This = That

The other day when I was on the app store, I found a nice little app called this = that.  The object is to take  5 numbers, parenthesis and use the order of operations to find the given answer.   There are three buttons in the lower right corner that are used by the student.  The Deal button is the used to request a new round while the Clear button is the same as the reset button.  The Check button is used when the student believes they have the right answer.  If their answer is incorrect, it simply says shoot to let  the student know.

The student simply clicks and drags the number into the proper square.  If they click on the question mark, a list of operations pops up so the student can select which one they want.  Once they have the equation finished, they click the check button and it lets them know if their answer is correct.

For every correct answer, they get a certain number of points.  I like this app because it provides great practice for students to become fluent using the order of operations.  I believe all my math students from lowest to highest will be able to use this and all of them will be challenged to find the correct answer.

Interactive Books pt 1

I am at the iBook Hack in Zeeland, MI.  I am learning to create interactive books using iBook Author. During the welcome speech, I realized I don't have to create books for my students for every thing I want to teach.  I need to check what books have already been published on the topic I need first before trying to write something.

I did a quick look at Geometry and found quite a few free ibooks that looked possible.   The next step is to preview the books to see if the material is exactly what I want the students need. 

  There are several advantages to using these free iBooks.

 First, the books are already written.

Second, students can download the book to their own mobile device.

Third, its already created.

Next thing I need to do is talk to the IT department to see if we can download these to the classroom set of iPads.  Not all my students have access to the internet at home so I need to have the books on the ipads so they can work on the assignment after school.

Time Zones and Math

Today's post came in the middle of my trip.  I am on my way to Michigan and as I checked my itinerary I discovered a beautiful warm up problem.

The warm up question is "How can I leave Grand Rapids, MI and arrive in Chicago, IL, one minute apart?"  To answer this question, a student needs to know the two cities are in  two different time zones in addition to being in two different states.  I could even ask how long the trip is between the two cities. 

  Any questions involving travel and time zones require students to use higher order thinking skills because of the time zones involved.

Another problem I could ask would be "If you take off from Honolulu, Hawaii at 9:30 PM and the trip is 5 1/2 hours long, at about what time would you land in Anchorage, Alaska?  This requires students to know that Alaska is two time zones ahead of Hawaii during the summer.  If the trip happens in winter, the time change is only one hour.

Which brings us to the fact that only two states and part of another state do not participate in daylight savings time, so if you asked a question involving one of those places, it could add another twist to the problem.

I think that I could look up some real flight schedules for various airlines and have students calculate the flight time so they know about how long the flight will be based on the information given.

So many possibilities.  I am already planning on using these types of problems.

Coordinate Plane

This morning I found the app Coordinate Plane by Mary Kuchta.  It is a nice little app that has students plot the coordinates given in quadrant 1.   It is very easy to use and not hard to figure out.

If  the student touches the correct location on the grid, a green dot automatically appears and they score 1 for a hit.  If they get mixed up and choose the wrong location a red dot appears and they have a point added to the misses column.

The first shape is a triangle with three points.  The second shape is a trapezoid with four points.  So as they work their way through the rounds, the number of points used to create shapes increases and the shape might end up being an arrow or other concave shape. 

Once they complete the round, they receive stats on how many hits and misses it took them to complete the shape. 

I think this will be an awesome addition to my Pre-Algebra class to build prior knowledge and scaffold their abilities.  Once they've mastered the material in this app, I can move them to Descartes Dots which will introduce and provide practice in creating shapes using all four quadrants of the coordinate grid. 

My Pre-Algebra students tend to have weak skills so I need to build those skills up and have them prepared for Algebra I in a year.

I probably will not post tomorrow because I am traveling all day.  We'll see.

Plan your life

My youngest asked me about apps that would help her learn to budget and I realized we no longer teach that in math classesunless it is a personal finance class or a business class of some sort.  The thing is, I could offer budgeting in my pre-algebra class under the unit on decimals.
I searched the apps store and found only one possible free game called Plan Your Life Budgeting Game.

