# Thoughts on Teaching Math with technology

## Sunday, May 20, 2018

### Warm-up

If I weigh 5.2 pounds with clothing and 5 pounds without, what percent of my weight is my clothing?

## Saturday, May 19, 2018

### Warm-up

Each jelly bean measures .5 inch by .25 inch. How many can fill a cylinder with a diameter of 4 inches and a height of 6 inches?

## Friday, May 18, 2018

### Study Skills in Math.

Over the past few years, the number of students who know how to apply study skills has declined. Very few who arrive in high school know anything about study skills and I think I'm going to have to begin integrating it into my classes.

Some of these skills will include how to apply them to technology because we are using it more and more in class.

Mathematics is one of those subjects which require active involvement to learn the material. Students need to be active participants because very few become proficient by just listening and reading the material. Working the problems is an important part of active involvement.

When students do not do the assigned problems, they have less opportunity to understand the formulas, internalize their learning, and transfer their knowledge. In addition, math builds on previously learned material. You can't solve algebraic fractions if you never learned to work with fractions earlier on. Its hard to isolate a variable if you can't work with integers.

So to help students do better, I'll be having students learn to use Cornell Notes for note taking in class. This is the same system the science teacher has them use. This will make it more consistent across the curriculum. I hope to teach them to apply the same system to taking notes off of videos because I'll be showing some but I recommend they check You Tube for help. Furthermore, I hope to help them learn to review their notes on a regular basis by asking questions from their notes.

The next thing I want to do is take time to help students learn how to read a math textbook. They have not figured out how to read a math textbook because up until 6th grade, they just have to work their way through consumable books which are not set up in the same way as my textbooks. I don't believe the middle school math teacher requires them to read the textbook.

In addition, it is important for them to have a place where all the formulas are summarized, kind of like the reference sheets they get on tests. If they can't read a reference sheet, they have more difficulty doing well on the test. I hope to have students work on vocabulary words, both words for math and words they are likely to find on tests such as justify, or simplify.

I realize there are others but I think these are the skills that are the most important for my students to learn. These skills will help in college or if they go for additional training.

Let me know what you think. I'd love to hear.

Some of these skills will include how to apply them to technology because we are using it more and more in class.

Mathematics is one of those subjects which require active involvement to learn the material. Students need to be active participants because very few become proficient by just listening and reading the material. Working the problems is an important part of active involvement.

When students do not do the assigned problems, they have less opportunity to understand the formulas, internalize their learning, and transfer their knowledge. In addition, math builds on previously learned material. You can't solve algebraic fractions if you never learned to work with fractions earlier on. Its hard to isolate a variable if you can't work with integers.

So to help students do better, I'll be having students learn to use Cornell Notes for note taking in class. This is the same system the science teacher has them use. This will make it more consistent across the curriculum. I hope to teach them to apply the same system to taking notes off of videos because I'll be showing some but I recommend they check You Tube for help. Furthermore, I hope to help them learn to review their notes on a regular basis by asking questions from their notes.

The next thing I want to do is take time to help students learn how to read a math textbook. They have not figured out how to read a math textbook because up until 6th grade, they just have to work their way through consumable books which are not set up in the same way as my textbooks. I don't believe the middle school math teacher requires them to read the textbook.

In addition, it is important for them to have a place where all the formulas are summarized, kind of like the reference sheets they get on tests. If they can't read a reference sheet, they have more difficulty doing well on the test. I hope to have students work on vocabulary words, both words for math and words they are likely to find on tests such as justify, or simplify.

I realize there are others but I think these are the skills that are the most important for my students to learn. These skills will help in college or if they go for additional training.

Let me know what you think. I'd love to hear.

## Thursday, May 17, 2018

### More Multiplication Apps.

As commented earlier, its harder for students to figure out common denominators for fractions if they are not fluent in their facts but there is another aspect of multiplication they need to be good at and that is when you multiply the numerator and denominator to change the fraction.

Many of my students struggle when multiplying two digit numbers by two digit numbers. So I found two apps which can help a student with that type of procedure. First is the Math edge multiplication app. It is different because it has two different choices. The first is step by step which has students practice their multiplying two digit by one digit or two digit by two digit number a step at a time.

