Happy Halloween

 

Warmup

 If 160 million people spend $2.1 billion on Halloween candy, how much does each person spend on Halloween candy.

Warmup

 If children can consume up to three cups of sugar in their Halloween candy and three cups equals 169 cubes of sugar, how much sugar is in each cube. 

Finding The Best Way To Brew A Cup Of Coffee Mathematically.

 

In the teachers lounge, there always seems to be a coffee maker with a pot of coffee brewing.  As soon as it empties, someone starts a new batch because teachers survive on coffee.  I am not a coffee drinker so it didn't bother me but most of the staff were into their coffee.  According to a reprint in Scientific American, someone created a mathematical model designed to determine the best way to brew a cup of espresso.  The model came out of the question on why coffee can taste different at home vs at the store, at work vs the airport.  Apparently, it came down to the brewing method.

One factor is the coffee itself because the type of coffee and it's country of origin factor into its quality.  There is also how the coffee is roasted, the water its brewed with, but the method used to brew the coffee has one of the higher effects on the end result.  The mathematical model looked specifically at espresso because it requires such precise measurements making it the most complicated to brew.  In addition, espresso forms the basis of cappuccinos and lattes.

The method used to espresso requires that hot water be forced through finely ground coffee. The amount of coffee, water, and fineness of the ground along with the water pressure, temperature, and amount of the brew are all crucial to the final product. This process ends up balancing around 2,000 chemicals to get the proper taste.  Even when things are done the same way every time, it does not automatically guarantee the same result every time.

So a group of people made up of mathematicians, chemists, materials scientists, and baristas got together to create a mathematical model to figure out the best way to produce a consistent cup of espresso at a coffee shop every single time. The model was used to predict how much solid coffee is dissolved in the final cup of coffee.  This is known as the extraction yield which is a percentage and is used in the coffee industry to assess various coffee recipes.  The object was to create recipes which produced the same cup every single time.  In other words, the flavor had to be reproducable.

Using a series of equations, they discovered that the model accurately predicts the extraction yields experienced in real life except for when the recipe used the finest coffee grounds.  This is because the water used to make espresso is forced unevenly through the coffee grounds causing some sections to become clogged thus under extracting the liquid and other sections are over extracted.  

They came to the conclusion that contrary that the barista needs to use less coffee that is ground a bit courser to get the consistently tasty results they desire.  Mathematically, using less coffee means that the water flows faster through it thus making the water flow and extraction more uniform.  The result is a fast, bright, sweet liquid that is slightly acidic every single time.  Since not everyone wants the same result, different tastes can be made by combining different brews or by changing the roast.

One thing that comes out of this model is that baristas are able to reduce the amount of coffee waste by one fourth per espresso shot which increases profit without compromising the taste. The savings could be as high as $1.1 billion a year for all cafes in the United States alone. Furthermore, since at least 60 percent of the worlds wild species are threatened with extinction, using less coffee means there is less demand and these plants have a better chance of recovering.

So now, you've learned another way people are using mathematical models to improve flavor, help the environment while saving money.  Let me know what you think, I'd love to hear.  Have a great day.

VR and AR Apps For Middle And High School Math.

Today, I'll be sharing some AR and VR apps that are more appropriate for middle school and high school math classes.  Several of them are actually rated for elementary school but can be used in middle school since many students did not get a proper mathematical education over the past couple of years due to the pandemic.  

The first one I explored was Wandermath which was developed by the Entertainment Technology Center at Carnagie Mellon University.  Although it is designed for 4th and 5th graders, it is a very interactive AR program.  The free iPad app comes with three scenarios, the birthday party, the skateboard park and the carnival, and each one focuses on a different skill. 

The Birthday Party has students helping the main character wrap gifts but in the process, students learn how two dimensional nets turn into three dimensional representations of a cube.  The main character talks to the students, explains the process, and waits till the student has finished the project before moving on.  The Skateboard Park has students helping the main character build parts of a skateboard park and focuses on volume.  At the end, the student has created the skateboard park for the main character to use. The last one, the Carnival, has students learn more about cartesian coordinates using water balloons for a fight. There is information for the teacher on each activity.  