It is really great because you go through selecting a job which in your first year means you are going to be a waiter.  That is the only job offered at that point.  You go through budgeting such as housing, food, transportation, etc and if you spend all your money in the first few things, you can't get food, or housing or entertainment.

 The app has you work on building a nest egg, plan various investments such as risky stocks with good returns, fixed deposits with low returns or invest in a safe stock with medium return.  Then it takes you to look at property.  You start with a small flat which you could sell but at this point in time you cannot  afford to buy anything better and choosing to rent is not an option.

In addition, there are one to two random events happen during the year so you either receive money or loose it much as in real life.  Once you have everything filled out and set, you touch the hourglass to make time pass and at the end of the year, you are ready to move on the the next year.

I love the concept of the game and the way it goes through everything to set the budget up.  I love the way it looks at how much you end up paying every year for all your expenses.  If you spend too much money on one thing, you won't be able to afford other things such as food.  Unfortunately, there is a major glitch in this program. It quits just after the first year and when you open it to continue, it always resets to start a new game.

On the other hand, if you take the basis of this game and have students use a spread sheet for the all the investments, expenses and earning, it would give them a better overall picture for budgeting. So until the app designer fixes this very major glitch, the program itself is not very usable in the classroom.

Clayanimation

I was over at Barnes and Nobel the other day.  While perusing the bargain section, I came across a do-it-yourself Clay animation kit complete with DVD and everything.  When I was there, I didn't think anything about it but over the past few days, my mind has played with ideas on how to use it.

1.  I could have two clay figures who solve a problem made out of clay.  Record it and add sound.  Perhaps the two figures could take apart or build a 3D figure and discuss it.

2.  Maybe students could create enough variables and constants out of clay to solve the problem using the clay figures to solve an equation.

3.  Perhaps a couple clay cars could be used to create a movie showing how to solve rate/time/distance equations. 

4.  Have students create part of a room out of clay and use that to help explain on video how to calculate the amount of paint, carpeting, etc for a house.

5.  Perhaps have the students create characters who are planning to cut down a clay tree and show the calculations to see if they can cut down the tree without hitting the tree near it. 

6.  Use trig to calculate the height of a ladder needed to paint the second floor of a house.  Students can create everything from clay and create a movie.

These are just ideas for using clay animation in the classroom.  I am going to try to move to a more project based classroom and want to use some projects that allow my artist type students to create something while learning math.

Math Ninja

While looking for multiplication apps, I found Math Ninja HD Free which is actually a game that helps students practice addition, subtraction, multiplication and division and is set up to do the game before they practice their math.

It is set up so students have the choice of three levels of difficulty, easy, medium, and ninja.  In addition, the student can chose to practice problems from addition, subtraction, multiplication, or division or from all four.  They also have the option to customize their choice.

Once the game starts, they have a mad tomato man who wants to take over the world but the math ninja is the only thing that stands between them.  The ninja starts with a blow gun and unlimited darts to use to keep the robo-cats and robo-dogs from taking over.  The student uses their finger to aim the darts.

If the student takes out all the robo animals, there are math problems at the end of the round.  If the answers are correct, the student gets a monetary reward.  With the reward, the student is able to buy more weapons to fight the animals with. 

Each round gets a bit harder and as long as the ninja is able to take out the robo animals, there is a chance to advance but if the students is not able to get rid of all the robo animals, they loose.

So the math facts are what help the student gain additional weapons and practice. I would say this app is good for both elementary and middle school plus possibly it could be used as remediation in high school.  I think I"ll try it out to see how well the students like it.

Outrageous Acts of Science

Last night I ended up watching two hours of Outrageous Acts of Science on the Science Channel.  It was awesome and it used both math and science to prove or disprove certain videos that went viral on the internet.  Although they spoke mostly with scientists, they did speak with a few mathematicians and they even showed the math involved in a video.

One segment was on a bicycle.  Not just any bicycle but one that was built to be about 20 feet tall and ride-able.  It was a cool bicycle but I would be so scared to ride it.  The owner of the bike had a helmet camera on top so you got the same view he did.  Wow.

