Math Solving Apps And Distance Learning.

 

In these times of uncertainty, it is hard for students to get the personalized help they need when learning mathematics.  Although my school is mostly green, a certain number of students are in quarantine each and every day.  Just this past few days, we’ve had COVID hit, so all students are on distance learning and we’ve had teachers out for various reasons including quarantine.  

The science teacher is off long term, so he sends his sub regular work packets but the students have discovered that with a bit of searching they can find the answer keys to those work packets and simply copy everything down so they don’t have to do much.  I suspect several of my students are doing the same thing for their math assignments or are using a app that will show them the steps and the answers.

I suspect this because one of my students who struggled, suddenly began turning in work that was 100 percent correct.  Unfortunately, when I gave the test, he failed it completely.  He also made a comment about “Photo Math” so I think he was using that program or a similar one.  This is a very real issue both in distance and in person learning.

I am not opposed to using technology to find the answer but most students just copy without trying to figure it out.  I’ve looked at one app where they have a few steps written down but the steps are not written out in typical math language.  

For instance, I gave it the problem 2x + 3 =7.  For the first step it wrote 2x = 7-3 and for the explanation it said to move the 3 to the other side and change the sign rather than telling students to add -3 to both sides.  So it tells the user the short cuts without the mathematical reasoning.  

Sometimes, I assign just a few problems but I require students to show their work and explain what they did for each step.  The reason for the justification is that students who use the apps have to slow down and include everything.  If they use an answer key, the answer keys often do not list the explanations for each step so the student either doesn’t include that part or they have to figure it out.

In addition, when students have to write out justifications or explanations for steps, it lets the teacher know if they really understand the process and the concepts involved in finding a solution.  Furthermore, this is good  because it helps students develop the mathematical vocabulary necessary to communicate their thinking to others since many have trouble with this.  

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

algebra game

I reported on an algebra application over the summer.  It has a blue background with a monkey on it and is written by Monkey in the Middle apps people. I had my first period class play the game and they enjoyed it. When you click on the first topic - words into equations, it gives you three choices, a game, flashcards or a timed challenge. The game has you helping a monkey go up the platforms and along the way you get 5 multiple choice questions.  If you get the questions correct, you keep going but if you miss the question, the monkey has to start again.  I had one student who did not want to quit when the bell rang.
I am finding games provide a venue where I can have students practice and reinforce skills which they need to work on and not having to take extra time to reteach the skills.  I like doing the games during the last 5 to 10 min of class.  One student even said "Where did the time go?" today when I asked them to clean up.  He is one who normally complains about time going too slowly.

Algebra Card Clutter

I found this app while I was checking free apps on itunes.  It is focused on helping students learn to order numbers of all types.  When you open the app you have a choice of full course (levels 1-14) or the advanced course (levels 8-14).  Each level focuses on specific numbers such as naturals, integers, fractions,  decimals, absolute values, and square roots.  When you play the game, it will automatically start at the lowest level.  It shows 5 cards with 5 numbers which the players has to tap in order from lowest to highest.  If you select the correct card in the correct order, it will fly off the page.  If you are incorrect, it will not move, so you have to make a different choice.  There are only 5 cards in each level so you would not get a chance to really practice with additional cards.
Although I like the idea, I am not sure I would use this in my classroom as it does not provide enough real practice in ordering numbers.  Many of my students would just touch the cards until they get all the cards off the screen before moving on.  There does not seem to be a mechanism in the app to have students practice different numbers until they are proficient at ordering them.
The only way I see using this is to let students practice a level on the app and then do a worksheet asking them to order the same type of number. 

