Teaching Eachother Through Videos

As we are winding down the year we are studying pre-algebra. The boys are struggling with showing their work and explaining the problems. They really want to just put the answer down. We have discussed that just putting the answer does not help if they do not know how they got there. The technology teacher, Melissa Smith, suggested that I have the boys make a teaching video on Voicethread. I was not sure how this was going to go, but I was on board to try anything that would help my students. This was their last project of the year and it had amazing results. I am going to incorporate this activity in almost everything I teach. As I reviewed the boy’s videos, I realized that even though they were writing the process and putting the right answer, in the end, they “really” did not know what they were doing. I also had the boys evaluate each other’s videos. By listening to the critics, I could hear who was struggling and who was not. I spent the next class period explaining what I saw in the video and what they needed to work on. They were also able to go back and hear what they were saying. Having them talk out loud also helps them to understand what they are doing.

Similes For Integer Rules

I asked the boys to write two similes. One on negative times a negative equals a positive and one on a negative plus a negative equals a negative. The boys brought them the next day and shared them with the class. We discussed each one and decided if it worked or did not work. The boys gave feedback and had to support if they thought it was good or needed work. This was a great activity for me to see if they really understood the rules. It was so much fun for me and the boys to listen to each other and take feedback from each other. I would love to share some of the examples that they created.

negative x negative = positive

negative + negative = neg

I also had them write headlines to show their understanding of the concept. Here is an example on the things they came up with.

How Fractions Relate to Racism

Holly Butora, the boys reading teacher has just had them read the Cay. The Cay talks about racism in the story. As they read the book, the class would talk about what racism looked like and how it was being played out in the book. After many class discussions the class was asked to write a simile about racism. They then turned their simile into a worldal that compared racism to a real world topic. These boys choose fractions. I am showing this as an example of how deep the boys are now going to really learn about what they are doing in math. I was so impressed on how the boys were able to take a topic like fractions and compare it to racism.

Tax and Sale

This week we continued talking about percent. I had the boys look up sales tax in all the different states and compare the different sales tax. They were sad to find out that their state has the biggest sales tax. We looked at local and state tax and talked about the differences. The boys had fun comparing the states.

Here is the website that the boys used in class.

Random Guy -- Sales Tax

Percent Problems

We have been talking about different types of percent problems. This week the boys have been working on word problems that involve part/whole or is/of. They have had fun trying to find the unknown (variable). One boy said, "This is fun because it is more like a game than math." I am telling them to treat it like a game. The boys are finding the answer first and then explaining why as a form of checking themselves. This is where Random Guy is coming back into the picture. One of the problems I gave them this week was:

On field day Barry entered 16% of the events open to his age group. If he entered 12 events, how many events were there altogether?

One boy even did a podcast of his explanation to help the other Boys in the class.

Example

The boys have also started asking about sales tax and how you find it. We talked a little about the process and next week we will be comparing the different states and their sales taxes. We went on a field trip this Friday and one of the boys asked his mother for a little more money so he would have enough for sales tax. I thought that was cute. The boys are very interested in sales tax and how it makes a difference in their purchases. The lesson really has them thinking about how math can effect their everyday life.

How Fifth Grade Looks at Geometry

Here is an example of what the fifth grade wrote about their thoughts on Geometry and what they learned from this unit. I had them share their thoughts with the class as they presented their project. I was very excited to see that the boys now look at the world through a geometry perspective and see how much math plays a part in their life.

One group even brought up that making pills has geometry involve and how big to make the containers that the pills will go into. Teaching with discovery has really allowed these boys to own their learning and question things they are learning.

Geometry and Building

The boys' final project in Geometry was to create their own dream house. They had to make a blue print, use perimeter, circumference, and area, write about how they see Geometry in the world, and build their dream house out of things around their home. When they used perimeter, circumference, and area the boys had to ask a question about why they needed to use perimeter, circumference, and area. Then they answered the question in the project.

**** Some examples of the Geometry projects. --- These are some videos that the boys made of the full project.

Here are some pictures of their houses.

Infusing Technology Into The Math Curriculum

Here is what the technology teacher at my school is doing with the boy's explanations on how to solve different math problems. We felt this was a great idea. They are now taking their writings and making quick videos for their peers to watch.

Infusing Technology Into The Math Curriculum --- Here is a blog about how to make the videos. This is written by our technology teacher.

