Students often find ratios difficult to manage without having a real context to relate to. Years ago, I saw the results of a class which was quite impressive.

The students started by designing a house. They had to draw plans for their dream house complete with bathrooms, bedroom, kitchens, etc. The plans had to be done correctly with a scale, doors, windows and everything normally expected.

Once the plans were created, they had to build a scale model out of wood so they could see it, just like those scale models you see on television shows. The models give a better sense of proportion for the rooms when we cannot visualize it.

When they build a model, they see that a 2 foot by 3 foot bathroom might be a bit small, or the 30 by 60 foot bedroom might overwhelm the rest of the house. There is always an esthetic element one has to keep in mind when designing a house. I know I hate houses with two sides heading back at a diagonal. To me, the main room acquires a squashed feel.

In addition, I prefer open floor plans with a higher ceiling so the rooms feel bigger. If the rooms are divided up so you have a separate living room from the kitchen, and the dining room, it can feel more cramped. By building a scale model, they see if the feel is as they desire.

I like some of the new apps because they allow a person to populate the rooms with furniture and drapes for a more complete feel. A 10 by 10 foot bedroom may seem large enough empty but when you add a bed, dresser, desk, chair, and night stand, it may suddenly seem too small. These apps supplies furniture in the correct size.

So with a couple of apps, the students has designed the house and populated it with furniture. Then building the model, gives a better feel so you can move around it and check it out. It also adds the hands on element for those who need a physical component.

Please let me know what you think. I'd love to hear from you.

# Thoughts on Teaching Math with technology

## Friday, August 18, 2017

## Thursday, August 17, 2017

### Identifying Mistakes.

I've decided to start the year with error analysis in my two lowest performing classes. These are the classes with students who do not have a solid foundation in Math. These are the students who throw out a paper once its been returned. They do not know how to learn from their mistakes.

I found this lovely sheet of addition and subtraction problems, some correct and some with mistakes. The sheet requires them to check the math and make corrections as needed. I took this one step further and requested they identify the mistake made by writing it down.

One of my students asked if I wanted to turn them all into teachers. I laughed and explained they need to know how to identify the type of error they made so they can get better in math. Many students actually worked together trying to determine what was done incorrectly. Most of the mistakes were things like forgetting to add the carried number, forgetting to borrow, adding instead of subtracting.

The reason for this exercise is that I do not plan to record grades until a student has made all the corrections and included the reason for the mistake. I hope this exercise will help students determine where they still do not fully understand the topic.

Will the idea work? I don't know yet. Most of my students have the mindset, even in English, of I've done it once, why work on it more? In English, they think the first draft should be the final draft and hate rewriting to improve it. In Math, they did the problems so that's it. Its important to have them learn the material correctly the first time but if not, they need a tool to learn self correction.

I suspect this attitude develops in math because many of the elementary teachers do not stress correcting the work. I admit, I've not done this except on tests in the past but since reading that students need to know how to explain steps, etc, I am changing my focus to include correcting even daily work.

I'll report back in a few weeks to let you know how it goes. Let me know what you think. I would love to hear.

I found this lovely sheet of addition and subtraction problems, some correct and some with mistakes. The sheet requires them to check the math and make corrections as needed. I took this one step further and requested they identify the mistake made by writing it down.

One of my students asked if I wanted to turn them all into teachers. I laughed and explained they need to know how to identify the type of error they made so they can get better in math. Many students actually worked together trying to determine what was done incorrectly. Most of the mistakes were things like forgetting to add the carried number, forgetting to borrow, adding instead of subtracting.

The reason for this exercise is that I do not plan to record grades until a student has made all the corrections and included the reason for the mistake. I hope this exercise will help students determine where they still do not fully understand the topic.

Will the idea work? I don't know yet. Most of my students have the mindset, even in English, of I've done it once, why work on it more? In English, they think the first draft should be the final draft and hate rewriting to improve it. In Math, they did the problems so that's it. Its important to have them learn the material correctly the first time but if not, they need a tool to learn self correction.

I suspect this attitude develops in math because many of the elementary teachers do not stress correcting the work. I admit, I've not done this except on tests in the past but since reading that students need to know how to explain steps, etc, I am changing my focus to include correcting even daily work.

I'll report back in a few weeks to let you know how it goes. Let me know what you think. I would love to hear.

## Wednesday, August 16, 2017

### Performance Tasks

Today is Wednesday. That means its a short day so I started students on performance tasks. If you are not aware, performance tasks allow students a chance to determine an answer based on information provided.

