 

Unfortunately, students who have fewer resources at home, tend to learn less than they do when they are in school In addition, research shows that giving students access to virtual classes is better than nothing.  The biggest point of virtual classes is that it does provide a chance for teachers to interact with students but there needs to be improvements made to online classes to improve student learning.

I don't know if many students struggle with online because of the way the classes are organized due to districts trying to make it so virtual classes mimic in person classes or if it's just the distractions.  I'll be investigating that next.  Let me know what you think, I'd love to hear.  Have a great weekend.

The Mathematics Of Knitting

I am one of those knitters who does it when I have a bit of time or when I'm watching a video and need to keep from phasing out.  I was thrilled when I found an article about a physicist who was working on unraveling the mathematics of knitting.  

If you look, you'll notice there are at about 100 basic knots, which if you vary the combinations, you  alter elasticity, strength, and the three dimensional structure of the finished product.  

One of the first steps in this process was to sit down and list all the possible stitches before figuring out how to classify them. 

Although yarn by itself is not very elastic, the elasticity doubles when it is made into a knitted fabric. Elisabetta Matsumoto is researching this topic.  She hopes to create a dictionary of stitch types, the various combinations of stitches, and the resulting fabric.  She is basing her research on knot theory which says that a knot is a tangled circle, or a circle embedded with crossings that cannot be undone. 

 Knot theory is what explains how knots are formed and is used to explain how DNA folds and unfolds and much more. She uses knot theory to explain how each stitch entangles with each of it's neighbors. She has discovered that when small changes are made such as moving how the yarn crosses in a knot, can influence the mechanics of the finished fabric. 

Knitting is actually a series of slipknots in a row. These slipknots when placed rows and columns form a lattice similar to a crystalline structure. When a knitter uses one stitch such as all knitting or all purls, the edge of the fabric curls where as if these two are combined by alternating rows or columns, the fabric lies much flatter. Although the two fabrics may look the same, the amount of elasticity is different. 

She argues that knitting is a type of coding while the yarn is the programable material. For a presentation, she knitted a swatch that illustrated a type of plastic surgery called Z-plasty.  Z-plasty is a plastic surgery technique which can improve both the functional and cosmetic appearance of scars.  

Matsumoto is working with several programmers to get the computer to think like a knitter by teaching it about the properties of yarn, the mathematics of each stitch, any intentional stitch defects, constraints, the twists and compresses of yarn blends, the number of plies, its thickness, and how floofy it is. Floofy is a term that refers to the location of the fuzzy fibers that stick out. 

Eventually, they hope the program will be able to predict the properties of the finished fabric.  They hope this information can be used for growing human tissue or used in wearable electronics.  Let me know what you think, I'd love to hear.  Have a great day.

Improving On-line Teaching.

 

I know of at least two districts here in Alaska who have had to move to online teaching due to the number of Covid cases locally.  I know that the numbers are running between 800 and 1,100 per day which is higher than it was back in the spring.  The districts that shift to online teaching, usually have students who have decent access to the internet or the district has set up some sort of intranet for the town to use.

It is important to plan ahead to create an online class that is engaging and allows for student choice, proper feedback while covering the content and providing students with opportunities to master the material. 

First thing is to identify what must be covered, essential contact. Teachers need to think about what concepts need to be covered, which can be touched on, and which ones can be eliminated totally.  For instance, one might briefly review solving multiple step equations in one class period in Algebra 2 but totally eliminate matrices and Cramer's rule.  Which topics are the most important?

If possible, move instruction to asynchronous by offering videos either remade or self-made on demand and save the synchronous for going over example problems, work with students and correct misconceptions.  When you provide videos on demand, they should identify key objectives and include a way for students to check and monitor their own understanding.  This helps make it so students can work more at their own pace.

Instead of looking at homework, look at student learning. Rather than grading the work they turn in, look at evaluating them on their reflections and revisions.  Provide the final answers so students can check their work but give them the opportunity to revise their work so they can be graded on that. 

Take time to intentionally design opportunities for interacting with students. One possible way is for students to pretend that they have a partner who does not understand how to do the current topic and have them make a video in which they explain how to do it. In other words, let students make a peer tutoring video since they can't do it in person. When a student creates a video to explain things, they develop a deeper understanding and these video can be viewed by students who struggle with said topic.  Don't be afraid to assign collaborative tasks using multimedia or storyboarding and let students work together in breakout rooms.

