Constructing Shapes

Personally, I think Ava Rectanglethat geometry is one of the more concrete concepts for students to grasp in primary grades; quite literally.  There are tons of ideas of how to construct shapes on the internet, in math books, etc.  I love the activities with spaghetti and with Popsicle sticks and gumdrops, but those activities can be limiting when working with shapes with curved sides.  These activities can be misleading when students decide to extend shapes and we have to be very careful that we not provide fixed and limiting language such as, “the gumdrops are the vertices” because that is not true in a shape like the one to the left.

We recently bought a set from Learning Resources that, in my opinion, is the best out there for allowing students to construct two and three dimensional shapes and combine shapes to make new ones.  I used these in my small groups to let students explore and then name their shapes.  We use Seesaw in our classroom as a learning portfolio and after students made their shapes, they took a picture and labeled them on their Seesaw accounts.

The standard I had in mind with this exploration was: 1.GA.2: Compose two-dimensional shape or three-dimensional shapes to create a composite shape, and compose new shapes from the composite shape.

It’s so interesting to watch and listen as students construct their shapes.  Just as with any creative activity, students who are identified as struggling learners by standardized tasks excel at the task and take the initiative and go further with their learning because they aren’t inhibited by language or symbols that they aren’t yet able to make sense of.  Often the accelerated learners on standardized tasks do the bare minimum to complete the task and move on.  I think these observable behaviors tell us a lot about the mindset of the student and their past experiences with learning.  They also tell us which students value play and which value praise.

Misconceptions:

David 2David Open SquareOpen-ended tasks like these are my favorite because they allow opportunities for students to explore misconceptions like the one here.  This student doesn’t yet understand that a shape must be closed.  This was an opportunity for me to quickly see that and perhaps more importantly for other students to notice and provide feedback.  The picture on the right is the square after he corrected it (and his understanding of shapes).Jamie Oval

This student had a misconception about circles and ovals which I may not have found so easily without this time to explore and create.

Differentiation:

These tasks are low entry, high ceiling opportunities because all students can make a shape and most students end up stretching their knowledge andAva Triangle vocabulary because they end up making shapes that they cannot name.  This leads to all kinds of discussions on how to categorize shapes and the difference between two dimensional and three dimensional shapes.  I provide students the written names of shapes once they name them and ask how to spell it or if they cannot name it and I am helping them name it for the first time.  Here are some examples of two-dimensional shapes students created:

Three-dimensional shapes:

Combining Shapes

YoumnaThis student started out with a square and built onto it to make it a rectangle.  She discovered how to Pyramid w Oval Haydencombine shapes to make new ones.

This student combed a 3D and a 2D shape to make a sculpture.

LamarThis student is one of my very low performing student sin most subjects, but in math he excels because he is able to make sense of his own learning through play and discovery. Sean Rect Prism

I used this picture earlier, but this student started with a cube and decided he wanted to extend it to see what it turned out to be.  He needed help naming it, but loved that he had discovered a “new” shape.

 

Conclusion

We shouldn’t limit ourselves to tasks that offer fixed outcomes.  We must search for tasks that allow students to be creative and “build” their own meaning.  As you know, I am a huge proponent of STEAM integration in primary grades and this is just one example of a task that melds mathematics and 21st century skills.  We need to let kids explore more and allow ourselves as educators to do less talking and more listening!

3 Act: How Much Joy?

This task supports a couple of different standards in first grade, but I feel it best fits 1.OA.B.3 if used with the Act 2 problem “there are three groups of five and four more.”  It would fit standard 1.NBT.B.2 if using the Act 2 prompt “there is one group of ten and nine more.”

It would be a great place to start before introducing counting on with coins in second grade for standard 2.MD.C.8.

Act 1:

What do you notice?  What do you wonder?

How many candy bars are in the bag?

Act 2:

1.OA.B.3: There are three groups of five and four more

1.NBT.B.2: There is one group of ten and nine more

Act 3:

Act 3 Joy

Act 3.1 Joy

Act 3.2 Joy

3 Act: A Delicious Mix

I always draw inspiration from the candy isle, doesn’t everyone?  Tonight I was planning to buy some candy for another 3 Act task I was planning when I spotted a bag of 3 different chocolates…on CLEARANCE!  Immediately I thought of fractions and so the 3 Act task below was born!  Please comment and tell me how I can  improve it or add extensions as I am wiped for the day and just wanted to end it with some math:)

Ideally you will introduce this task during your unit on fractions so that students’ minds will be in “fraction mode” and propose wonderings that relate to fractions.  If they go to how many in each bag, you might need to funnel their thinking or let them go down that path and then use the fractions as an extension.