Next is something called Fog Stone Island math program put out by Cignition.  It appears to be web based and free.  It is geared for grades four to eight and can be assigned via Google Classroom. This program primarily focuses on fractions from equivalent fractions to adding, subtracting, multiplying, and dividing fractions, to ratios and proportions, to adding and subtracting decimals.  Honestly, it has a three dimensional land where you fly over it and each topic has you going through a video to answer questions to build a well or ranching or farming.  It does provide sample lessons that can be used with certain topics.  This is quite basic but would be good for classes who are missing a foundation on fractions.

The last app I'll look at is Arloon Geometry, an app for both IOS and Android but it does cost money.  It is designed specifically to help students learn more about geometry using AR.  Students begin by choosing a topic - prisms, regular polyhedrons, bodies of revolutions, or pyramids. Once the topic is chosen, the lesson begins which includes a three dimensional representation of a shape and it allows the student to break it down into its net. In addition, it lets the student explore the sides, edges, etc of the shape and provides information, and quizzes them along the way.  I did not try this program because I didn't want to spend the money on it but I tried the other two.

There are a couple of companies out there who offer math programs to districts which utilize VR and AR such as Prism who offers an algebra course for grades 4 to 12. Another is Classvr who offer Mathematical resources but I have no idea how much they cost for their products.  I tend to stay away from companies and prefer to use apps and software but there really aren't that many available for the upper grades.  I'll revisit this topic later.  Let me know what you think, I'd love to hear.  Have a great day.

VR And AR In Math

 Over the years, I've been following VR(virtual reality) and AR(augmented reality) especially as it applies to math because I love having an excuse to play with technology in order to figure out the best way to use it in the classroom.  Most of the apps that are classified as VR or AR generally deal with showing shapes in Geometry.  I did see one example where they had the busts of mathematicians. If you clicked on the bust, you'd bring up information on that person but I've not found a good use for it in math.  The only other ones were geared for elementary students, not for middle school or high school students so I decided it was time to revisit the topic to see if things have become more applicable. (All links go to the web page of the company so you can find more information.)

One of the biggest arguments for using VR in the math classroom is that this technology allows students to "see" math in a new way.  Virtual reality especially provides a new way of immersing students in their learning.  It helps students block out both auditory and visual distractions of their surroundings so they are able to focus more on the topic at hand. It can help them connect with the material in a new way, especially when the new material involved spatial relationships such as volume, surface area, edges, etc.

When students use virtual reality, it helps provides opportunities for students to improve their spatial awareness, while at the same time, it presents materials in a three dimensional form such as volume that makes it easier relate to and calculate.  They can rotate the object to see all three dimensions necessary to calculate volume.  Furthermore, the use of headsets to create the environment, means that students who have not developed their fine motor skills can still participate fully.

The University of Illinois at Urbana-Champaign has a wonderful list of programs and apps that can be used in the classroom.  They've reviewed a variety of programs, provide the location you can get the program, cost, and the date they looked at it.  I'll do a full column on why VR and AR are good in math but in the meantime, we'll look at a few apps and programs out there that can be used in class right now. They cover math from middle school into high school and even up into college.  

Geogebra does have a Geogebra AR app that can be downloaded and used in the class.  The directions to set it up and use it are quite clear and can be used on both apple and android operating systems. Furthermore, Geogebra has multiple AR activities available including domain restrictions, tornado inside a cone, and so much more.  

I'm starting with the ones you don't find in the App Store. Lets start with Calcflow that is designed to use with certain VR head sets and requires the use of a specific software program called Stream which is a desktop gaming platform.  You have to install Stream to use CalcFlow.  CalcFlow allows students to explore vectors using hands, learn more about vector addition and cross multiplication, check out certain types of graphs and so much more but it does appear it is only available for windows operating systems.

As far as apps go, there are several possibilities but not all are totally free.  For instance, there is a program called Math VR which goes with something called ACE-Learning systems. The app is free but to use the models, you have to have a subscription in Singapore dollars which is on their web page. They say they have an educational subscription but the cost is not listed. You have to contact them.   It covers topics such as simple and composite solids, volume, inequalities, graphs of trigonometric functions, trigonometric ratios and so much more.  They claim to have over 100 models available to use in class.  The app works on the iPad, iPhone or on an android operating system.

For Calculus, one can download CalcVR which stands for Calculus in Virtual Reality. The app can be found for both apple and android operating systems. This app works with google headsets or VR headset that is google headset compliant so you don't need to invest much to get started.  It works on a smartphone and is designed to have the person sit rather than move around. The nice thing about this site is that they include lessons to go with each topic and each lesson includes the objectives, pre-class activities, and uses Desmos lessons to help students learn the material better. I do not know what it costs but the app seems to cover so much material for Calc 1, 2, and 3.  Although it looks as if it is more for college, it could easily be used in a high school calc class and works for Analytical Geometry too.