It bolds the two digits it wants you to multiply and you type in the answer using the number pad. As you type in the answer, it shows up on the screen. If a digit has to be carried, it will float up to the area for carrying. If you make mistake, the answer is in red and fades away. Once the multiplication is finished, you have to do the adding to complete the process. The flash cards limit you to selecting multiplication tables for zero to five. If you want to go to the 12's you have to upgrade.

The other is Multiplication!! which is free and designed to have students practice multidigit multiplication. This differs from the other one in that it has a square to type in the digit. You are required to type in everything here including the numeral you are carrying. If you place the incorrect digit in the space, it is red and will not move on until you place the correct digit in there.

Every problem involves a different number of digits but it is not timed and there is a tutorial to show students how to do each problem.

The last two are games to practice simple multiplication. One is M: Mission: Multiplication which has students controlling a rocket to fly through the ring with the correct answer. It has an old fashioned feel to it but it was created by a high school student a couple years ago. It requires a bit of finesse to get the rocket where you want it. The number in the ring turns red if it is incorrect and green if it is correct. I don't last long because I"m always crashing into an asteroid belt. Best of all, it is free.

The other is Marble Math Lite, a nice little game where you guide a marble through a obstacle course. Sometimes you hit a flashlight so you have to complete it in the light provided by the flashlight, while other times you hit the wrong answer, or get a free ride card. It asks the questions in three different ways such as 2 times what is 10 or what factors give you 48, or 3 times 4 is. You have a chance to look at the problem before you move the marble so you know where to aim.

Both games give you a chance to practice your multiplication tables but the marble one is easier for me personally to play but I think students would enjoy both. I hope these reviews help everyone. Let me know what you think.

Many of my students struggle when multiplying two digit numbers by two digit numbers. So I found two apps which can help a student with that type of procedure. First is the Math edge multiplication app. It is different because it has two different choices. The first is step by step which has students practice their multiplying two digit by one digit or two digit by two digit number a step at a time.

It bolds the two digits it wants you to multiply and you type in the answer using the number pad. As you type in the answer, it shows up on the screen. If a digit has to be carried, it will float up to the area for carrying. If you make mistake, the answer is in red and fades away. Once the multiplication is finished, you have to do the adding to complete the process. The flash cards limit you to selecting multiplication tables for zero to five. If you want to go to the 12's you have to upgrade.

The other is Multiplication!! which is free and designed to have students practice multidigit multiplication. This differs from the other one in that it has a square to type in the digit. You are required to type in everything here including the numeral you are carrying. If you place the incorrect digit in the space, it is red and will not move on until you place the correct digit in there.

Every problem involves a different number of digits but it is not timed and there is a tutorial to show students how to do each problem.

The last two are games to practice simple multiplication. One is M: Mission: Multiplication which has students controlling a rocket to fly through the ring with the correct answer. It has an old fashioned feel to it but it was created by a high school student a couple years ago. It requires a bit of finesse to get the rocket where you want it. The number in the ring turns red if it is incorrect and green if it is correct. I don't last long because I"m always crashing into an asteroid belt. Best of all, it is free.

The other is Marble Math Lite, a nice little game where you guide a marble through a obstacle course. Sometimes you hit a flashlight so you have to complete it in the light provided by the flashlight, while other times you hit the wrong answer, or get a free ride card. It asks the questions in three different ways such as 2 times what is 10 or what factors give you 48, or 3 times 4 is. You have a chance to look at the problem before you move the marble so you know where to aim.

Both games give you a chance to practice your multiplication tables but the marble one is easier for me personally to play but I think students would enjoy both. I hope these reviews help everyone. Let me know what you think.

## Wednesday, May 16, 2018

### Optical Illusions

It is the final couple days of school so we are basically done with teaching and we are providing fun things for students to do. I'm teaching one art class while the English teacher is teaching the other. She does the usual drawing and I'm working with students to create optical illusions, mostly because I can't draw worth anything.