I found some lovely performance tasks at Inside Mathematics. All the tasks are divided into grade level complete with answers and examples for grading.

Although I teach High School, many of my students are English Language Learners who need a bit more scaffolding. I chose a task from the 7th grade level in which they had to determine which of the cereals had a higher protein level. I enjoyed the task because it had them using ratios in context.

I sort of walked them through the task but I required them to be a bit more independent than last year. I began the class by asking them "What is a ratio?" The answers to this question indicated they were not sure what a ratio is. After some discussion, I asked "What are some examples of ratios used in real life?" This stopped everyone cold because they connect ratios with the math classroom and not with life outside of school.

I guided them to snow machines and ATV's because these engines use an oil to gas ratio. I have no idea what it is but I've heard the ratio has to be right. These machines also have miles per gallon and miles per hour ratios. They started getting the idea because someone suggested certain stats in basketball.

Unfortunately, they struggled with setting up a proportion to determine the amount of cereal required for 9 grams of protein. They already knew that a person got 12 grams of protein from 100 grams of cereal. It took a bit but they managed to find the answer.

Disaster struck when they had to compare two ratios to determine which cereal had the higher ratio of protein. Several students based their answer on the denominator of the ratio written in fraction form. They did not bother looking at the numerator. Because one denominator was 9 and the other 25, they assumed the one with 9 was bigger.

This lead to a discussion on comparing fractions and needing a common denominator. One student suggested finding decimal values instead which was fine but several students set up the division problem incorrectly.

The great thing about this exercise was the way it exposed weaknesses in student knowledge. This will make it easier for me to start the year and work on strengthening these areas. This helps me plan future topics.

Let me know what you think. Have a good day.

I found some lovely performance tasks at Inside Mathematics. All the tasks are divided into grade level complete with answers and examples for grading.

Although I teach High School, many of my students are English Language Learners who need a bit more scaffolding. I chose a task from the 7th grade level in which they had to determine which of the cereals had a higher protein level. I enjoyed the task because it had them using ratios in context.

I sort of walked them through the task but I required them to be a bit more independent than last year. I began the class by asking them "What is a ratio?" The answers to this question indicated they were not sure what a ratio is. After some discussion, I asked "What are some examples of ratios used in real life?" This stopped everyone cold because they connect ratios with the math classroom and not with life outside of school.

I guided them to snow machines and ATV's because these engines use an oil to gas ratio. I have no idea what it is but I've heard the ratio has to be right. These machines also have miles per gallon and miles per hour ratios. They started getting the idea because someone suggested certain stats in basketball.

Unfortunately, they struggled with setting up a proportion to determine the amount of cereal required for 9 grams of protein. They already knew that a person got 12 grams of protein from 100 grams of cereal. It took a bit but they managed to find the answer.

Disaster struck when they had to compare two ratios to determine which cereal had the higher ratio of protein. Several students based their answer on the denominator of the ratio written in fraction form. They did not bother looking at the numerator. Because one denominator was 9 and the other 25, they assumed the one with 9 was bigger.

This lead to a discussion on comparing fractions and needing a common denominator. One student suggested finding decimal values instead which was fine but several students set up the division problem incorrectly.

The great thing about this exercise was the way it exposed weaknesses in student knowledge. This will make it easier for me to start the year and work on strengthening these areas. This helps me plan future topics.

Let me know what you think. Have a good day.

## Tuesday, August 15, 2017

### School Started.

Sorry about not publishing anything yesterday but I had to get my room ready for school. School started today. I have one class this year, "Fundamentals of Math" which is going to be my try it out class.

This class is for upper level high school students who have not done well in other math classes. My idea is to take the last set of MAP results, group them according to their scores, assigning work based on what they need.

I plan to do this using Google Classroom because I can place all the work there for each group. Just to let you know, I will be adjusting groups based on the strand. Google classroom will make it easy to create collaborative assignments using Google slides or docs.

In addition, I can create Hyperdocs so each group can work on their own while I provide some one on one time with students who are lacking basics. I discovered Hyperdocs this summer and fell in love with them because I can create a document with all sorts of interactive links. Anytime, I have them watch a video, I hope to make it so they have to answer questions at various times so they really pay attention to what is being said. Too many of my students will just enjoy the video because they do not know how to watch it to learn.

This is the class I am going to try things out on to make it more student centered so they are guiding their learning rather than having me teach it so much. I could teach it the traditional way but I have skill levels from low to on level, making it harder to do the old one methods fits all.

Many of these students have failed earlier math classes either because they do not have certain skills or they do not learn in a traditional classroom. I hope by changing the way conduct the class, students might find success they have not attained before.