Yes, most of these activities are designed for upper level students so on Wednesday, I'll be exploring VR and AR games and activities for middle school and high school students.  Let me know what you think I'd love to hear. Have a great day.

Warm-up

 If there are three apples to a pound and the tree produces 275 apples, how many pounds of apples did the tree produce.

Warmup

 

A new type of apple tree only produces about 250 apples each year while older varieties produce 750 apples every year.  How many times more apples does the older tree produce as compared to the newer trees?

Free Digital Math Games Part 1 - Middle School

 

Last time, I covered introducing students to digital math games in class and today, I'll be talking about places you can go for digital games to use in your classroom.  In addition to listing the games, I'll be actually talking about the games themselves and the sites. I will also let you know if it works on the computer or iPad or both.  There is nothing worse than finding a game and discovering it doesn't work on an iPad.  Note that the information is up to date as of this publication.  

These are some places that have games appropriate for middle school students.  The first site to explore is math playground.  Although math playground is focused more on the lower grades, it does have some really awesome games and activities one can use in the middle school and high school levels.  The first thing to know is that all games on this site are free and do not need students to log in.  

One thing they offer is called Thinking Blocks.  Thinking Blocks provide visualization of what is happening for certain operations (addition, subtraction, and multiplication), fractions, and ratios. In addition, they have a tool which allows students to create a visual for any word problem in the same way the practice thinking blocks are set up.  When you click on the Thinking Blocks you want, you are shown several different choices where you can start and work your way through or you can choose the one facet to work on specifically.

I played with the Thinking Blocks fractions.  I had to play around with it to determine how to use it but once I did it, it was easy to do.  It provides a simple word problem and coaches students to work their way through to the end.  It does work on both the computer and the iPad.  It does not appear that one can get it in app form for the iPad but access via the browser works fine.  In addition, you can print out worksheets of word problems.  

There is also a section on pre-algebra filled with games students can play.  Many of the games involve signed numbers, factor trees, pemdas, etc.  I tried a couple games and what I found is that some of the games were easy to figure out, others did not have enough direction to determine how to play the game so I'd advise you to try the games out to see if they are easy to play.  The other nice thing about this site is that you can assign the game via google classroom. The game also gives you information on what the topic the game reinforces.  

Another site that has a couple of games that might be interesting is Jlabs.  Although it is primarily a science site, it does have a game that is rather fun but again it does have issues.  It is Looking for the top quark.  It is similar to battleship in that place your 6 quarks on a grid that is either a small, medium, or large grid but the grids are really not that large.  After placing your quarks you can play the computer or a friend.  It worked on the computer but not on the iPad.  I think it might be old enough that it doesn't work with the iPads. 

The last site I'm discussing today is math nook.  This is another site filled with math games that you can choose by grade or topic which makes it really nice.  I went for math games dealing with exponents since middle school usually focuses on it to help students become better grounded in it.  I decided to try math racing exponents game since many students like this type of game.  The interface looks quite retro but as soon as I clicked on play, it provided the rules so I understood how the game works. 

I had to use the left, right, up, and down arrows to operate it since I couldn't swipe per say.  The way it works is that I have to avoid other cars and choose the problem that gives the answer that matches the number assigned to my car.  It was a bit long between problems and cars but it wasn't bad.  I suspect students need the time as they are not fluent.  The version 2 of this game uses negative bases while the first version only uses positive bases.  The racing games do work on the iPad with the finger.  

On Monday, I'll look at free digital games for use at the high school level.  In the meantime have fun exploring these sites.  Let me know what you think, I'd love to hear.  Have a great weekend.

How To Use Digital Games In The Math Classroom

 

There are days when we choose to assign digital games to the class.  There are lots of different games available but there are things we can do to make them even more effective.  My high school students tend to love Kahoot, Jeopardy, and a couple of other games.  Yes these are whole class games because all the students play.  

Some of the games are web based while others are in the app form and can be used on the device.  Some games require students sign in, while others use a code to allow them access and the code is provided by the teacher.