They used mathematical equations to show how much more unstable the tall bike is over a regular bike.  They discussed force, etc.  It was fascinating. 

Then there was the one of using something like a small surfboard to ride on top of barrels. It was wild watching the small plastic barrels roll under the board so the guy looked like he was actually surfing.  When he wiped out, other people just jumped on and belly surfed on the barrels.

The scientists took time to explain how much faster the outer part of the barrels were spinning vs the center.  They explained the why and the math on it.  The kids who "surfed" were giggling and having a great time.

I love watching television shows that explain real life applications of math in such a fun way.  There were some segments which discussed the science in such a way that I could easily have my students research the actual mathematics involved in the science and use that on a worksheet I create. 

Furthermore, they have videos listed on the website that I can access and use as part of my lessons in class.  I love finding things like this.

Mythbusters, Indiana Jones, and Math.

I love watching Mythbusters because they show so many practical applications of science and math in real life.  They do not always show the exact math they are using but in the episode focusing on things Indiana Jones did with the whip, they took time to show the actual math for two of the stunts.

One question they examined had to do with the idea that Indiana Jones used the whip to cross a ravine by causing the edge to wind around a tree branch.

 To calculate the length of a jump Adam could make safely, they used markings on the ground for distance, then using a high speed camera, they recorded his jump on film.  By putting marks on the film above every mark they were able to create a parabola and calculate the distance he needed for his "ravine."

Up until they added some "bark" to the "tree branch" Adam could not use the whip because the whip had absolutely nothing to "hold" onto and he would continually fall.  Once the "bark" was added, the whip held and Adam could swing across the ravine as many times as he wanted without falling.

The second use of math was showing how they calculated the speed of the tip of a whip.  The question simply was "Can the tip of a whip go faster than the speed of sound.  Again they used the high speed camera, lots of swearing as they tried to find the whip motion and once they got it on film, they showed how they calculated the speed.

It was cool.  I want to show that episode in my math class so they can see how math can be used in real life.

Division!!

After downloading and playing with Multiplication!!, I discovered Division!! created by the same people.  It assumes students know their division facts but need practice in division problems. 

It operates about the same as Multiplication !! in that you get the screen with the name of the app.  You hit the start button and you get a problem.  The app takes you through the step by step process. 

It uses the green cursor to let you know where you are in the process and the cursor turns red if you put in the wrong number or you bring down the next digit.

The first time I played this, I subtracted 7 from 8 to get 1 and then brought down the 5 but the cursor turned red because the app only wanted  me to do 8 minus 7.  It brought down the 5 for me.

Once I finished the problem, the app displayed the answer in two forms, a fraction or using the R to indicate remainder.  It has a tutorial, the help and hint buttons and you move on to the next problem when you've completed the problem.

I plan to use this app next year.  I have high school students who struggle to complete the division algorithm.  They either forget the 0 as a place holder or they mess up on their multiplication.  For instance in the line where I had 15, many students will say 7 goes into 15 one time, subtract 15 - 7 to get 8, bring down the 9 and try to figure out how many times 7 goes into 89.

I think I am going to require my students to practice their division using this app.  I love the step by step.

Due to traveling issues, I probably will not be posting tomorrow as I will not have access to the internet and the library is closed on Sunday's.

Multiplication !!

While searching for apps to help my students learn their multiplication tables, I stumbled across this one called Multiplication!! by Horizon Business Systems.  I got the free version of the app.


The app assumes the student already knows their multiplication tables and are ready for the next step of multiplying two numbers together.  So the app is designed to take students through each step of the multiplication process including carrying values.

The app shows a problem, with a green cursor in the ones position. The student types in the value, hits the enter button  and if a number is carried the green cursor goes up above the next value. The student inputs the value, hits the enter button and the cursor moves to the tens position.  The app continues until the problem is completed.

If at any point the student puts in an incorrect number, it shows red and the cursor will not move on.  If they get it right, it says good job and the student clicks next for another practice problem.