5th Grade Math Videos ---- Here are some examples of what we have done so far. We are hoping to make many more videos like this in the future.

Math In The Reading Classroom

I wanted to share some examples of what two boys did in their Reading class yesterday. I was excited to see them pulling their definitions into their Reading class.

Thoughts .......

So far this year I feel I have grown as a teacher so much! I am becoming a better teacher. Making the boys dig deep and immerse themselves in the content has given them and me a chance to look at math in so many different ways. The boys have made connections that I could have never imagined. I am able to show the boys that what they are learning now will be used in their other other classes and why. For example knowing exactly why the units are cubed in Volume, lead to the question, "How and Why" This lead into how to multiply exponents. Some of the boys are learning about Laws of Exponents now because the questions they were asking. I am very excited to see where this will lead the boys in their future math classes.

I would love to hear your thoughts.

Geometry Projects

The boys have put themselves in the role of a Creator. They were given the assignment to create their dream club house, play house, or hunting blind. They could build it from things around their house, Sketch-Up, or legos. We have been talking about how Geometry is all around us. I wanted to end this unit with them taking on a role where they could experience hands on Geometry. I will be showing you their projects soon.

"I used to think, but now I think" --- Geometry

I asked the boys to type or write out a "I used to think, but now I think" on Geometry. I wanted to share a few with you.




I use to think Geometry was just shapes and sides. Now I think Geometry it more complex than J.K. Rowling's writing style.

I use to think Geometry was just a bunch of shapes. Now I think it is mathematical term like multiplication or division.

I used to think Geometry was useless. Now I think Geometry is in our everyday life.

I use to think Geometry was just a bunch of Shapes. Now I think Geometry is something we use everyday.

I use to think that Geometry does not involve anything in real life. Now I think that you can find Geometry everywhere.

Geometry Unit

I am so excited about what has come out of this unit. I will continue to teach Geometry this way in the future. The boys have really immersed themselves in geometry and want to learn more. They could not believe that we have only touched the surface of what geometry is all about. They keep wanting to learn more. The classes were run by what questions the boys wanted to learn about and the tests were based on their questions.

As we got into the unit and started to learn about the formulas the boys were able to figure out some of the formulas because of the definitions that they have learned. For example, I had them figure out the area of a triangle on their own. They knew that a triangle was half of a parallelogram and the formula for a parallelogram was base x height. Knowing this information they were able to come up with the formula for a triangle and explain why. ((base x height)/2) This was exciting for them. They also figured out that circumference has two different formulas and can explain why. They knew that a diameter was made up of two radii.

The boys also started to ask questions about volume and why the formula changed depending on the bases of the 3D object. When we got into these questions the boys realized that you can write volume as Area of the base x Height of the whole object. This then lead into what happens if you have something inside the 3D object taking up space in the object.

This lead to the questions, "What does a 4D shape look like?" and "Do they exist?" These question lead into some great debates. The boy continue to research and ask questions.

Random Guy

We have brought Random guy back into the classroom. The boys are now teaching him about geometry. The boys are having so much fun with Random Guy. Over the year, the boys have found this exercise is a great way to check their work. I would love to share some of their Random Guy writings with you. As they write to Random Guy they are told to write their thoughts and not worry about all the grammar. I feel that if they are not as concerned about their grammar, their explanations will be more complete.

I have provided some examples below. In some of the examples the boys left out why they had to subtract. We talked about why that was important to put into to the explanation. I am very proud of the boys for what they came up with. This was given to them with only one measurement and they had to find out the other measurements and the formulas. Not all of the following examples are perfect scores. I wanted to show different examples of the progress the boys are making. I have discovered during this process that the boys are better able to see their errors and I am better able to assess their needs so that they can fully understand what they are doing.

In some of the following examples the boys and I talked about how some of the details were left out. For Example, "Why subtract the area of the circle from the area of the square?" or "How did you get 8 units as the length of one side of the square?" I feel the boys are doing a great job. The boys that wrote this knew the answers to the questions I asked, he just forgot to put it into the explanation. This is another great learning tool. The boys are able to use peer editing and teaching each other at the same time.

Here is the question that the following boys wrote about.

Area and Perimeter

Today we talked about area and perimeter of a parallelogram. We talked about the formulas, how you label the units and when we can use area and perimeter in everyday life.