Digital games can really improve the attitudes of students who find themselves engaged and successful. There are certain things we can do when having students use digital games in class to make everything better.  First of all, when introducing students to new games, set up a teacher versus the classroom game. This is a good way because students love beating the teacher and this increases their desire to play. The class is playing as one player while the teacher is the other.  This game gives students a chance to learn the rules and how the game works in a fun, engaging manner. 

The way this works is the teacher works the problem but everyone in the class has to work their problem individually and then they have to agree on the answer.  This allows everyone a chance to try the problems. One game this works well for is connect four math games and you can find several for free here.   This free one for 8th grade to check it out. 

Once students have been introduced to the game and its time to play it with the class, divide the students into groups of 3 to 5 people and leave the students in the same group for a two to three weeks at a time rather than trying to change them up every time. Only switch up groups when you feel the students need a change.  

Don't forget about using games made with power point or google slides.  An example of this type of game is Jeopardy but you can find quite a few from various sources or make your own.  No matter which way you go, make copies of the game so you have one set of slides per group and label each set with a title.  Make sure permissions are set for anyone with a link can edit and make sure the students in the group for the set has the link so they can access it.  Finally, make sure students know who is in each group starting the games and notification can be done digitally or in person. 

Now, here are some suggestions on places to go to get games for your classroom.  If you are into making your own games, check out Matt's list here from Ditch your textbook site.  He is offering templates for free. Another person who has instructions on creating your own games is Alice Keeler.  Check her instructions out.  Slides mania has several free templates for games here. This one offers a spin the wheel, cardtegories, frogtastic, two truths and one lie, and several others. 

As far as commercially produced digital math games, they are out there but one has to take time to regularly check sites because some of them disappear, some are bought by other groups, or they suddenly change from free to offering a 30 day free trial.  Let me know what you think, I'd love to hear.  Have a great day.  

Math Card Games

 

There are those days when you've just called role and the fire alarm goes off, or they announce a lock down or they've scheduled an assembly that starts or ends partway through your class and you do not have time to teach a regular lesson.  This can be the perfect day for playing card based math games with your students.  It is possible to get a bunch of used cards from the casinos for quite cheap so you can have a huge supply in your room.

Although these games are geared more for middle school students, you have high school students who can also play this game, especially since many are lacking certain skills due to Covid.  Card games make a nice change of pace from worksheets and lectures.  It gives students something physical to move around, see, touch, and experience.  In addition, it makes it fun for students to practice the concept or topic again and again.

1. Multiplication war - this is a variation of the multiplication game played in elementary grades.  The ace is worth 11, Jack is worth 12, the Queen is 13 and the King is worth 14.  The other cards value is the face value so the 2 is worth 2, the three is 3 and so on.  In addition, all black cards represent positive numbers while the red cards represent negative numbers. This game is played by two people for each deck, so the cards are dealt evenly between the two players so each one has 26 cards.  

Begin by flipping the top two cards on each pile.  The students multiply the two cards together and the one with the highest product is the winter and claims all four cards.  They turn two more over and multiply and the person with the highest product wins.  If the two people flip cards that result in the same product, the four cards are set to the side and they flip over two cards.  The person with the highest product wins the cards in this round and the four that were set aside.   When students have gone through all the cards, they take the ones they've gotten and start through the stack again.  The winner is the one with all the cards or the one with the most cards at the end of the time.

2. Exponent war- this is a variation of multiplication war.  Again it is played by two students per deck of cards.  The cards are dealt evening between the two students.  This time the face cards are worth 10 each or they can be the jack is 12, the queen 13 and the king is 14, and the ace is worth one or 11 but this needs to be decided before the game starts.  The top two cards are flipped over, the first card is the base number, the second is the exponent. The student with the highest product, gets all four cards.  If the two cards end up with the same product, the four cards are set to the side and participants draw two more cards.  The person with the highest product gets all four and the four set to the side.  The game is over when one person has all of the cards or has the most cards when the time runs out.

3. Hit the target number - uses multiplication/division, addition/subtraction, order of operations, and mathematical reasoning.  The ace is worth 1 or 11, the jack is 12, the queen is 13, and the king is 14. Divide students into groups of between 2 and 5 people and each group gets a deck of cards.  Students choose a target number of 1 to 30.  Then one person turns over the top 5 cards from the deck.  The students work together to find the way to combine the numbers using any operations necessary to arrive at the target number. If students cannot find a way to get to the target number, flip another card.  When they reach the target number, take these cards out of play, choose another target number and flip over another 5 cards. 