Factoring

As I was working on deciding exactly what my students should know in each class I teach, I realized that factoring is extremely important in more than algebraic fractions.  I discovered a nice game on prime numbers and prime factorization that also shows factoring in a way students can see how prime numbers are used as factors.  It is Prime Smash by Panasonic  and Risupia.  This game has three levels where balls bounce up one at at time and you decide if they are prime numbers or composite.  If they are prime you tap and if they are composite you swipe the number to split it up, tap a prime or swipe a composite and you break it down till it has been totally factored. Sometimes the program splits a number into a prime and a composite or two composite numbers.  You have to think quickly when you play this game.
It has a nice fun facts sections that defines prime numbers, defines twin primes, shows emirps and Palindrmic primes, and talks a bit about how to distinguish prime numbers and how they are used for incription.  This is a free app and a really nice one.
I am having fun on the easy level learning to play the game.  I've tried the medium level but its a bit fast for me quite yet.  This game is actually lots of fun once you get the hang of using it and I can see having students play this game on a regular bases.

Preparing lesson plans

I am rewriting my lesson plans to utilize technology better.  One of the things I've done is to look at what I usually teach and divide the topics into units and not as a weekly thing.  Next I am breaking down the units into the concepts they really need to know to move on in Math vs trying to get through the chapters in the book.  Once I identify the concepts, I figure out what they should already know.  For instance in algebra 1 and 2, students will be using fractions with variables.  I know they struggle with finding LCM and GCF using only numerical denominators.  In order to find the LCM and GCF, they need to know prime factoring.  So my first unit in algebra 1 will be a review unit to cover prime numbers and prime factorization, LCM, GCF, expressions, and order of operations.  Simultaneous to breaking down things, I have been checking the iTunes Store for apps that can easily reinforce these concepts.  I am also going to set up work in Subtext and a couple other apps to ensure that they actually read material associated with the topic.  I want to make sure that any technology I use will further their understanding of math.  Tomorrow, I am going to review a nice game on finding primes.

Middle school math 7

I downloaded the grade 7 free app by the same people who made yesterday's app.  The first four topics are free and include adding and multiplying negative numbers, absolute value and order of operations.  Each topic has three levels and it keeps track of your score and your time.  Again the student can send results to the teacher. Both apps offer the student a chance to reset s ores and do the whole level again. In this game, the student helps the monkey move down a ladder, stopping every so often to pose a question.  I think this app is much more appropriate for middle school, pre-algebra, and lower performing algebra students.  I plan to have my algebra one students play these games over the first week or two of school to help them review after a summer off from school.  I hope my students like the app.

Middle school Algebra 8th grade.

The app shows up as Math 8 on my ipad.  it is an app that has a lite version and a paid version.  It has a monkey on the face of it and is a game where you tilt the ipad to move the monkey to the right or left.  If you get the monkey in the right spot, it gives you a problem. After 8 problems it gives you a score.  Each of the 4 topics has 3 levels  and you can do all three levels to become quite familiar with the process.  The four topics that come with the free versions are 1.  Words to expressions, 2.  Evaluating Expressions, 3 solving 1 step equations and  4. 2 step equations.  If you purchase the paid version, you can get linear equations, multi-step equations, solving inequalities, systems of equations, rational equations and exponential functions.
I think the free app will really do lots of good in my class as I can see having my students practice changing words to expressions using this app.  Since many are ELL, this will allow them to practice the topic in a fun filled way.  Actually all 4 topics are ones that my students need practice in.  I can see even using this app in Algebra II as a review for solving one and two step equations.  I like what it has to offer and I can use it for Pre-algebra, Algebra I and Algebra II to reinforce the skills. 
I think my students will enjoy using this program and will practice the skills since it is a game and it will prepare them better to do the actual work associated with the topic when I finally hand out practice sheets.  The company that makes this also makes a middle school grade 7 and 6.  I looked at those and just looking at them, grade 7 has students practicing using negative and positive numbers. 
I plan to download the grade 7 free app to check it out.  I just discovered there is a way for students to e-mail scores to the teacher so that I can monitor their progress.  The full versions are 99 cents and allow you to access all levels, not just the first four.  Furthermore, they are labeled the same except with the word pro. 
I am going to recommend getting this for school in the fall and I am going to integrate it into lesson plans.

App for teaching volume

I found a nice little app called Geometry: Volume of solids lite.  It has short videos explaining volume for rectangular prism, cylinder, sphere, pyramid and cone, the most common shapes our students are required to learn.  I downloaded it last night and plan to check it out over the weekend so I can give a more accurate review.  I watched a bit of the pyramid one and it had a 3 dimensional representation of the shape that turned around so students get a full look at all sides of it.  The introduction takes time to show how they derive the volume formulas for the shapes.  The best thing of all is that this is a free app.  I plan to explore other apps by this person.
Last day to get the book free.