Area = base x height
Perimeter = You just always add up all the sides.

One of the questions in class was, Why do you square the units when finding area and do nothing to the units when finding perimeter?

Some of the boys talked about how you are multiplying like units together and that is why you square them in area. You add in perimeter so you do not need to do anything to the units in perimeter.

One boy made a connection to a two dimensional plane and squaring the units in area. He talked about how a plane is two dimension and you only have length and a width, or a base and a height. You have no depth. Therefore, you need to square your units. You have two units you are multiplying together. Then he talked about how perimeter means you are going around a plane. Lines make up planes and lines are one dimension. Therefore you do not need to do anything with the units. The boys really liked that way of looking at area and perimeter.

Making Connections

This has been an amazing few weeks for me as a teacher. As I talked about earlier, I decided to teach my Geometry unit differently this year. I first had the boys set up a slide show from their research of different Geometry words that I had given them. Then I set the class up as a discussion, debate, and investigation format. I could have never dreamed about how well it went. The boys came up with amazing questions and connections. They had to back up everything with proof. I cannot wait to hear what they come up with next. We are going to be starting to add in some formulas into the discussions.

I would love to hear about different ways your school is teaching geometry.

Geometry Vocab Discussion Cont.

Here are some examples of questions that came from our class discussions this week.
1. Does every polygon with equal angles, have equal sides? -- This question came up when we were talking about equilateral triangles. After the boy asked the question, another boy raised his hand and said, "No". I said, "Why?" He said, "A rectangle has equal angles, but not equal sides."

2. What can you call a diagonal in a square that cuts the 90 degree angles in half?

3. Question two lead into the discovery that two right triangles make up a square. Also that the sum of all the angles in a triangle is 180 degrees and 180 degrees + 180 degrees = 360 degrees. 360 degrees is the sum of all the angles in a quadrilateral.

4. Are all angles that make up complementary angles acute? -- We used the definition of complementary angles and acute angles to come up with our answer.

5. Do all right triangles have complementary angles? --- They boys used the definition of a right triangle, the definition of complementary angles, and that the sum of all the angles in a triangle is 180 degrees.

6. Do 4 radii make up a circumference?

7. Do 6 radii make up a circumference?

--- To solve questions 6 and 7 we had to look at what circumference equaled.

8. Why do you call 22/7 Pi?

10. Could a diameter also be called a line of symmetry? -- This question came up when we were talking about what cuts a circle in half. One of the boys said a line of symmetry. We talked about how a diameter is like a line of symmetry in a circle. I loved how he made the connection.

*** The boys discovered on their own that if C=(pi)d, then circumference also equals two times Pi times radius. They were very proud of themselves for discovering this formula.


Similes:
The earth's core is like the diameter in a circle, because they both go straight though the center connecting each side.

Geometry Discussion

For the last few days we have been talking about geometry and how it is all around us. The boys were given words they were required to research on their own and then teach their words to the class. We used Google Docs to put the slide show together. I asked the boys, "How does Geometry shape our world?" The discussions we have been getting into are amazing. The boys have really been digging deep into the vocab and seeing how it relates to the world around us.
1. Where are rays represented in our world?

Is a piece of hair a ray?

Are your fingernails rays?
We have decided with a lot of discussion that both these things are rays. The boys supported this answer by explaining how your hair starts at the scalp like the end of a ray and your hair can grow forever on the other end like the other end of a ray. The same thing happens with your figure nails. One end can go on forever and the other has a stopping point.

2. Are points considered a zero dimension if points make up lines and lines are one dimension?
When we talk about the definition of a point it talks about a point having no depth and no length. Therefore we concluded that a point does not have a dimension. A point does have a zero dimension.

3. Is a circle a plane and made up of lots of little lines?
I left the boys with a question to think about over the weekend. I asked them, "Can you prove that circles are polygons?"

Similes of The Week:
An angle is like two or more jets moving into a formation or peeling away from each other. vertex is the point where they start before pealing out.

Intersecting lines and parallel lines are like fraternal twins. They are in the same family, but have different characteristics.

A point is like the Holy Spirit you know they both exist, but you cannot see them.