The best thing about creating optical illusions such as the one in this entry, is that it can be done with straight lines.

We started with something simple that didn't require much. we used a hand, straight lines, and a few curved lines to make it look as if the lines were painted across the hand. I did this to introduce them to the concept.

The next thing we drew was a triangle similar to the one in the picture. They started with three triangles, extended a couple of lines, erase the corners and voila, you have a wonderful triangle whose sides run into another. They are often referred to as "Impossible Triangles". A couple of students had a great time with it.

The third piece we worked on was a set of stairs going down into the paper. Three students got to this one and had an absolute blast. The hardest part was extending the stairs up so it looked like it went into the ground. One person used red instead of black which gave it a really interesting look. Another got so excited that she wanted to do more so I have to find some for her to do tomorrow.

I already plan to use an optical illusion where it looks like a square hole pushes down into the paper. It is such a cool illusion. I also have to figure out how to do a double triangle that looks like its made of the letter Z and the reversed Z. I have an idea of how to do it but I will have to play with it tonight.

Students often find this really interesting and fun. Yesterday, I took over a fifth grade class for an hour so the teacher could give make up tests. They did fairly well but I discovered many of them are not that precise when they follow directions. Its like they are in too much of a hurry but most of them managed to finish two different ones and they were happy with the results.

I can see where we can use this when I next teach two dimensional shapes in Geometry. Imagine spending a day or two playing with optical illusions and relating them to the two dimensional shapes. yeah. Let me know what you think, I'd love to hear.

The best thing about creating optical illusions such as the one in this entry, is that it can be done with straight lines.

We started with something simple that didn't require much. we used a hand, straight lines, and a few curved lines to make it look as if the lines were painted across the hand. I did this to introduce them to the concept.

The next thing we drew was a triangle similar to the one in the picture. They started with three triangles, extended a couple of lines, erase the corners and voila, you have a wonderful triangle whose sides run into another. They are often referred to as "Impossible Triangles". A couple of students had a great time with it.

The third piece we worked on was a set of stairs going down into the paper. Three students got to this one and had an absolute blast. The hardest part was extending the stairs up so it looked like it went into the ground. One person used red instead of black which gave it a really interesting look. Another got so excited that she wanted to do more so I have to find some for her to do tomorrow.

I already plan to use an optical illusion where it looks like a square hole pushes down into the paper. It is such a cool illusion. I also have to figure out how to do a double triangle that looks like its made of the letter Z and the reversed Z. I have an idea of how to do it but I will have to play with it tonight.

Students often find this really interesting and fun. Yesterday, I took over a fifth grade class for an hour so the teacher could give make up tests. They did fairly well but I discovered many of them are not that precise when they follow directions. Its like they are in too much of a hurry but most of them managed to finish two different ones and they were happy with the results.

I can see where we can use this when I next teach two dimensional shapes in Geometry. Imagine spending a day or two playing with optical illusions and relating them to the two dimensional shapes. yeah. Let me know what you think, I'd love to hear.

## Tuesday, May 15, 2018

### multiplication and fractions

Right now, I juggle the balance between meeting IEP goals and helping all students learn. I have students who require a calculator for doing math but if you've ever tried to do fractions on a calculator, it can be extremely frustrating.

The problem with most calculators and fractions is you have to find the button for fractions and it usually takes two to three repeated motions. Other calculators do not have a choice of providing fractional answers in fraction form, only in decimals which is not great when you try to explain that 1/3 and .33 are not exactly the same.

I learned to work with fractions growing up but I also knew my multiplication tables. Unfortunately too many students, even the best ones, struggle with this. Many of them do not have a solid grasp of multiplication. Unfortunately there are still places in this world where fractions are used such as if you purchase lumber, fabric, cook, discounts, etc.

One of the best ways I've found to have students practice their multiplication facts is to let them play games designed to let them learn their facts while having fun. Today's apps can really help with this. I'm not talking about the ones designed to do a electronic drill and kill but the ones that give the students challenges, rewards, everything found in their beloved video games.

The other thing is that the games have to be designed for older students, not first or second graders. I've explored a few free multiplication apps and reviewed them here for you. A couple are games while others are flash cards.