Consider rethinking assessment by using three different ways.  First, think about using automated assessments such as quizzes that use multiple choice questions and can be completed within 15 minutes.  Second, use oral exams by having students spend 5 to 10 minutes to explain how to do a problem, and finally, let students create a culminating project at the end of the unit.  Allow students to have a choice in the final unit project which can enrich both understanding and experiences.  

Think about changing up the way you create lessons when you switch to online.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

 

If a pound of bananas wholesale for $0.62 per pound and sell for $0.89 per pound in the store, what is the mark-up per pound?

Warm-up

If a stalk on the banana plant has 228 bananas iron average, how many bananas will be harvested from 2548 plants?

How to Handle Packets.

 

The new school year has started and many have already begun bouncing between in person, hybrid, and virtual.  One would think by now, we'd know what we are doing but I work for districts where many students do not have access to unlimited internet or data.  In cases like this, we've had to create packets and send them home.  There are so many things to think about when creating packets that for students will be the primary way they learn the new material.

I realize that there are ways to send home certain support materials such as video lessons via a thumb drive but that is assuming one of two things.  Either the student has a computer at home or they have a thumb drive that works with a digital device such as a cell phone or a device.  Otherwise, the school wide network has to be opened so students can download the appropriate videos.

It is better to create packets with enough materials for students to learn and there are certain things to keep in mind to make it a positive learning experience.  One of the first things to decide is what do you want the students to get from the packet or what we'd call the end result.  So it is important to figure out exactly what the learning goal will be.

Then determine what criteria will be used to assess how well the students learned the material. Did they attain the learning goal.  In between the result and the assessment lies the answer to the question of how will students communicate any questions or concerns in regard to anything they don't understand.  Can they e-mail or text you?  Will you have "office hours" on zoom?  How will you communicate with them so they get the help they need. In addition, it is good to check with the textbook publishers to see what types of resources are available to use in packets. 

So there are three C's to keep in mind - communication, considerations, creation.  Let's look at each of these individually.  Communication is not only with the students but their parents and or guardians.  It is important to let both students and parents to discuss exceptions, deadlines, options for late submissions, and methods for returning the work.  In addition, provide detailed instructions via both the packets and texts to make sure they know what is going on.  Don't forget to provide any information for the family in both English and in their native language to elevate communication that one additional step.

When creating packets, there are several things to consider. First, identify any standards and benchmarks students are expected to meet with this assignment. Take time to design activities and learning experiences  that align to the standards, address the standards, and also assess their learning.  Make sure the activities take into account the different student learning preferences and resources available at home. Think about how students can complete the assignment should they have issues.

Now you are ready to create the packet.  Take time to organize the materials so they are easy to follow, with any visuals or examples students can use.  Make sure they are in sequential order and include any definitions for all new and technical vocabulary. It is always good to review vocabulary to review and reinforce their prior knowledge.

In addition, spell out the learning objective for the students and include how they will be evaluated on meeting the goal. Also include any materials such as graph paper, dice, compasses are included so students have everything they need to complete the activity. 

Furthermore, when thinking about assessing the assignment, include more than one way to evaluate their learning.  Remember, not everyone has a fantastic internet connection, so it is important to include a quiz, a reflection, a sometimes, always, or never.  Figure out how often you'll grade these and inform the students so they know.

If possible, add in some hands on activities such as cooking where recipes are doubled or halved if they are doing fractions, perhaps build something out of wood?  Think about organizing the unit into a project that covers the material from start to finish.  Creating packets can be as hard as trying to teach virtually. Let me know what you think.  I'd love to hear.  Have a great day.

The Latest Value For Pi

Pi, that lovely number that is the ratio of circumference to diameter and is classified as an irrational number because the digits do not repeat and do not end. It is needed to determine the volume and area in circles and spheres.  It's been known for a long time and in 1706 the Greek letter was assigned to the ration. 

On the latest front of mathematical news, Swiss researchers have managed to calculate pi out to 62.8 trillion figures using a supercomputer.  They set a new record for precision. The calculation took 108 days and nine hours to arrive at this value. The calculations were twice as fast as Google cloud in 2019 and 3.5 times as fast as the previous record set in 2020.  They are not revealing all the digits quite yet because they are waiting for the Guinness Book of Records to certify their results.  The last record calculated it to 50 trillion.

Now most people can't picture 62.8 trillion digits but to give you an idea, think of it this way.  If you took all the digits and printed them out, they could fill the British Library ten times over.  The British library is over 112,000 square meters.  It covers 14 floors spread out over 9 floors above ground and 5 below. There are at least 13.5 million printed and e-books.  