4. Collaborative fractions.  All face cards have a value of 10 and the ace is worth 1 or 11.  Divide students into small groups and make sure each group has a deck of cards and each student has a pencil and paper.  Decide ahead of time if the students will add, subtract, multiply, or divide the fractions.  Draw four cards, the two largest cards are the denominators, the two smallest cards are the denominators.  Students then take the two fractions, apply the operation to them, and come up with an answer using paper and pencil. The answer needs to be in its simplest form.

These are four games to get you started.  Have fun and let me know what you think because I'd love to hear.  Have a great day.

Warm-up

 If a Soursop tree produces 19 fruits per year from each tree and you have 27 trees, how many fruits will you harvest on average in a year?

Warm-up

 A Soursop tree grows on average 17.5 feet per year.  The tree begins bearing fruit at about 6 years of age.  How tall is the tree when it begins to bear fruit?

Ways To Engage Students In Math Class

 

It seems as if students arrive in math class with the idea that it is boring and not fun.  I admit, there are things we can do to make it more fun but not in the same way they can in English or Social Studies. It is hard to show a hit movie that was made from a book in class unless we want to talk about certain mathematicians.  We have to rely on other ways to keep students engaged.

Student engagement means they are participating in class with a better attitude towards the subject.  They are more likely to complete and turn in work when they are engaged and more willing to work through problems. In addition, they are more likely to attend school while producing higher quality work. At the same time, they develop a deeper understanding of math so they do better on official assessments.

One way to engage students is to find real world examples of the concept or topic being discussed.  I admit, some examples are harder to find such as real world examples for piece-wise functions but other examples are easy.  No matter what examples chosen, you need to show your students how it works or how it's used, not just say it.  Back to piece-wise functions, a real world examples are the price of candy such as Twix or postage stamps.  The price remains the same for years before the price goes up or down.  

Allow students the opportunity to choose whether they will work in a team, in a small group, or by themselves.  Some students prefer to do it on their own while others want to work with friends. If you want to make it a bit more exciting, offer a reward to every team, group, or individual who does the problem correctly. Another way to offer choice is to give a bunch of problems and let students decide which 10 they want to do even if it is only the first ten possibilities.  This way, they feel more capable.

Incorporate props into the discussion.  Use props that get students involved in this.  The prop might not be directly related to the lesson but it might be used in the example.  For instance, if you are doing piece-wise functions, think about reproducing stamps from history to show when the prices went up.  This makes the example more real.  Another possibility would be binomial multiplication.  You could start with a square that is x by x inches.  Then add to one side so it is now (x + 2) inches while the other side is (x - 1) inch.  This rectangle is then multiplied to show the area and one could substitute numbers to give a numerical answer.

Implement as many hands on activities as possible because these help students learn more about the concept or topic being taught. In addition, provide differentiation during instruction and during any of the work, quizzes, or tests.  The differentiation in tests may look this way.  The test has four parts with 6 questions each.  The six questions are two easy, two medium, and two challenging and the instructions tell students to complete four of the questions in each section.  This goes back to choice but the problems are also differentiated so they are not all on the same level.

Have students solve a problem that has more than one way to find the answer or is open ended and has more than one answer.  This shows students that not every problem is done in exactly the same way or may have more than one answer.  When students work problems that have more than one answer, it can lead to a lot of discussion and makes it harder for the students to determine they have the "wrong" answer.

In addition, make the classroom safe so students can share answers without being made fun of or told they are stupid.  They need to feel safe to share. The expectation of no negative behavior or comments needs to be established from the start. Let me know what you think, I'd love to hear.  Have a great day.

Math And The Lottery!

 

I don't know about you but when I go through a state that offers lottery tickets, I indulge and buy one or two with the idea that maybe (yeah, right) I'll win and become a multimillionaire. I also know that the US is not the only country with a chance to win the lottery. When I was in Madrid, there was a line at this one lottery shop because more people had purchased winning tickets and wanted to win.

Not long ago, 433 people won the government backed lottery in the Philippines.  The 236 million peso prize would be shared among those 433 people. Since this many people won, there were calls for the government to investigate because 433 people should not win.  The odds appear impossible. If you take probability into account, it really isn't impossible. 