Announcement.

From midnight (12:00 AM) to 11:59 PM on April 30, 2013, my e-book is being offered from free at Amazon.com. The title is "Teaching Math Using the iPad".  I hope some of you will be kind enough to take advantage of this.

update on two apps and a new one.

I spent some time going through the Boss T Maths I downloaded the other night.  It appears the one I found are just samplers rather than the full versions. The first one, Expanding and Factoring, shows you how to expand the distributive property or factor it from the expanded form to the original problem.  The examples are for a(b + c),  a(b-c),  (b+c)a and (b-c)a.  The app provides some vocabulary and a geometric representation.  Once you get to the practice problems, you can access the ones for the first examples but the others are locked and  you need to purchase the full priced app.  You can access the first practice problems for factoring ab + ac and evaluating ab + ac.  Again, if you want to any of the other problems you have to upgrade.  I was rather disappointed in that I was unaware of this being a lite version rather than the full version.
The special binomial products is set up in the same manner as the other.  You have to upgrade to access all parts of this app.  I think I could still use this effectively with my students for reteaching or guided practice using the examples.  Although I cannot access all of the practice problems, I can always create problems with the answers contained in a QR code so once my students have finished the problems, they can check their work.
I found a book making app Book Magic.  It allows kids to make their own books.  I can see this being used by elementary students to create books on shapes,  processes,  etc.  The app comes with basic shapes and it also allows the students to draw pictures, import photos or other material.  This is a bit too simple for older students. 

Journaling

I am looking at incorporating journaling in my math classes as it is important to include more writing in my class.  I found a nice program Journalize which I got on the day it was free.  It looks just like a journal but it allows you to import pictures, etc and I am thinking it would be great if I could have students keep journals in some manner so they can write about what they are having trouble with, write a letter to a penpal explaining what they did in class, create a drawing and import it.  Make it more friendly than the usual write it down on a sheet of paper or keep in a book.  Too many of my students loose their pencils, binders, etc.  The less paper I have to have them deal with, the more they turn in.
I found two programs from Boss T Math.  One is on the distributive property and the other is on special binomial products.  It comes with instruction and quizzes and seems to be done in a very mathematical way.  I have downloaded them and will play with them over the weekend.  This company makes 7 more and all but one are free at this point in time.  I'll give you a report on the two apps on Monday

Infographics

I've been reading about infographics and I think it is something worth trying.  Since my college prep is in the middle of a project, I think on Monday I will give them a choice of actually writing the short report or preparing an infographic on logs and natural logs and their use.  I think they might have more fun doing the infographic rather than a report since it is a bit more creative.  From what I've read about infographics, these would be great for the probability unit as students can see the real life applications of probability.  Bingo is a huge business out here and parents will often go play to 3 or 4 in the morning.  Maybe an infographic on the probability of Bingo would be a good place to start the unit. 
I am hoping to discuss a couple math apps I discovered on iTunes that will help students with the distributive property and with the special binomials such as (x^2 - 4).  I even have ideas of how to do a graphical representation on Geoboard but I want to do more research on other apps that might help me with the graphical representations.
If anyone knows of one, let me know.