Perhaps you wonder why people want to calculate the value of pi to 62.8 trillion digits?  The more digits known, the better the precision for finding things.  When using pi to the tenth digit to calculate the circumference of the earth is found to the precision of within a millimeter.  When you use it out 32 places, scientists can calculate the circumference of the Milky Way to the precision of a hydrogen atom.  With the use of 65 digits one can calculate the size of the observable universe within the shortest measurable distance.

At this point in time, knowing the actual digits out to 62.8 trillion figures doesn't appear to have a scientific use but the quest for calculating so many places has been going on for a very long time. Mathematicians have been doing this since ancient times but it's been the methods used that have changed over times especially once Calculus came into use.

As mathematicians search for a new, better way to calculate pi, they learn more about pi itself. Each time a new formula using an infinite sum is found, it only adds a few new numbers to the digit. The infinite sum used to calculate the record setting value in 2020 was discovered in 1988 and only added 14 new digit places for each new term added to the sum.

On the other hand, one advantage to finding more digits in pi is that it allows super computers to be developed and tested to be better. In addition, it tests the high precision multiplication algorithms as they are worked out. These calculational discoveries will help improve weather casting, DNA sequencing, and COVID modeling.  

Just image how calculating more digits for Pi benefits everyone in so many other areas of their lives.  Let me know what you think, I'd love to hear.  Have a great day.

The Universal Equation Of A Birds Egg

Have you ever wondered how to mathematically model an egg?  I have.  The only way I ever managed to come up with any equation to describe an egg was to fall back on a piece wise function.  If you ever really look at an egg, one end is nicely rounded while the other tends to be a bit narrower thus a piecewise function would allow me to combine two different equations.

 Well, researchers from the University of Kent, a research institute, and Vita-Market LTD have actually come up with the universal mathematical equation which can be used to describe the egg of any bird found in nature.  Up until this point, no-one has been able to formulate the equation.

Eggs by their very nature have to be large enough for an embryo, small enough for the body to squeeze out and lay, and structurally sound enough to bear weight while functional enough to come alive.  In addition, the egg is considered the perfect shape.

To find the universal equation of any egg, scientists had to determine the basic four shapes - sphere, ellipsoid, ovoid, and conical shape specifically the pyriform. So they based the formula on the length of the egg, maximum breadth, shift of the vertical axis, and the diameter based on one fourth of the egg length. 

By finding this universal equation, scientists are closer to understanding the shape of the egg itself, how and why the egg evolved, and new applications in various studies.  Although there have been mathematical descriptions of egg shapes in food research, engineering, agriculture, biosciences, architecture, and aeronautics, the new equation opens up more fields with its breakthrough mathematics.

This new universal equation allows for a competent scientific description of a biological object which will improve egg incubation while making poultry selection much easier.  It also allows for accurate and simple determination of the physical characteristics of the biological object. Scientists use the external properties in the development of technology for incubation, sorting, processing, and storing eggs.  In addition some of the characteristics of an egg can be used in architecture because the general shape is stronger thus holding maximum loads using a minimum of materials.

It is said that this universal equation strengthens the connection between mathematics and biology. It opens up additional avenues of research and understanding.  Let me know what you think, I'd love to hear.  Have a great day.

Warm up

 

If one tree loses 550 leaves on average and there are 7 such trees on the property, how many leaves are there to rake? If 360 leaves make a pound, how many pounds of leaves have you raked up?

Remembering 9/11

 

Remembering those who lost their lives on 9/11

Traveled Across Too Many Time Zones

Just flew from Iceland to the states and I am incoherent. Will be back Monday as normal.

The Geometry Of Musical Rhythm.

The geometry of musical rhythm is a book written by Godfried T. Toussaint.  I stumbled across it while looking for new books on geometry and the title captured my interest.  It is subtitled "What makes a "good" rhythm good?. The author states that this book offers his personal take on mathematical and computational analysis of musical rhythm.

In addition, one of the main themes contained within the book is where the author explores the mathematical properties associated with good rhythms.  He looks at the mathematical property of a sequence and highlights the rhythms that use said property.Furthermore, he takes time to discover the properties associated only with the rhythm he's looking at. 

Godfried begins by defining rhythm, looking at what a steady beat is and explores timelines and meter before moving on to specific rhythms and the distance contained within a rhythm.  He also looks at classifying rhythms, binary, ternary rhythms, syncopated rhythms, plus topics such as Euclidean rhythms, rhythms o stars, crystallography, radio astronomy and so many other topics including regular and irregular rhythms.