I have included an additional picture for the reduced fractions that can be used as an extension or in place of the original depending on your instructional purpose.

This task will address standard 4.NF.B.3.A if using the 1st Act 3 slide with unreduced fractions with the same denominator.  You may choose to address standard 4.NF.A.1 by extending to the 2nd Act 3 slide and having students reduce the original fractions.

Act 1:

What do you notice?  What do you wonder?

What fraction of each kind of candy are in the bag?  Make a too high and a too low estimate.

Act 2:

What information will you need to find a solution?  What do you know?  What do you need to know?

A Delicious Mix Reeses Act 2A Delicious Mix Rolo Act 2Act 2 Total

Act 3:

Where you correct?

A Delicious Mix Act 3A Delicious Mix Act 3 Reduced

As always, let me know how I can make this better and if you see a more appropriate standard alignment!  I look forward to the feedback!

Thanks for the feedback!  Here are some suggestions from MissMathTeacher314: This addresses standard 3.NF.A.1 as well for fraction identification and defining equal parts.
Extensions could include: How many more kisses than rolos? How would you equally share these with 4 friends? How many bags would you need to buy to have so everyone in their class would get 3 peanut butter cups?
You could give the simplified fractions of the Reese’s and the Rolos for Act 2 rather than the exact count. Flip the script to ask how many pieces of each candy are in the bag rather than asking for the fraction.

Stop Motion Number Stories

The last couple of days we have been making stop motion videos to represent addition IMG_0453.JPGstories.  The learning goal was to use objects to represent an addition story and then tell the story and write the addition sentence that was represented.  My main goal was really to get students familiar with stop motion in this context and to get the process of shooting the videos and writing the caption in #Seesaw to become easy.

As all things go when teaching 6-year-olds new tools, the process was long and it took me two days of small groups to work with each of our 37 students, but the result was worth every minute!

twitter1.pngMany of our struggling and reluctant learners lit up when they got to pick out animals for their videos!  I didn’t have to convince them to complete the assignment…they wanted to!  Which as you know by now, are the type of assignments I love to give!

Since my goal over the past two days was more process specific to the tools being learned, I scripted most of the stories for students on Seesaw to speed up the process, but made sure they knew how to add a comment for next time when it is up to them to do the writing!

It was great to hear a couple of students say, “I’m going to create a subtraction story now!”

IMG_0452.JPGMy goal is to have Stop Motion Math be a station choice in our room and provide open ended prompts or learning targets to prompt their creations.  Things I would like to do in the future include providing number sentences that need to be represented with a story, providing word problems to solve with a video, and expand into all other standards as a means to show mastery of a concept.

I had so much fun doing this today and saw so much excitement, that I decided to start a website called http://www.stopmotionmath.com that will be up shortly to showcase examples of student work and problems and prompts and ideas of how to use this in your classroom.

We use the Stop Motion Animator extension from the Google Chrome Store.  My partner teacher used this earlier in the year for some literacy tasks, so I will ask her to share those as well.

So excited to do more of this with our kiddos!

Here are some video examples:

Can you guess their story?

Brooklyn’s Video:

Brooklyn’s Post:

Brooklyn1.png

Francis’ Video:

Francis’ Post:

Francis1.png

Aiden’s Video:

Aiden’s Post:

Aiden1.png

Sean’s Video:

Sean’s Post:

Sean1.png

Lamar’s Video:

Lamar’s Post:

Lamar1.png

Alyvia’s Video:

Alyvia’s Post: Alyvia1.png

How Do I Change Math Class Tomorrow?

As Dan Meyer put it, “math class needs a makeover.”  It breaks my heart to hear students say things like, “I’m not good at math” or “I hate math!”

In my opinion, one of the first things that needs to change is the focus on correct answers and the need for speed.  This leads students to believe that the only way to be good at math is to be right (quickly).  The other practice that needs to be eliminated is the language we use as teachers such as “that’s right” or “you’re so smart.”  