I will let you know how it goes. Have a good day and let me know what you think.

This class is for upper level high school students who have not done well in other math classes. My idea is to take the last set of MAP results, group them according to their scores, assigning work based on what they need.

I plan to do this using Google Classroom because I can place all the work there for each group. Just to let you know, I will be adjusting groups based on the strand. Google classroom will make it easy to create collaborative assignments using Google slides or docs.

In addition, I can create Hyperdocs so each group can work on their own while I provide some one on one time with students who are lacking basics. I discovered Hyperdocs this summer and fell in love with them because I can create a document with all sorts of interactive links. Anytime, I have them watch a video, I hope to make it so they have to answer questions at various times so they really pay attention to what is being said. Too many of my students will just enjoy the video because they do not know how to watch it to learn.

This is the class I am going to try things out on to make it more student centered so they are guiding their learning rather than having me teach it so much. I could teach it the traditional way but I have skill levels from low to on level, making it harder to do the old one methods fits all.

Many of these students have failed earlier math classes either because they do not have certain skills or they do not learn in a traditional classroom. I hope by changing the way conduct the class, students might find success they have not attained before.

I will let you know how it goes. Have a good day and let me know what you think.

## Sunday, August 13, 2017

## Saturday, August 12, 2017

## Friday, August 11, 2017

### Gaining Student Attention.

Recently, I've been reading several books, looking for ways to improve my methods so I keep student interest and create hooks to improve their desire to pay attention.

The first suggestion, I ran across was actually via a short video where the teacher recommended you wait till all the students are quiet. If you start while some of the students are talking, they are going to ask you to repeat the information. By waiting till they are quiet, they are actually going to pay attention and hear instead of being involved in their own conversations.

The next four suggestions come from Pow Toons blog and the third suggestion is seconded in the book "Teach Like a Pirate"

1. Change your focus from teaching a topic to teaching for the student. Make it so they feel as if they benefit from the content. Creating benefit creates desire so its important to create desire. Instead of telling them what they are going to learn, create headlines to tease them with upcoming topic. Headlines make a promise designed to create desire so students want to learn.

2. Convince students they are going to miss out on the benefits if they do not pay attention. As part of this, let students know what might happen if they miss the information. They need to know the pain of lacking information. You provide the motivating reason for learning the material.

3. Create a movie trailer designed to capture student attention. I have done with using imovie on my Mac. I created a spy trailer teasing students with a preview of the next unit. It caught their attention because when it was done, they wanted to see it a second time. The suggestion is based on the fact Hollywood always teases audiences with upcoming movies before showing the current movie. They build desire which is what a teacher does by creating trailers for the next topic. Don't tell, show.

4. Be willing to use animated videos which have both an auditory and visual component to help meet student needs. If you have students create their own animated videos, you have a kinesthetic component. With all the web sites and apps, its easy to create animated videos.

I'd like to thank Pow Toons for these ideas. I plan to try the three that I've not used before. I can hardly wait to try. Please let me know what you think.

The first suggestion, I ran across was actually via a short video where the teacher recommended you wait till all the students are quiet. If you start while some of the students are talking, they are going to ask you to repeat the information. By waiting till they are quiet, they are actually going to pay attention and hear instead of being involved in their own conversations.

The next four suggestions come from Pow Toons blog and the third suggestion is seconded in the book "Teach Like a Pirate"

1. Change your focus from teaching a topic to teaching for the student. Make it so they feel as if they benefit from the content. Creating benefit creates desire so its important to create desire. Instead of telling them what they are going to learn, create headlines to tease them with upcoming topic. Headlines make a promise designed to create desire so students want to learn.

2. Convince students they are going to miss out on the benefits if they do not pay attention. As part of this, let students know what might happen if they miss the information. They need to know the pain of lacking information. You provide the motivating reason for learning the material.

3. Create a movie trailer designed to capture student attention. I have done with using imovie on my Mac. I created a spy trailer teasing students with a preview of the next unit. It caught their attention because when it was done, they wanted to see it a second time. The suggestion is based on the fact Hollywood always teases audiences with upcoming movies before showing the current movie. They build desire which is what a teacher does by creating trailers for the next topic. Don't tell, show.

4. Be willing to use animated videos which have both an auditory and visual component to help meet student needs. If you have students create their own animated videos, you have a kinesthetic component. With all the web sites and apps, its easy to create animated videos.

I'd like to thank Pow Toons for these ideas. I plan to try the three that I've not used before. I can hardly wait to try. Please let me know what you think.

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