In addition, he provides a notation for the different rhythms he speaks about in the various chapters.  In chapter 7 where he discusses six distinguished rhythm timelines, he focuses on 5 onsets (emphasized beat) in a span of 16 pulses or beats from around the world.  The Bossa-nova has onsets on 0,3, 6, 10, and 13 while the Rumba is 0, 3, 7, 10, and 12.  The two are quite similar with two onsets that are different and three the same.

In chapter 8, the distance geometry of rhythm, he takes the same six rhythms from chapter 7 and creates geometric visualizations of them. Instead of using a flat bar, he creates circles with smaller points labeled 0 to 15 and he colors in the points that match up with the ones in the earlier rhythms before connecting these points together with straight lines to create pentagons.  Some of these pentagons have mirror symmetry or are palindromes.  Furthermore, many rhythms contain isosceles triangles within the pentagons but not all. 

He also creates both full interval and adjacent interval content histograms tot show how these 6 timelines appear in this visualization.  Then in chapter 9, he goes through a classification for these rhythms from the earlier two chapters.  He created a flow chart beginning with the simple question of if there is a 90 degree angle?  From there he moves to the number of isosceles triangles contained in the rhythm and finally asks about an axis of symmetry. In addition, he created a decision tree to classify the same rhythms based on local shape features of the interval histogram or the inter-onset interval distances.

Godfried relies on the circular visualization to show the rhythms of other musical types. As he goes through these, he also include the mathematics to explain things like balanced vs uneven rhythm.  It's a fun book but it does require one pay attention to the material as one works slowly through it.  The material in here would make a fun lesson here and there to show students who love music the connection between what they play and the mathematics.  Let me know what you think I'd love to hear.  Have a great day.

 

When Math Goes Wrong!

I've been touring Sweden and Iceland for the past week or two.  In Sweden, I visited the museum of a ship that was ahead of it's time and sank due to the ship designer messing up on his mathematics.  This happened back around 1625 when the King of Sweden decided he needed a brand new warship. 

Instead of one layer of guns, he wanted two.  He want it to be the mightiest one out there so he could defeat Poland.  So he contacted the head of the ship yards and ordered the new ship. In those days, they didn't draw out the plans like we do today.  The ship master, had all the information in his head so he just ordered the materials needed and off they went.

Since the desire to have two floors of cannons was a radical new idea, the gentleman in charge, just added enough supplies to build the second row.  Once all the supplies came in, 400 men worked hard to build the ship.  In the picture you see a scale model of the ship up against the side of the real one.  The final ship was 63 meters long by about 57 meters tall.  It was described as being the equivalent of a four story building.

One day in August, when the ship was complete, the King and other dignitaries gathered to send off the mightiest ship.  It had sailers, the admiral in charge of the navy, a few women who were there to be with family members and would be let off just before the ship left the coastal region.  The ship set sail on a nice day.  It wobbled a bit but nothing bad until the wind picked up.  At this point the ship started listing so much, water flooded in through the gun ports.  People struggled to escape but about 15 were trapped including two women and the admiral but the ship sank.  

The designer of the ship didn't take into account the added weight of the second row of guns.  Back in those days, they put rock in the bottom of the ship as a counter balance to the weight further up.  If done properly, it kept the ship upright so it could handle the wind.

Unfortunately, the ships designer made the bottom of the ship too narrow and didn't use enough weight so the ship was top heavy.  As the ship set sail, it wobbled due to having the center of gravity in the wrong spot.  When the wind began, it threw everything off and the ship listed and fell to one side.  Once it listed, the ship could not right itself.

The designer based everything on prior experience rather than doing calculations so he got the math wrong.  If they'd drawn plans, calculated weight and such, they might have built the ship so the bottom was wider so it could accommodate additional stones and this would have countered the extra weight.

The ship is the Vasa.  It sank in August 1628 about 100 meters out into the bay.  It stayed buried until 1959 when it was finally discovered again.  The Swedish government raised the boat, preserved it, and it is now in a museum. The ship is impressive. Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

If an octopus can scoot along at 25 mph, how long would it take them to cover 678 miles?

Warm-up

A dolphin's top swimming speed is about 54 kilometers per hour. How many miles per hour is that?

5 Different Ways To Start Class

 

When I was in my teachers education program, I was told to put something up on the board to get students started while taking roll, or getting them into the right mindset for class.  It might be called a warm-up, bell ringer, or one of several other names.  Unfortunately, we tend to do the same thing every time because it's easier.  So today, I'm going to look at 5 ways to start class so everyday is not the same. 

