Triangle exploration lesson

          This week we started our triangle exploration unit. Students were given a Tupperware that contained enough snap cubes to form lengths of 2, 3, 4, 5, 6, 8 and 10. Starting with the three shortest lengths, 2 ,3 and 4 the partners formed a triangle, if possible, using the cubes. If the lengths formed a triangle they decided what type of angle was the largest angle. They also found that some of the lengths did not form triangles.

These students found the lengths they chose formed an obtuse triangle.

These students formed a right triangle.

     As they worked they filled a sheet to to collect their information. Then looking at the sides that did not form triangles they wrote why they thought they didn't form triangles. There were some interesting observations like: "It just doesn't fit.", "It won't close.", and "they aren't long enough." It was a great visual for the students. On day two when we discussed this we actually lined the two shorter sides next to the longer side to show they were not greater than the third side. We also looked at  sides that did form triangle and the two shorter sides were longer than the third side.They kids did a great job on this activity. Of course, you know they did want to start building towers. I do need to find a building towers activity because they would love it. Suggestions anyone? 

       Click here to get a copy of the Triangle investigation sheets. This is adapted from
                           Alexander Sabatino, Jr's Picking Pythagorus Lesson.

     Everything went well until "that class" came in. I don't know if you have one of these but I have one this year. They are challenging in every area you can imagine, yet I keep trying to do group work with them. What's the matter with me? Well anyway, one of the students came in, let's call him  "T" and he quickly grabs the Tupperware and says he will pass them out. Before I can utter a word, he has eight Tupperware stacked in his arms and yes, you guessed it, he dropped them. All the snap cubes, 100's of them are all over the floor. At least "T" was busy for awhile picking them all up. Oh the joys of middle school.
     This lesson worked well  and the kids enjoyed it. It gave them an great visual for the triangle inequality rule. I will definitely be doing this again next year.
   
                                                           Til next time,
                                                                  Jan

A peek at my Pythagorean Theorem Unit

      At last, my finalized Pythagorean Theorem unit. I feel like I have been working on this forever. I love all of the activities that I have found and it was difficult to narrow it down to the following lessons. Here is a list of the major activities that I am doing with my students starting next week. This is going to be fun!

     

Pythagorean Theorem Investigation

     I will introduce Pythagorean Theorem with the Starburst candy activity. I was inspired by Pam Lucken's video to use Starburst candies as a manipulative to form the sides of the triangles. I have seen the same project using other manipulatives as well. I just think candy will be fun. My goal is for the students to be able to discover the Pythagorean Theorem on their own. When they have finished the activity it will go in their interactive notebooks.

Students will need:

•   A copy of the Starburst Triangle Investigation and direction sheet.
•  A plastic bag with 340 Starbursts in each bag. (Maybe 350 to account for accidental eating.) 
•    A plastic bag with triangle measurement sides for the six triangles they will model.
•    Paper, pencil and straightedge.    

                                                   

Click here for: Starburst triangle investigation and
Triangle Exploration Worksheet ( adapted from Alexander Sabitino, Picking Pythagorus.)
Directions for Starburst Exploration, Starburst triangles to measure pg 1, 
starburst triangles to measure pg 2

         My students will follow the directions on the Triangle Exploration worksheet and create triangles with the side lengths given on the cards in their envelopes. They will determine if the sides form a triangle, classify what type of angle is formed by the largest angle and if the area of the smaller sides cover the largest side.

Pythagorean Theorem Foldable

The next day we will make this foldable and place it into our INB'directions for Starburst activitys.

Click here for Pythagorean Theorem foldable template.

Interesting Lessons

     Time for some interesting problems from Mrs. Hester's Classroom and Embrace the Drawing Board. Check their entire lessons on the link provided. I love these two lessons.

Lessons from  Mrs. Hester's Pythagorean Theorem Lesson.

And here are some more wonderful INB pages from Mrs. Hester's Classroom.

Lesson Will the TV fit, from Tim's 3 act from Embrace the Drawing Board.

Pythagorean Triples

    In the past, Pythagorean Triples have been one or two problems where the topic has been mentioned and not much more. I plan on spending a few day on triples this year.

     OK, I don't have this foldable completely finished but thought I would give you a preview. Final foldable will be posted soon. Promise!

And here are some videos.