1. Times Table Game offers both a free version and a paid version. The free version offers a chance to learn your factors from 1 x 1 to 6 x10 but anything higher, you need to actually purchase the paid version to get everything. The format is you have a problem with four choices. You choose the answer. If it is correct you get points and if not, it flashes the problem with your chosen answer and a question mark all in red. There are two formats, one is timed and the other is not.

2. Multiplication Table Game has three modes, learn, practice, and test. Learn is exactly what it says. It shows the table for the number you want and you learn from times one to times 10. Practice has you choose the one you want to practice such as 8's. A problem appears on the blackboard with 8 choices at the bottom for answers. If you incorrectly identify the answer, it has a red x and it has you choose another answer.

The test gives you 20 problems to complete and if you miss a problem, you get automatic feedback. There is even a 2 player option where they share a tablet and players are given the same problem to play against each other. Each works on answering the problems but it records the first person with the correct answer and it keeps giving problems as they are answered. When one person hits 15 correct answers, they are proclaimed the winner.

3. Multiplication or Division Flash card game is another one which you have to buy the app to receive full access to everything. Although it is geared for second and third grade, I believe it would work in high school because of the way it is designed. When you click on multiplication you have a choice of practice, quiz games, or match games.

Practice only allows you to practice 1 to 4 . You have flash cards which can be used in the normal way regular flash cards are used. You are given a choice of two quiz games. One is the flash card quiz which has you selecting the correct answer out of three or the speed challenge where answer as many as you can in a certain time.

The last is the match game which gives the player one of two choices. The first is to match the equation to the answer while the other has players match the equation with another equation that has the same answer. This is the part of the app I love because it helps students connect equations which have the same answer rather than looking at them separately.

Tomorrow I'm going to review a few more including two which help students learn to do multidigit multiplication. Let me know what you think, I'd love to hear.

The problem with most calculators and fractions is you have to find the button for fractions and it usually takes two to three repeated motions. Other calculators do not have a choice of providing fractional answers in fraction form, only in decimals which is not great when you try to explain that 1/3 and .33 are not exactly the same.

I learned to work with fractions growing up but I also knew my multiplication tables. Unfortunately too many students, even the best ones, struggle with this. Many of them do not have a solid grasp of multiplication. Unfortunately there are still places in this world where fractions are used such as if you purchase lumber, fabric, cook, discounts, etc.

One of the best ways I've found to have students practice their multiplication facts is to let them play games designed to let them learn their facts while having fun. Today's apps can really help with this. I'm not talking about the ones designed to do a electronic drill and kill but the ones that give the students challenges, rewards, everything found in their beloved video games.

The other thing is that the games have to be designed for older students, not first or second graders. I've explored a few free multiplication apps and reviewed them here for you. A couple are games while others are flash cards.

1. Times Table Game offers both a free version and a paid version. The free version offers a chance to learn your factors from 1 x 1 to 6 x10 but anything higher, you need to actually purchase the paid version to get everything. The format is you have a problem with four choices. You choose the answer. If it is correct you get points and if not, it flashes the problem with your chosen answer and a question mark all in red. There are two formats, one is timed and the other is not.

2. Multiplication Table Game has three modes, learn, practice, and test. Learn is exactly what it says. It shows the table for the number you want and you learn from times one to times 10. Practice has you choose the one you want to practice such as 8's. A problem appears on the blackboard with 8 choices at the bottom for answers. If you incorrectly identify the answer, it has a red x and it has you choose another answer.

The test gives you 20 problems to complete and if you miss a problem, you get automatic feedback. There is even a 2 player option where they share a tablet and players are given the same problem to play against each other. Each works on answering the problems but it records the first person with the correct answer and it keeps giving problems as they are answered. When one person hits 15 correct answers, they are proclaimed the winner.

3. Multiplication or Division Flash card game is another one which you have to buy the app to receive full access to everything. Although it is geared for second and third grade, I believe it would work in high school because of the way it is designed. When you click on multiplication you have a choice of practice, quiz games, or match games.