You’re So Smart

You’re so smart is one of the most damaging things you can say to a child.  What is smart?  What do we value and what are we showing them that we value?  Being smart needs to mean learning as a means in itself.  Or rather, the journey of learning.  This is not fixed but ever-evolving as we seek out and synthesize new information.  

As a parent, I have been guilty of this.  I’ll blame it on ignorance, but the truth is I kept it up for years as a teacher and a mother.  I knew the words tasted sour in my mouth, but they continued to come out and I continued to damage my child’s self-worth.  Harsh?  It’s true.  

Here is an example:

My oldest son started the district gifted program as a first grader. I was so proud!  From the time he was born, I had told him how smart he was.  He had finally been classified by the school system in the same way.  My job was done.  From that day on, his life would be rainbows and butterflies.

The reality was that from that day on, he began to feel even more isolated.  He went on to the full-time gifted program in sixth grade and I ended up pulling him out.  His stress level was through the roof, he was failing ALL of his classes, our family time was dominated by reprimands of his failure to finish his homework (which was unending), and the school’s solution to the problem was to medicate him.  We had failed him.  We taught him that learning was about homework and work completion  and not about creativity and problem solving.  The other message we sent was one of conformity; You must fit it in this box to be “smart” or successful.

He told me a few years later that he felt like the test had been wrong, that they made a mistake.  He wasn’t gifted.  He went on to say that he felt pressure to always have the answers and when he didn’t his failure was paramount.  Teachers expected more of him ALL THE TIME and living up to that expectation was stifling.  I had taught him and the label had taught him that intelligence was fixed.  We told him he was special, but not in a growth sort of way.  He had already arrived at being “smart” and now he would have to maintain the title.  

Luckily, my second child was eight years after my first and my message as a parent is vastly different.  I praise reflection and strategy and kindness and determination.  I allowed him to be tested (telling myself that I could better understand his needs if I did, a lie to be sure).  I realized that I had some lingering pridefulness attached to the label that I am still working out.

However, this time, when I presented it to him, I framed it very differently than I did with my first.  I told him that there was a school with additional opportunities for learning that he might enjoy.  I let him choose whether or not he wished to attend.  He attended in second grade and decided to not attend this year.  

My message to parents is now this: if you want to compliment your child academically, focus on effort and inquiry.  Say things like, “wow, I can tell you really worked hard on that,” or “I love hearing about all the new things you are learning, I can tell how much you it.”

You’re Right

“You’re right” takes all of the learning away from the student and places the teacher in the seat of a referee.  Student work becomes not a creative endeavor, but a race to impress the teacher.  The focus is taken off of learning and put on performance (which is what is done when training circus animals).  

If we really want students to be problem solvers, we need to ask the right questions and probe for understanding.  Students need to own their solutions and the first way to do that is to change our language as teachers.  Guided Math in Action has a great list of prompts for students to use to prove their solutions..  It is one of my favorite to use with students, and illustrates how to help students own their own learning and be confident in their solutions.

I have a couple of examples I would like to share about this topic.  One comes from my own child who is now a high school Junior (the one referenced above).  I can pinpoint the day he first viewed himself as a failure in math.  It was third grade and his teacher was a wonderful lady who was energetic and nurturing.  She had been teaching for almost thirty years and all the students loved her.  She (like many still do) believed that the best way to master multiplication facts was to put students through a battery of timed tests.  She had a cute little board that she used to keep track of their progress where they would build their ice cream sundae as they completed their facts.  I always knew when it was a testing day, because my son would come home with a look of failure on his face.  Math was no longer about creativity for him, it was about being fast and being right.  He did not perform well under time constraints and though his idea of fun in the car was to practice multiplication problems and discuss his creative strategy for solving them, it had lost its luster once he was asked to do it quickly.  He has taken Algebra 3 times and finally passed this year due to a teacher who really understood his learning style.  He hates math and instead of wanting to pursue a career in astro-physics or chemistry like he previously had dreamed of, he decided that he was too bad at math to go into those fields.

Another example can be provided by a seventh grade girl who I have been tutoring for about a year and a half.  She was failing sixth grade math and had severe anxiety about it.  The first time we met, I gave her an assessment on number sense.  She would quickly (very quickly) give me an answer in a very fast, short response, then look at me in terror and say, “is that right?”  I knew immediately that this girl did not struggle with math, she struggled with confidence due to the experiences she had been provided.  We quickly came to an understanding, one that students know well.  “I don’t care how fast you come to a solution as long as you can walk me through your strategy and prove it.”  I have had the exact same experience with every student I tutor.  They are terrified of being wrong, and they have no way of proving they are right because that has never been the focus of instruction.  She now has a B in math and no longer looks at me to determine if the solution is correct.  