Begin class with a video.  It might be a video which could introduce the topic such as a scene out of a show where one of the characters is able to say how long it will take the car to arrive. Or it might be a video clip from one of the three act tasks, or maybe it is a trailer type feature you made yourself using iMovie.  What ever the choice, it is going to be something short and sweet which grabs their interest and is related to the concept.  

For instance, you might show bridges or water sprinklers when talking about quadratic functions, or a short cooking lesson for fractions, or even a racing car when discussing rate and time.  You might take pictures you found or hand written formulas and integrate them into one of the trailers you can make in iMovie.  These templates come with music, text boxes, and it is easy to put one together.  It is short and can be quite fun.

Another way to start class is by showing one or more items associated with the concept.  If you are doing interest, you might place money out or for ratios, one can of frozen orange juice and three cans of water. For distance formulas, you could put a toy car out and for the quadratic formula a ball works nicely.  The idea is that you put the object out in front of the class so they can ponder on the up coming lesson.  Give them a minute or two to think about the object before asking them how they think the object relates to math.  Let them brainstorm before you dive into the lesson.

Begin the class with a question that either asks them what they know about a topic, asks them to relate a topic to something they've learned, or what they think about something.  The question could be in a poll, in a google document, or requires whole class discussion, or a small group conversation.  Starting with a question starts the students thinking about the topic.  The question might be general or specific, be based on the topic or a real world application of the concept, or even as simple as what do you know about.....?

Instead of starting seated, throw some movement in.  A simple way of incorporating a bit of movement is to have students use a maker to write an answer to a posted question on a paper or white board while standing.  They then hold their answers up over their head so the teacher can see them.  The teacher goes through the answers, asking each student to sit as their answer is scanned. 

Another variation is to prepare several copies of the same worksheets containing  3 to 5 questions.  Pass the worksheets out to all the students and have them answer the first question.  They need to put their names next to the problem when done to show they did that one.  Then they fold the papers into airplanes, stand up and throw the planes to each other on the teachers command so they have a new sheet.  They sit down, answer another problem, fold it up again and fly it to another student.  When all questions have been answered, collect them to assess later.

Finally, begin class with a mistake.  The mistake might be a common one students made on an assignment, it might be one you created, or one found online. One site Math Mistakes has a collection of math mistakes you can use for inspiration.  Spend the first few minutes of class having students figure out where the mistake happened and how to correct it.  This could be done as a whole or small group activity.  It could be done via google slides, flip grid, or other digital method or it could be done via a discussion.  This activity helps students learn to identify mistakes and use this as a way of learning the material better.

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

Making Your Own Math Memes.

 

Every so often, I want to start class off with a math meme but I don't want to spend hours looking for just the right one.  Instead, I've chosen to make mine so they apply to what ever topic I want to touch on.  The one to the left is something I created for probability.  Students enjoy reading things like this and if done correctly, it can grab their attention and are more likely to participate.

Fortunately, there are several online sites that can be used to produce specific memes.  I've gone through and tried them out so I can let you know how easily they work.  For the meme to the left, I used the meme generator here.  You can create an account or sign in with Google so that all the memes you make are saved or you can just do a screen shot to save the memes. 

First thing to do is decide if you want to create from scratch or you want to start with the meme ready to go except for the text.  I chose the template and just typed in the text.  I hit generate and it was done.

As stated earlier, you can customize the memes by adding photos, flipping photos, change the font, color of the font, insert stickers, draw and so many more things.  The site includes information to do this and it includes links to the GIF maker if you'd rather make an animated meme.  You can go crazy and have fun.  In fact, if you wanted, you could have students make their own memes on the current topic just to provide an opportunity for them to share their knowledge.

Another site,  meme generator offers a chance to choose the background and you type in the words such as in the meme to the right.  It is also quite easy to create a meme.  I made the one to the right and it took me two minutes.  If you don't see anything you like, you can upload a photo to use.  The directions are there under upload.

Although it was easy to use, the site was quite cluttered with ads and such that made it harder to find things.  I didn't find it as well organized as the first site I reviewed.  I also didn't find any place in the site to make animated memes.

Then there is Kapwing. This one is a lot harder to use because you have to select the image or upload an image, select the type and size of the font, add any animated portions, and determine layers, etc.  Basically, one has to build the meme from scratch.  

The program isn't too hard to use, if you don't mind spending a little more time to create it.  However, this site allows you to add video or music for an extra depth.  At the end, you can export the finish product to use.

I'll look at a couple more sites that you can use for making your own memes.  Let me know what you think, I'd love to hear.  Have a great day.