Lets look at this in detail.  Every person who buys a lottery ticket chooses six numbers between 1 and 55. The numbers are drawn randomly so the winner is the person whose six numbers match the six drawn numbers.  So mathematically, you have to multiply the 6 in 55 times 5 in 54 times 4 in 53 times 3 in 52 times 2 in 51 times 1 in 50 or you have a chance of 1 in 28,989,675 of winning the lottery.  Although it is not known how many tickets were actually sold, it is estimated that around 10 million were sold.  

It is assumed that every person who purchases a ticket has an equal chance of selecting each of the possible 28,989,675 combinations but that doesn't agree with human nature since there are certain combinations that are more popular than others.  This is why experts recommend one use a random number generator when buying the ticket since it won't increase your chances of winning, it will decrease your chance of having the share the prize with someone else.

The numbers that actually won this drawing were 9, 18, 27, 36, 45, and 54 which are all multiples of nine. Since it is a recognizable sequence, it is a sequence that many people would have chosen for themselves. The same thing happened back in 2018 in the United Kingdom when the winning tickets were multiples of seven or in 2020 when the numbers ended up being consecutive from 5 to 10 in a drawing in South Africa.

The thing is the chances of drawing 9, 18, 27, 36, 45, 54, are exactly the same as drawing the numbers of 3, 12, 13, 25, 36, 37, and 55 although to the human mind, the second set is seen as more random than the first set.  This is because the human mind really has no concept of what is truly random. One study indicates a person is more likely to choose an odd number if asked to select a random number leading the the assumption that certain numbers feel more "random" than others. 

It is possible that these 433 people chose these numbers "randomly" or the numbers were "randomly" generated but either way, people have trouble wrapping their minds around the fact that 433 people all ended up with the same numbers so in their mind, something weird is going on.  This may be why people are calling for an investigation.  Let me know what you think I'd love to hear.  Have a great day.

I Love Bingo.

 

Bingo is a game I absolutely love to use in class.  I've found that I can use Bingo for any level and any type of math.  No matter when I play bingo, I do it the same way for every type of math.  The nice thing about bingo is that it is a fun way to review or practice the current concept or topic. Overall it is low-prep and engages students.

To prepare, you need a bunch of blank bingo cards with 25 open spaces.  If you need blank cards, this site has one you can print out and make multiple copies to use in class. To make the cards last longer, laminate the cards, and have students use dry erase markers because the cards can then be wiped clean and used again.

Next you create at least 40 problems that have different answers so you have 40 answers.  Write the problems on individual sheets of paper, fold them and place them in a box. Write the answers on the board and ask students to select 25 answers and write them on their cards in any order.  One reason I let them choose the answers is because it gives them a feeling of ownership in the game and helps them buy in to the activity.

Once everyone has filled out their cards, you are ready to start.  Every student needs paper and pencil so they can work out the problem to find an answer.  If the answer is on their card, they mark it off, if not they wait for the next problem.  I will admit that my students usually work through the problem and call out the answers but when they do not come up with the same answer, it leads to people double checking their work and even arguing.  

I've used bingo for just about type of math I've done.  I've had classes where my students couldn't multiply so I'd have them fill their bingo cards out with products and then I'd call out various problems.  I've also done it for division.  In addition, I've put numbers on the board and they had to apply the order of operations to come up with an answer.  If they could do that, they'd mark it off on their cards.  It was also a great way to have students work with fractions, decimals, percents and the have them practice going from one form to another.

In Algebra I and II, I've done solving one, two, and multistep equations where students had to solve them to find the answers.  Then there is slope from points, from graphs, and tables. Multiplying binomials and factoring trinomials, perfect squares and cubes, systems of equations, various functions and so much more.  You can pretty much do bingo for any topic you have problems and answers.In Geometry, one can do bingo with perimeter, area, volume, surface area for all the different shapes.  It could involve a description where students have to come up with the geometric shape or calculate the number of degrees for various shapes based on formulas. This also works with vocabulary where students choose the definitions and you draw out the vocabulary or vice versa. 

This is one of those games that can be done a couple times a week or as a way to review in preparation for a test.  I've found my students love the game and are willing to play it but I do alternate this game with other activities such as search and rescue or Kahoot so they do not get bored with the same game.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

 If four bananas weigh about a pound, how many pounds will a bunch of 200 bananas weigh?

Warm-up

 If a bunch of bananas contains 200 bananas on average and each bunch is broken down to clusters of 6 bananas, how many clusters will there be for the store?