Lessons Learned

What I have learned, thanks to many phenomenal authors and researchers and my experience teaching diverse learners, is that all students have individual strengths and passions and they all deserve diverse learning experiences in math and outside of math.

Perhaps we need to quit asking all students to “master every standard” and agree on a set of skills required to be contributing members of society and then let students find their passion and develop it.  We need to remove the labels and focus on the individual.  I do still believe that students need to be exposed to new ideas and problems so that they can find their passions, but asking them to master every concept is no longer something that our world requires of them and perhaps never did.

I will end with this, it is my belief that the most powerful thing we can do for a child is teach them how to learn.

A Few of the Resources That Have Helped Shape My Beliefs

Mathematical Mindsets

Mindset

Number Talks

Teaching Number in the Classroom

Guided Math in Action

Dan Meyer

Jo Boaler

Twitter – #Elemmathchat

 

3 Act Task: The Package Problem

We have had a question we have used for years in Title One Math that continually stumps students in division situations because of the context of the problem.  It is an excellent way to get students to think about the remainder in a division problem as it applies to different situations.  We lovingly refer to this as the package problem.  The question is, I have 34 cupcakes. They are packaged in packages of 6.  How many packages will I need?

When I was making and packaging my annual Christmas pretzels this year, I took a few pictures and thought this might be an excellent example of the package problem.

There are many different scenarios for this task which is what I think makes a really rich task.  You can ask, “How many packages of three will I be able to give out as presents?” or “The pretzels are packaged in packages of 3.  How many packages will I need to package all of the pretzels?”  The first question ignores the remainder because it is irrelevant to the situation.  The second question requires students to look at the remainder as a necessary part of the problem, but allows them to recognize that the last package will not be complete.  If I pair the first question with a third question, “How many will not be packaged?” attention is called to the remainder and can lead to a discussion such as, “Why did I make 2 extra?” or “How would I package them if I wanted to give a bag to each of 6 friends?” or “If I didn’t want to have any pretzels remaining, how could I package them?

Problem solving is all about context.  In my opinion, the reason students don’t do well with word problems is because they are not exposed to multiple contexts in mathematics when skills are taught in isolation.  Hence, the power of 3 Act Math Tasks (thanks Mr. Meyer).  I hope you enjoy this task and would love your feedback as always!

When I was taking pictures for this task, I was elbows deep in melted chocolate so I forgot to take some of the pictures I needed for the different contexts.  My plan is to make another batch soon and add those:)  So for now, I have the third act addressing the first question.

I’ve added a link on the 3 Act main page of my site to the google folder with all of my tasks, videos and pictures.  That way you can choose the pics you’d like. I love to use Nearpod for my 3 Act Tasks when I teach for the awesome opportunities for student input and data analysis:)  However, every time I run a Nearpod session it breaks the link to my blog, so I thought Google might be a better way to share these:)

Act 1: 

IMG_9263.JPG

What do you notice?  What do you wonder?

How many packages will I need for the rest of the pretzels?  Write a too high and a too low estimate.

Act 2:

act-2-pretzel-1Act 2 Pretzel 2.png

There are 26 pretzels.  Pretzels are packaged in bags of three. (Insert preferred question here) Act 3 addresses the question, “How many packages of 3 will I be able to give out as presents?” (Students might count the one package that is already shown in the picture and come up with 9)

Act 3:

Act 3.1.png

or this depending on whether they count the first package in Act 1.

Act 3.2.png

Extensions:

How would I package them if I wanted to give a bag to each of 6 friends?” or “If I didn’t want to have any pretzels remaining, how could I package them?

Personalized Learning Paths

I have been working on a project for quite a while to better personalize learning for our students in numeracy.  My teaching partner and I began one for literacy as well, but have a lot of work to do (I’ll blog about that when we are closer).  We are using the same idea for our other standards through the lens of our inquiry units, so those will also be rolling out as we complete them.