     I love Robert Kaplinsky - Wizard of Oz, Pythagorean Theorem problem. See if you can find all the errors in the video before looking at his answers. I can't believe that so many of my students have never seen this movie. I may be dating myself but we watched it every Thanksgiving when we had only 4 channels to watch on TV. My how times have changed.

       Some teachers would probably use this at the beginning of the unit, but I want my students to have lots of practice with Pythagorean Theorem before they see this video. I am going to use it at the end of the unit. They will have practiced many times and be able to verbalize or write down the errors they see.

        

And of course, Dan Meyer's 3 act, taco cart lesson. Check his site to see all 3 acts with questions and more. It is outstanding and the kids love guessing to see who will get to the taco cart first.

Distance Between Two Points 

     I'm excited to use Mary's lesson distance between 2 points at Curiouser and Curiouser. Read Mary's post to see the rest of the lesson. I'm hoping that the hallway outside my classroom is large enough for this. If not I will go to the main hall of the building. I like how the students will need to decide how to measure the sides. I've already started to think about how to group the students for this activity so they will be successful. Thanks Mary for posting this lesson.

     I know that I will  add to my plans throughout the unit. My lesson plans change depending on the students needs. Look for photos of students in my next post.

 Til next time,

      Jan 

Pre-teaching before Pythagorean Theorem

      The Pythagorean Theorem unit is going to be so much fun to teach this year. I have never had the time to go into this topic with the depth that I plan to this year. There are so many great activities it is hard to narrow it down. My Pre Algebra students need to review some of the prerequisites for this unit so I took the 1 1/2 before spring break to review some of these concepts.

1. Measuring and Classifying Angles
     The students always love working with the protractors and after 4 long days of state testing it was exactly the type of activity they needed. We measured and drew angles adding these pages to our INB's. This foldable came about by accident. When I printed up the flash cards for perfect squares and square roots (see below) there were empty flashcards on the last page. I printed the flashcards on card stock and couldn't bear to not use it. In my mission to use scrap paper, I created this foldable. :)

The students used protractors to draw their own angles where the green post it is.

     I love utilizing materials that I have. In hindsight I may arrange these horizontally next year so they all fit onto one page.

2. Measuring and Classifying Triangles
     We completed this foldable and practice sheet from 4mulaFun  for our INB's. It was a good review of triangles for the kids and they are getting so much better with the cutting and pasting  activities. I finally gave up on glue and have the students tape their foldables in their notebooks. They were a nightmare with the glue, it was everywhere and the tops would get clogged. I used glue sticks but they didn't last long at all. Tape is expensive so any ideas from my readers is appreciated.

3. Sum of the angles of a triangle.
     I didn't really need to review this topic for Pythagorean Theorem but my students background is lacking so as long as we were talking about triangles and angles, I added this in for them. I can't believe I never saw this activity before to show the sum of the angles of a triangle equal 180 degrees. It takes no preparation on the part of the teacher and I used paper from my scrap basket. YES! I had the kids take scraps of paper and draw an acute triangle, right triangle and obtuse triangle. The size or angle measures were up to the kids to decide. Then they colored or marked all the angles of the triangles. I then had them rip the angles and reassemble them to form a straight line. So easy and a great visual for them. It took a few tries to get the angles lined up so it is like a puzzle. They loved it.

Tear the triangles into three pieces. Then assemble to form a straight line.    

A great visual for showing the sum of angles of a triangle.

     Yes, I know the top triangle isn't lined up in a straight line. Funny none of the kids caught that! Not to worry, I will fix it.

4. Creating a geometry star
     It was the day before spring break and nobody wanted to be at school. There was an assembly and the classes were shortened to 36 minutes and the kids were, you know, a bit excited. What to do? Since we were studying triangles we did this quick project. Most of the kids finished in the 36 minutes and they were busy the entire time, calm and happy. Isn't that the way it should be before break? Again, I like this because all that was needed was paper, pencil, ruler and colored pencils. Easy. And it gets better, it is free on teachers pay teacher from Virtually Montessori. After break I will post some of the pictures the students created.