If a student gets stuck there are both a hint and a help button available.  The help button will put the correct digit in the spot and move the cursor on.  The hint button types a message in the gray area above the number bad.  It might say something like write the tens value of  8 x 5.

I see this app as usable from perhaps grade 4 on up.  I would use it in my pre-algebra class for students who still have issues multiplying two numbers together.  I plan to recommend this app to the special education department because I know she has students who struggle with multiplication in general and I believe it would help.

Times Table App

As I looked at multiplication apps, I downloaded Times Table by The App City.  It is an interesting app in that it is not a game but a calculator that shows the answer and a visual representation.  It does not provide a way to drill  their multiplication facts.

The app lists every multiplication fact between 1 x1 and 10 x 10.  All the student has to do is touch the button and it shows the problem, shows the answer next to the problem and on the button the student pushed and it shows a representation.


For instance, if the student chose 8 x 6, the problem prints at the top with 8 x 6 = 48, the 48 shows above the button and between the multiplication table and the
8 x 6 = 48 are 8 groups of 6 to represent the multiplication.

I've given some thought to whether this app is appropriate for my classroom and I've decided no because the students do not get a chance to practice their multiplication facts.  I do plan to share this with the Special Ed teacher so she can put it on the ipads she has in the classroom.

This app would be appropriate for students who have difficulty in learning their times table and are allowed to use a calculator.  This calculator has the visual element which is important in understanding the concept behind the facts. 

Sushi Monster

This game, Sushi Monster, is put out by Scholastic, the same group that puts out the books for book fairs, weekly reader magazines and assessment testing.  As I stated yesterday, I am looking for apps that allow my students to practice their multiplication facts.  The students who arrive in my 9th grade Pre-Algebra class do not usually know their multiplication facts and rather than lament them not knowing the facts, I want to find games to help them learn.

So I found this app.  It offers practice for both addition and multiplication facts so is usable by many grades from early elementary on up.  When a student begins, they must start at level one and complete a number of problems correctly before they move up to the next level.

I started level one for multiplication which is designed to practice multiplication facts up to 12 times 12.  Once you move up to level two, you end up moving to larger numbers such as 300 and 900.   I jplayed with this long enough to move up to the second level because I wanted to know what it took.

The game starts with two numbers in the upper left hand corner so you know your target numbers.  Four factors in the form of sushi are served on the outer ring around the monster.  The player selects the two factors that make the target number.  If a student is not sure, they can skip and move on and the program will put that number in at the end.

If the student selects the wrong factors, nothing happens so the student has to go back and rethink their answer.  Once they get the right factors, the monster eats the sushi and you move on to the next set of problems.  As the student progresses through the level, the number of problems increases from 2 to 5 each round and so does the number of factors.  The number of factors will always equal the number of problems.

Over all, I plan to have use this app in my Pre-Algebra class and have students work on it regularly.  I want them to increase their knowledge of multiplication facts so it becomes second nature.

Multiplication

Although I teach high school math, I still have quite a few students who do not know their multiplication tables so I've downloaded several multiplication apps to review.  The reason I'm looking at multiplication games is nothing more than selfishly wanting my students to have the best foundation for doing math. 

I saw some research that indicates if a student does have their multiplication tables down cold, they use more of their short term memory trying to figure out the answer to the simple multiplication problem, leaving less space for learning the material.

Today I am looking at Multiplication Genius, the free version which
covers 2 to 5, 9, 12 and 19's.  In order to get 2 to 19, you have to purchase the free version.  There is a reference page under the times table which shows every multiplication problem from 2 x 2 to 19 x 19.  This part of the app would be excellent for my special students who need the extra element during class.

When you click on the New Game,you are given a choice of Easy - 9's, Medium - 12's or Hard-19's but as far as I can tell the 9, 12, or 19 is the biggest number you can multiply by.

The problem is given and you are given 4 possible answers to choose from.  If you are right, it says good job, if you select the wrong answer, it says better luck next time.  It pretty much gives as many problems as a student wants to do.