Physical Games In The Math Classroom.

 

Although it is easy to find games for the digital devices in your classroom, sometimes it is better to organize physical games so students have to move around.  Movement is important for students to help them learn better.  Movement means students get more oxygen moved to the brain, helps them fidget less and focus more and is known as the "Miracle Grow" for the brain.

One of the best ways to incorporate movement is by using physical games that force students to get up and move. The games don't have to be complicated or require a lot of equipment.

One is called Snowballs.  One takes several baskets and clip a problem to the top of the basket. Students are asked to solve the problem and throw the correct number of pompoms or scrunched up balls of paper into the associated basket.  They throw it from a distance and this can be done individually or in small groups.

Another game is the flyswatter game which is good for fluency type problems such as changing percent to decimals or fractions to a percent which most students need a bit extra practice.  Begin by writing 10 answers on the board (be warned they might rub off if written on a white board).  Tape a line that is parallel to the board and about 5 feet away.  You will need two flyswatters for the game.  

To play, divide the class into two groups such as boys vs girls or left side vs right side.  Ask the students to line up on the line with the teacher in the middle between the two groups.  Make sure students know that you will not call out the problem unless it is silent.  The teacher will call out a problem like 42% is what fraction in reduced form.  The first two students armed with flyswatters will run up and swat the correct answer.  The first person who swats the correct answer earns a point for their team.  The next two people get the flyswatter and the teacher reads the next question.  When they get through the whole line, the team with the higher scores wins.

Next is Find it and Fix it which is an error analysis game.  It can be used for review or for test/quiz error analysis.  Go through the test, work, or quizzes to determine which errors are common to most of the students.  Then photocopy about 10 different incorrect problems and post around the classroom.  Ask students to rework the problem and analyze the error and place on the answer sheet.  As they finish one problem they can move on to the next until they have analyzed all the problems.

How about playing Round Robin.  Place students into groups of four  and give each student a different colored pencil. Place one problem on each piece of paper. Arrange the room so that the problems are spread out around the room.  Assign a group to start with a specific problem. Each group takes one copy of the problem and everyone signs their name at the top of the page with their assigned colored pencil.  Each person will work one step in the problem using the assigned colored pencil. At the end, they should have solved the problem.  If someone in the group thinks a person made a mistake in their line, they may ask respectfully to double check their line.  At the end of the problem, the whole group moves on to the next problem and continues until they've finished all the problems.

Finally for today is Find Someone Who - Everyone is given a sheet of paper with problems while seated.  Then everyone walks around the room, stopping to work a problem on someone else's paper and has to initial it when they've finished.  An example would be John and Frank stop to solve problems. John chooses to answer problem 5 on Franks paper while Frank completes problem 2 on Johns page.  When John finishes the problem, he initials the box and gives the paper back to Frank and Frank initials the box when his paper and they give the papers back and move on to solve another problem on another person's paper.   This can continue till all the problems are finished.

Let me know what you think, I'd love to hear.  I tried to look at games that were a bit different than the usual ones.  Let me know what you think, I'd love to hear.  Have a great weekend.

Math Stations In Middle School And High School

When I went to college to get certified to teach math, I was taught to do whole class work.  There was nothing on small groups or even math stations because you didn't even consider those when working with upper grades.  Over time, I've come to the conclusion that there is a place for math stations in the classroom for all grades. 

There are many reasons teachers might say they can't incorporate math stations ranging from excuses such as the school doesn't have enough bandwidth, to the class periods are not long enough, students might use it an excuse to be off task, not enough time to prepare or the biggest one is that you don't know how to do it.

One of the most important things to keep in mind is that you have to start small when implementing math stations.  Choose one day of the week to use math stations for the whole period.  This gives students a chance to work through the stations so they can practice what they've learned.  You can set up the stations so each station focuses on a specific skill that they learned over the past week or few days.  In addition, when most of the students are doing math stations, the teacher can pull small groups of students so she can work with them on skills they struggle with. 

Traditionally, we think of having students move from station to station but if it gets crazy when students change stations, you could have the materials in tubs, boxes, or folders that move from table to table so the supplies are moving, not the students.  In addition, you do not want to have groups that are too large.  If you have only gone over three skills and a room with 30 students, you might have six stations so there are two stations for each skill.  This way you have only five students per group, instead of ten and students only need to visit one station per skill so they do three stations, not six.