         

5.  Square numbers and square roots.

     We are making flash cards to memorize perfect squares and square roots. You can go to kitzkitz  to make your own flashcards to print. We  will cut the flash cards and then put them into envelopes in our INB's. This idea is from Mrs. Hester's Classroom. I only had the kids do the perfect squares for this lesson. They learned this very early in the year but now I have them memorize the squares through 25. The envelope to make the pocket is from homeschoolshare. They have a fantastic collection of templates you can use that are free. They also have templates for foldables that you can type on and print up. Check them out, they are a great resource.

                Here is the link to the flash cards for perfect squares and square roots (make sure to download the document to see square roots as well.) The originals are large and good for a math center but they use seven pages of paper. When I printed the individual flash cards for the students, I printed 4 pages on one page. That way I only used two pieces of paper per student. I'm always trying to save paper when possible.

I gave the students  the smaller version of the flashcards and they fit in the pocket nicely. You could also have two pockets instead of just one.

     I hope there is something here that is new that you will be able to use. One thing I am noticing with Common Core is that everyone is teaching the same topic at the same time so there is so much available for us to use with the kids. It is amazing. I am finishing up my Pythagorean Theorem unit and hope to post it by the end of the week.

                                                                 Until next time,

                                                                         Jan 

    

Blueprint lesson #3

      You know how there is a lesson that you just know is going to be great. I mean it will be so great, right? You can't wait to have the kids come to class and just absorb all of the awesomeness of the project. They come in and all of your best laid plans just flop! UGH! Well that was my blueprint lesson. These blueprints were just too difficult for the kids to understand. They gave it a good try but I have to go back to the drawing board on this one. Literally. I need to have more structure to the lesson and perhaps start with having them make some  basic blueprints first. I don't want to give up on this idea because there is so much here that the kids can learn. So I guess I am going to drag all the blueprints home over the summer and create very specific assignments for them. I did change my plan and the students measured angles and classified them. I am going to have them design the outside of a house using the angles they measured. Our spring break started today so after break if time permits.
      Here are some pictures of the kids at work. It turned out to be a good experience for them even though it wasn't what I expected it to be. Making it more focused will help.

This group of boys were very engaged.

   

Hmmm. Interesting picture.

So here they are trying to figure out how to read all of the information on the drawings.

This group tried hard to come up with some good questions.

           The one thing about teaching is that everyday is different and this one certainly was. Now it is spring break, time to relax and read a book! What a treat.
   
                                                              Til next time,

                                                                   Jan

Housing Blueprints - Day 2

     Today was the last day to connect with students before I have to post grades for third quarter so I was not able to start my blueprint exploration with the kids today. I was able to post some of the blueprints around the room and my students were very interested in what we will be doing with them. I also placed a couple outside my room on the bulletin board for the other students to look at. As you can see there is so much that can be applied to math. We could say everything in these blueprints applies to math!

This blueprint screams slope to me. I hope the kids see that as well.

This blueprint has so many area and volume components to it. Love it!

This one is a little hard to see but it is stairways and doorways.

            It will be fun to see what the students create for their problems. I have a feeling it is going to be one of those busy, exhausting, but great days. 

I'll post again tomorrow. 

Jan

Housing Blueprints

     I am fortunate enough to have blueprints of all the phases of building a house. (My husband's occupation.) I had these laminated and I post them around the room. The day that the kids walk in they are so excited and just want to spend a day looking at everything that is on them. There is measurement, scale, proportion, slope, area, volume, and the list goes on. I have 15 different blueprints in total and I just don't have the time to drag them home and make problems over all of the various units. This is the last week before spring break so I have decided to use the blueprints as students exploration lessons for my Pre Algebra students.
     The students will be in groups of 4 and given a sheet to create 2  math problems related to the blueprints. I will have rulers, protractors and dry erase markers available at each station. We will have a short discussion of all the possible topics for their questions.  The students will be able to make questions that are based on their abilities and I will steer them to the levels I think are appropriate for them. I may even assign different topics per group. One group may measure the perimeter of the driveways where others will have to create a problem to find how much asphalt will be needed to construct the driveway. Some may find the slope of the roofs and others may find how many shingles will be needed to cover the roof. I am excited about this because the kids will create the questions for me and then I will have a bank of questions to use for future lessons. YES!!!
     Check back tomorrow and I will post some pictures of the blueprints and my classroom. I will post some of the problems the kids create in next weeks post. I am excited and I know they are going to love this lesson. I wish I could make a copy of the blueprints but they are so big. If there are builders in your area maybe they will donate old blueprints to your school. Let me know, I would love to see how you apply these in your classes.