I am hoping to figure out which of about 4 multiplication apps I have that would interest my older students in such a way, they don't feel "stupid", their words, not mine.   This looks like a good one just to practice their multiplication facts.


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Real life applications of shapes

I was reading a blog on finding geometric shapes in real life.  The author showed several examples and as I read the blog entry, I got to thinking of how I could use this in my high school math classroom.  I came up with the following ideas.
1. Create a book filled with pictures, general information and perhaps the formula for area and perimeter of the shape.
2.  Create a comic strip with one character talking to another on a tour of the house pointing out the shapes.
3.  Create a video/movie/podcast to share where students found various shapes.
4.  A photo scavenger hunt outside of school.
5.  Perhaps divide the students up into groups and assign a shape to each group to find and create a presentation on where to find the various shapes with examples and where these shapes were found.
6.  A pod news cast with each group providing a small segment, a pair of news anchors and they would have to plan everything.  Perhaps even broadcast it throughout the school.

These are just a couple ideas just off the top of my head.

Sum of Exterior Angles of a Polygon Lite.

There is a nice little app which I might have talked about before but I took time to explore it more so I decided to review it.  It is the Sum of the Exterior Angles of a Polygon Lite  is the free version of the 99 cent app.

When you first open up the app you see this triangle with angles and a play button.  There is no real information until you hit the play button.  Once you tap the play button, the app opens up and you see a brief animation which introduces students to how you identify the exterior angles.    It is a nice introduction to the topic. 

After the introduction, a blank work space appears with instructions for using it.  You use your fingers to create the polygon by taping on the space for the vertex.  You can create any polygon from a triangle on up.  There is an erase button at the bottom and a slider to the right that is used after the shape is drawn. 

It automatically forms the exterior angles once the polygon is drawn as seen in the photo to the right.  When you move the slider down, the sides move closer and closer together until they disappear and the exterior angles form a 360 degree circle. 

This allows students to see why the sum of exterior angles is 360 degrees.  Furthermore, when you are ready to do another polygon, you hit the erase button and draw the next one.  It is easy to create regular polygons.  What is even neater is that there is a work sheet for students to do that is found by clicking on one of the buttons and the button next to it shows the same worksheet with possible answers.

I plan on using this when we do the sum of exterior angle theorem in Geometry.  It is a nice way to let students explore the topic before the theorem is taught and it would be good as a review, remediation or scaffolding.

Distance Rate Time Solver by Center for Algebraic Thinking.

As you know from previous entries, Center for Algebraic Thinking has produced many apps that can be used in the classroom.  Recently, I found Distance Rate Time Solver which helps students solve these types of problems.

This app has two problem modes and two explore modes.  The problem modes are for solving word problems given by the app while the explore mode is to help solve problems you choose.

First if you look at the problem mode for objects traveling towards each other,  you are given a word problem which you read and then type in the information for each object with speed, delay and distance.  It covers problems like two trains leave Boston and NYC at 80mph and 60mph, when will they meet and how far did each travel before meeting.

After animating the two objects and seeing what happens, you then put your answers in to see if you are right.  If your answer is correct, the answers will be in green, if not they are red.  You can ask for it to display the answer if you are not sure what it should be. 

The practice with the outside forces cover problems like your boat is traveling 10mph and the water is going 5mph, how long will it take to go 50 miles.  Again you input the information and try to figure out the answer.  If you need to you can animate the situation.

The last two sections (the exploration) allows you to do the same type of problems such as those found in the text book. The steps are the same as in the problem mode.

All four modes work very well as long as you realize this is a solver.  I would love to see this app provide explanations  to the student on how the answer was found in the problem mode because the app is providing the word problem being solved.  Yes it does show the correct answer but if a student only copies down the answer without being shown how the problem was solved, they may never gain the knowledge they need to independently solve such problems.

Otherwise I do love the fact that students can enter the information needed to solve the problem and the app animates it so students have a visual for solving but without the explanation, it is harder to learn.