Similes About Dividend and Divisor

Here are some examples of what my boys came up with when we were talking about divisors and dividends. The boys really got into writing these and could not wait to share with friends. I love how I could pull in some History, Science, and English while teaching the difference between a divisor and a dividend. This activity really helped the boys when they were reading division word problems to pick out the dividend and divisor.

• The divisor is like the butcher and the dividend is like the meat because the butcher is cutting up the meat like a divisor divides the dividend. The divided is like the meat because it is being divided up.

• A divisor and dividend are like a spectrometer and the test molecules. The spectrometer divides up the molecules for verification. (SCIENCE)
  

• A divisor is like a lighter and a dividend is like a fuse because the lighter takes away from the fuse like a divisor takes away from the dividend.

• The divisor is like a fish and the dividend is like a net. You can only put so many fish into a net.

• A dividend is like a wooden house and a divisor is like termites because the divisor divides the dividend into pieces. Termites bite into wooden houses and tear them to pieces too.

• A divisor is like a buzz saw cutting up wood because it splits it up. The dividend is like the wood being split up by the buzz saw because it is being cut up.

• The divisor is like a cheese grader. It grades the dividend into small parts. The dividend is like a block of cheese. It gets graded up by the divisor, which is like a cheese grader.
  

• A divisor is like an apple core. They both divide things into groups. A dividend is like a horde of fish. They both are divided into groups.
  

Explaining about how wording can make a difference.

We have talked about how every word problem is a little different. We have to put on our investigating hats and look for all the evidence. What is the problem asking us to solve? Are we using division, multiplication, subtraction, or addition? What would we do if we were in the situation? Then I have the boys write two sentences on why they chose the operation that they did. This helped them to evaluate their answer. Some of the boys were able to see why what they chose was wrong at first. Their answer did not make since and they reevaluated what they needed to do to solve the problem. I felt this was a great activity for the boys because they saw that even if they were wrong at first it was ok and were able to go back and get the right answer before turning in their problem.

An Example of two students comparing two word problems.

How to Solve Word Problems

We have been really digging deep this year to learn about the process of a problem and learn about every step we need to use to solve a problem. What are the parts? What do the different parts do in the problem to help solve them? These were questions that I asked the boys every day. For example, we have been talking about a divisor, dividend, and quotient in a division problem. We talked about what they mean to a division problem and wrote similes for the divisor and dividend. I will share the similes with you later.

The boys have really been able to solve and learn about word problems so much faster this year. I feel it is because we have dug so deep into what is involved in solving problems. I used to believe the only way to learn math was to do skill and drill. I now believe this is not true. Kids start taking ownership of their learning when they truly know what is going on and understand.

It was amazing what the boys where saying. I did not even tell them what the problem was about. Their assignment was to read it with their group and decided the operation. Then they were asked to write why they picked the operation that they picked.

This video shows what I am talking about.

Click Here

How To Videos

Here are two examples of the boys making their own how to videos. These videos are the results of the boys spending time writing out how to solve math problems and working on what goes into solving a problem. I let them put their own personalities into the videos. I hope you enjoy. :)

Video One

Video Two

Making Corrections on Their Tests

Here are some examples of how I have my boys correct their tests and quizzes. They have to give me a reason on why they feel they have missed the question after reworking their problem. The boys enjoy this because it allows them to see what they need to work on for the next test.

The First Trimester -- Discribing a Problem

The boys and I have been talking about how detail in their description makes a big difference when explaining a problem. I started off having the boys solve a problem and then they explained, in their own words what they did to solve the problem. Most of the boys just wrote the steps and did not give any detail. As we continued through out the trimester the boys started putting detail and getting more exact in their explanation of the steps. One of the boys on a test question even used this to check his work and noticed he had done a step wrong. He said,"Mrs. May, this really helps." As the trimester went on I noticed boys were really thinking about the steps as they solved their problems. They even were able to explain to their classmates how to solve different problems and explain why. Some of my students that have struggled in math, stepped up and started participating in class and teaching others. The boys that have always been strong in math were noticing that they were having trouble explaining what they were doing, but enjoyed the challenge, as they called the description process.

Here are some different examples.
I feel these are great examples of how hard the boys are working.






I was wondering if any other schools are using this process to teach fractions? I would love some suggestions on how to make this even better. We are in the process of turning this activity into how to videos. The boys are going to share them with the fourth grade when they are done. I will share the videos when we have finished.