Three apps

I downloaded three apps I found on a list of apps you should have if you are teaching math.  One seems to have disappeared and I've been unable to find it.  The three I found are Ooops, Virtual Manipulatives, and iSpy-x.
The basic premise of Ooops is that you get several numbers and operations that are equal to something.  You insert parenthesis to make the problem come out right.  It has 5 levels and uses all four operations.  Sometimes it uses one set of parenthesis, sometimes it uses two.  When you think you have the answer, you hit the check button and it shows the work with the answer your problem has and tells you if it is right or wrong.  I like this app in that it gives the students a better conceptual grasp of PEMDAS and how it can effect the results of the problem.
Virtual Manipulatives has actual manipulatives for fractions, decimals and percents.  It uses the bars that start at 1 and then are subdivided for 1/2, 1/3, 1/4, etc.  The 1/3 for fractions, decimals and percents has all the same color and you can move pieces so you can have students explore 1/2 = 1/4 + 1/4 or 50% = 10% + 10% + 10% + 10% + 10%.  Virtual Manipulatives is great for the upper elementary or middle school grades.  I could see using in high school with students who struggle with basic math or in a pre-algebra class.
Finally iSpy-x which is supposed to help students learn to solve simple problems such as 2 + x = 7. You can choose the one of three levels and on each level you can select the operation or used mixed operations.  I downloaded the program 3 different times and each time it had a different bug.  I could never get it to work on more than the easy level for addition.
I know that I am going to load Ooops on my iPads next year to use in the classroom.  I like it and it can provide great differentiated instruction due to the 5 levels it offers.

Virtual manipulatives in the classroom.

Currently I use two different ones in my math classes.  One is Geoboard for the iPad.  It is just like the real life geoboards we have in our classrooms except this app comes with two different boards and lots of colored rubber bands but no chance of loosing either the board or the rubber bands.  I've used it for students to create various types of triangles such as those classified by sides, or angles, finding the number of triangles in a polynomial as a starting point to find the equation telling the interior measurements of the angles, tessellations, transformations, etc.  If you use a geoboard in real life, you can use this app to do the same thing.
The second app I've used in geometry is Geometry pad.  It allows students to use a coordinate plane for geometry.  It allows students to make all sorts of quadrilaterals and polygons, triangles, circles with radius, arcs, chords, etc.  There is an option for points, angles, lines, rays, segments, perpendicular bisectors, medians, altitudes and angle bisectors.  you can draw, type, use a ruler, and do certain functions.  I've used this one when the book has a coordinate plane problem, transformations, midpoints, diagonals, etc.  If I have to resort to worksheets for certain activities, I will have my students use this app to help them complete the worksheet. 
Due to iPads not having java, I am unable to use many of the virtual manipulative websites on the internet.  I found another app that has great ratings and I hope to down load it tonight to play with.  Its virtual manipulatives and focuses on decimals, percents and fractions.  Although it is rated for middle school, many of my lower performing high school students are weak in that area.  I think this could be used in that class to help them learn how decimals, percents and fractions relate to each other.  I hope to give more information on this app on Monday or so.

I have an app on the iPad called Free graphing calculator.  I have not been using it much but I had my students in the College Prep math class use it today because it allows you to enter in a log with a base other than 10 to graph without going through the change of base formula.  That will make things so much easier teaching logs and natural logs. 
This application does more than just graphing in that it has a calculator, a table window much like the handheld graphing calculators with the x and y values,  the graphing window and the window to enter equations.  It is really nice and combines both calculator and graphing functions.  Just like a TI-82.  I am finding it is quite handy to use without having to juggle a classroom set of graphing calculators.
I am still exploring all the functions it has.  I think I"ll be spending the weekend checking it out more so that I can report back on everything it does.
I think putting enough apps on the iPad to do the job without being addicted to the apps is important.  As a teacher I need to stay at least one step ahead of my students and show them ways the iPad can be effectively used as a tool and not a toy. 
I know many of my students would rather go on the internet to play games rather than doing their work simply because most of my student's parents do not work where a computer is used for its productivity.

Two math and one language arts apps

I received a note from NTCM and there was an article on two apps created by the SAS mobile education.  Both apps are for elementary, one math for grades K to 5 to help with number sense.  It is Math Stretch and described as a suite of activities.  I sent the info to a coworker and hope to hear from them.  The other elementary one is Read Aloud that reads a story and the child can follow the story as it is read.  The description states that there are 3 mode, read to me, help me read and read by myself.  I plan to download both and check them out.  I'll report back in a few days with my impression.
On the page, there is the SAS flash cards for high school students.  I want to check this one out as it seems to allow you to add pictures, voice, etc.  I don't know if you need the internet to use the cards or if it stands alone.
So this is one I want to check out for use in my classroom.
Enough for the moment.