One way to set up stations is to have one station where students meet with the teacher for focused attention, one station designed to have students work at the desk or on a specific assignment, another station with technology, and the last station is designed to be hands on with manipulatives.  This way, you are able to meet the needs of your students better.

To keep students focused on the stations without worrying, have a timer showing so students can glance up and see how much time they have left.  When the timer goes off, it signals time for students to shift stations and then it is easy to reset and start again.  There are several online timers you can use.  I like this site because it has some fun classroom timers.  These timers can also be used to teach students how to change stations.  Simply state your expectations, set the timer for a minute, and have them practice moving on time, otherwise use the timer to have students move stations to the next group of students.

Take time to change things up a bit while following the same routine.  For instance, on the tech station, switch up the program students are expected to work their way through.  It might be khan academy one week, IXL another week, etc.  The at your seat assignment might be a maze one week, or a focused sheet with specific problems another week.

Always have a way for students to check their work.  This might be done with answers on the wall or via a QR code that can be read or even answers put into Google Forms so they get immediate feedback, but this way students can check themselves and if they have questions, you need to think of how to handle that.  In addition, think about how long the activity is going to take.  You want to make sure the activity will take as long or longer than the time they have at the station.  You do not want to have one station that takes 5 minutes while the other takes 20 minutes.

This is a great way to introduce students to math stations so that you can use them in class.  Let me know what you think, I'd love to hear.  Have a great day.

The Structure Of A Mini-Lesson

 

Let's face it.  Some days your class gets shortened due to an assembly, a fire drill, or you want to use a mini lesson so your students have more time to work on the activity you have planned.  You might be scheduling a math workshop today or you might use the mini lesson as a way of chunking the topic or concept.  For maximum benefit, it is important to create a structured mini lesson.

When you use a structured mini lesson, you have everything you need to make it relatable to your students so they learn better.  Each mini lesson should consist of four parts.  

The first part is the connection.  This is where you take time to connect the material in this lesson with what they have learned previously, seen, or experienced.  In other words, you are taking time to activate prior knowledge so they see a connection between the new material and previously learned topics or concepts.  This section is not going to take very long, perhaps a minute or two to set the stage.

The second part is the teaching point  or the main point of the lesson. This is where you as the teacher models or uses thinking aloud, to model the strategy or concept you want the students to learn.  The teacher might use trigger sentences such as "Notice how......." or "Please pay attention to......".  This would be the "I do" part of a lesson.  In other words, this is where the teacher shows the students. If you have a substitute and still want to do the mini lesson or want to change things up, you can use a video clip of yourself or someone else teaching that specific skill.  The nice thing about the videos is students can rewatch any part they need to see again. They can also watch them at home should they need extra help and their parents can see what is happening in class.

The third part is where the students try it in what is referred to as active engagement.  This is the brief guided practice part of the lesson and shouldn't take very long, perhaps 5 minutes. This is an opportunity for the teacher to determine who understood it and who needs a bit more work.  In this section, the students might try out what they just learned, or they might talk about how they would do something.  Students might restate the lesson or steps shown, or they might have a partner talk to review what was taught. 

The final stage is where teachers prepare students to apply what they learned to individual practice. It is the closing part of the lesson.  This shouldn't last more than a minute or two.    So the mini lesson has an opening, the lesson, a quick practice, and a closing.  It is important to plan what goes in each section so your lesson is complete.

For the best results, limit the amount of student talk because this is just a short lesson. In the opening, rather than asking questions, use the KWL, anticipation guide, or word splashes to remind them of what they learned previously.  Rather than over explaining during the lesson, repeat the important teaching point throughout the mini lesson. Make sure you use think aloud, modeling, or just show them so they get the point.

In addition, always match the activity with the teaching point so it is targeted.  Always, use the contexts students are used to when talking about problem solving. You want to spend time on the guided element so you can work one on one with the students who need it most.  When you plan for you mini-lessons set up a short lesson with each section and fill in what you will do for the opening, teaching point, active engagement and closing with notes of how you want to talk about each area to get you started.  

So mini-lessons are easy to set up, have four sections, and are easy to plan.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

 If an orange tree produces 375 oranges per tree and you have 135 trees planted, how many oranges will you pick?  If there are three oranges in a pound, how many pounds of oranges did you harvest?

Warm-up

 

If one orange produces 1/4 cup of juice, how many oranges are needed to make 1 quart of juice?