                                                     Til next time,
                                                          Jan

Pythagorean Theorem - Real Life Lessons

     I have been searching for some real life application lessons for Pythagorean Theorem unit. You know the lessons that students can relate to, not the ones where you have a ladder placed against a building. I have found a two lessons that I absolutely love.

     The first is  Mrs. Hester's Pythagorean Theorem map lesson and it is exactly what I have been looking for. How often do our students actually handle a map and measure it?  And she uses a map of the town the students live in. Now that is something they can relate to and understand. I am sure there is a lesson that could be developed using technology but that will be for a later post.
                                           

     Mrs. Hester has students find how much cable AT&T will need to install U-verse lines in the town the kids live in. Unfortunately there are not many straight roads in the town I teach in. UGH! No wonder I get lost in this subdivision when I decide to take the back roads as a short cut. I'm determined to find a spot in this town that has straight roads. Until then I may just use Mrs. Hester's map. I love this lesson!
       
      The second lesson is Tim's 3 act, TV space,  at Embrace the Drawing Board.

     In this lesson, Tim has an area below a shelf, between two speakers and on a stand that he wants to place a TV. Will the Samsung TV fit in this space? Tim has more pictures with measurements and discussion questions. This again is the real life experience problems I am looking  for my students to do. They can relate to the problem and who doesn't want a big screen TV? Thanks Tim for this awesome lesson.

     As I have said before, I don't think I am a very creative person but I don't have to be. There are so many wonderful lessons out in Blogland that I can pull for my students to use. I don't need to spend hours making them, I can adapt the lessons that others have so generously shared. If anyone has other Pythagorean Theorem lessons they know of, please share them. I would love to see more of these.

                                                             Til next time,

                                                                    Jan

Three acts by Dan Meyer (taco cart)

       I discovered math blogs for the first time last year when I was getting my masters and doing research online. I couldn't believe I didn't know all these resources were available. One of the first bloggers I found was Dan Meyer. How did I not know about him? If you are new to reading blogs or you lived under a rock like I did, I want to introduce you to Dan Meyer (watch his video) and his 3 act lessons. Watching Dan teach this lesson is exactly what I needed to see. Now I can model and practice this teaching strategy myself. I need to slow down my questioning, increase the wait time to give students time to process the information, and then have them share.
     The kids love these lessons and they are amazing. The lessons are broken into 3 parts. The first part is a short video that sets up a problem for students to think about and predict what they think will happen. The second act is giving some of the information that they will need to solve the problem. You give them this after some discussion in class. Then the third act is the reveal or answer. But really, watch his video because it is so much more than that. I am going to use Dan Meyer's three acts taco cart lesson for my Pythagorean Theorem unit.

Click here Dan Meyer's taco cart act one

    I can't wait to use this lesson with my 8th graders over the course of a few days.  I would love to hear from teachers that have used this lesson with their classes. Any tips or suggestions are welcome.
     This is a link to Dan Meyer's 3 act spreadsheet. You are not going to be able to stop watching them! Enjoy!
                                                       Til next time,
                                                               Jan

Slope pictures

    Here in Chicago we are use to cold, windy winters. This year has been extreme, even for us. Last week school was cancelled for Monday and Tuesday. When I woke up Monday the temperature was 24 degrees below zero! Same thing happened this week on Monday and Tuesday. School was cancelled and everyone in my house was going stir crazy including me. The real problem was I had meetings and a sub on Thursday last week and Wednesday this week. I needed to have a lesson for my sub so for my Pre-Algebra 2 classes I used Sarah from Math = Love's  lesson, Four types of Slope Pictures.  The students created a picture that included lines with 5 positive slopes, 5 negative slope, 5 zero slopes and 5 undefined slopes. They needed to draw it, label the lines as positive, negative, zero or undefined and color it. They had one period, 45 minutes, to complete it and it needed to be turned in before they left.
Here are a few of the pictures they created. I think they did a great job!

I have a couple of challenging classes behaviorally and always cringe when I am out. I received a glowing report from my sub saying she had a wonderful day with the students that my two challenging classes were outstanding! Wow! Thanks Sarah for the great idea!