Practice only allows you to practice 1 to 4 . You have flash cards which can be used in the normal way regular flash cards are used. You are given a choice of two quiz games. One is the flash card quiz which has you selecting the correct answer out of three or the speed challenge where answer as many as you can in a certain time.

The last is the match game which gives the player one of two choices. The first is to match the equation to the answer while the other has players match the equation with another equation that has the same answer. This is the part of the app I love because it helps students connect equations which have the same answer rather than looking at them separately.

Tomorrow I'm going to review a few more including two which help students learn to do multidigit multiplication. Let me know what you think, I'd love to hear.

## Monday, May 14, 2018

### Apps, Free apps, Paid Apps, Which One Should I Get.

I love free apps. I love them personally and I love using them at school. When given a chance I go for the free apps.

Over the years I've come to the conclusion that free apps fall into one of three or four categories.

First, there are the free apps for companies whose material you have to have a school subscription to in order to use such as Power School or certain reading, writing, or math programs.

Next are the apps you can subscribe to privately for so much per month in order to access their services. The only thing that is free is the app and possibly a trial. Some of these apps are designed by private citizens who are interested in monetizing their product.

The third type of app is the free app which shows people what the app can do but to unlock most of the features or the premium ones, you have to upgrade to the paid version. I like these because they give you an idea of what the product can do before you buy it.

The last type are those which are totally free and do everything you want them to do. The only problem with these apps is the developers often move on to their next app and these are not updated so they cannot be used after a while.

As a school teacher, I hate purchasing an app I have not tried. I am afraid of buying the app only to find out it is not what I wanted or it didn't do what I thought it did. For me, I love the light or free versions of the app. It gives me a chance to taste it and discover if it is something that will work for class.

I know an app that requires some payment is signaled by having the phrase "In-App purchases" but I can never seem to find the place in the adds which tells what you have to purchase. Are you purchasing access to the materials? The server? What?

Still, I'd like to know what I am going to have to pay for. Its nice to know before downloading an app if you have to pay for the service, for additional levels, or for premium items. Often, I can get by without the premium features. I'd also like to know if the app needs the internet to work or if you have an offline option. I often end up in places without reliable internet and cannot use apps that require internet connections.

The bottom line is I prefer the lite or free versions so I can test the app first before investing in it. This is important for school teachers because we hate buying apps only to find out they are not what we wanted.

Let me know what you think. Tomorrow I'm looking at multiplication apps for high school. Let me know what you think.

Over the years I've come to the conclusion that free apps fall into one of three or four categories.

First, there are the free apps for companies whose material you have to have a school subscription to in order to use such as Power School or certain reading, writing, or math programs.

Next are the apps you can subscribe to privately for so much per month in order to access their services. The only thing that is free is the app and possibly a trial. Some of these apps are designed by private citizens who are interested in monetizing their product.

The third type of app is the free app which shows people what the app can do but to unlock most of the features or the premium ones, you have to upgrade to the paid version. I like these because they give you an idea of what the product can do before you buy it.

The last type are those which are totally free and do everything you want them to do. The only problem with these apps is the developers often move on to their next app and these are not updated so they cannot be used after a while.

As a school teacher, I hate purchasing an app I have not tried. I am afraid of buying the app only to find out it is not what I wanted or it didn't do what I thought it did. For me, I love the light or free versions of the app. It gives me a chance to taste it and discover if it is something that will work for class.

I know an app that requires some payment is signaled by having the phrase "In-App purchases" but I can never seem to find the place in the adds which tells what you have to purchase. Are you purchasing access to the materials? The server? What?

Still, I'd like to know what I am going to have to pay for. Its nice to know before downloading an app if you have to pay for the service, for additional levels, or for premium items. Often, I can get by without the premium features. I'd also like to know if the app needs the internet to work or if you have an offline option. I often end up in places without reliable internet and cannot use apps that require internet connections.

The bottom line is I prefer the lite or free versions so I can test the app first before investing in it. This is important for school teachers because we hate buying apps only to find out they are not what we wanted.

Let me know what you think. Tomorrow I'm looking at multiplication apps for high school. Let me know what you think.

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