Our first grade students are 1:1 with Chromebooks in our classroom and we have spent countless hours and days and months now trying to decide how to best use these tools to boost student engagement and learning experiences(see the upcoming post about student scheduling to learn more about this).  We departmentalize for small group and teach all of the math lessons and two of our reading groups, while my co-teacher teaches most of our reading groups.

We have an amazing classroom space, 1:1 technology, and a great collaborative relationship between my co-teacher and I. However, we do face other hurtles such as limited storage space and trying to balance the usage of tech vs. hands on tasks.

We knew we wanted a way for students to track their learning that would allow for them to move freely from one standard to the next unencumbered by the learning paths of other students.  However, finding a mode of delivery that would allow for this has proven to be quite challenging.  In the end, you will see that we had to do some site-smashing to best meet our goal (and we hope it works).

What We Needed

  • Students to be able to track their standards met
  • Students to be able to access modules and activities for standards currently being practiced quickly and easily
  • Ability to link to websites for practice
  • Ability to provide modules that would not allow students to “fall down a rabbit hole” after completion
  • Ability for students to upload multiple types of assignements such as pictures of hands-on activity completed and assessment videos

What We’ve Tried and Why They Don’t Work Alone

Our district uses Canvas as our LMS and we love it for many of it’s features, most notably what we believe it was created for, a way to organize learning.  However, there are many other apps and sites that better meet the needs of emerging and non-readers and writers that are more user friendly for modules, online student assignments, direct instruction videos, interactive games and quizzes.

For modules, we used Canvas but were having trouble with the microphone. We talked to our Blended Learning Specialist and looked deeply at Canvas modules, but there are problems with the microphone that weren’t easily resolved and it was much more work for students to submit items than we thought reasonable.  We didn’t want them spending their learning time on accessing and uploading their assignments, we wanted them spending their time on constructing new knowledge.

We used Nearpod for whole-group modules, but we didn’t see a way for it to be used for students to work at their own pace.

We began by embedding our activities in Blendspace because of it’s icon-centric design, but found that it was too distracting for students when navigating because of the option to move to other activities on the pages they were accessing.  We also had a problem with some videos continuing to play while others started.  We had the same problem with YouTube videos because when the video stopped, they had the option to click on other videos and fall down the rabbit hole of “other videos you might like.”

We loved Vimeo for uploading flipped videos because it is a secure stand-alone program that allowed us to upload only that particular video.  However, Vimeo, like many other programs, costs money and we were soon reaching our storage limit.  We loved Screencast-omatic for recording flipped videos that captured onscreen material but then had to upload them to YouTube which led us back to the YouTube problem. We recently learned that it also offers storage for flipping videos of the same sort and it looks like it offers much more storage without distractions at the end.

We loved Seesaw as our online learning journal, but there is was no way to link it to our Canvas pages for content areas without them having to navigate the feed.

We loved Google Classroom for assignments and the quick add feature in the extension for classroom for sites.  We also loved the option in assignments to create a student copy automatically (and save to their drive), but assignments cannot be made for individual students or student groups.

However, our problem remained.  We needed a quick and easy way for students to navigate directly to their standard of practice and have quick access to the activities, but also have a way to track their progress and move along a continuum.

The Plan

standard-1We revisited Nearpod as they have recently added a student-paced lesson component that allows students to work through modules on their own.  We decided the options in Nearpod to add videos, activities, upload files and allow students to write on them and the different options for quizzes at the end would be the best fit for our learning modules at this age.

We decided probably the best thing we had seen to create these tracking sheets for the standards was to use Google Slides and share it with students through Google Classroom.  That way they could start at the task they needed to practice and work their way through.  We linked the Nearpod modules to the Google Slides as well as the other activities they needed to create and each one ended with an assessment of the standard such as uploading a video to Seesaw of them counting from 1-120 starting at different numbers.task-1

Our next issue was that while Seesaw is awesome, it only stays loaded on iPads and each student has to re-scan the code every 15 minutes on their Chromebook to add items from it.  Since most of our iPads are in use for OSMO in our classroom, we needed a way for students to have easy access to their stories so we printed a class QR code for each student’s clipboard and used shipping tape to tape them to the back.  Students always have their clipboards with them because they use them for their daily schedules and Lexia/Dreambox goal tracking.

We are still working through how to best store the hands-on activities for easy access for students, but think we may have some ideas on that as well.

Above are examples of a Domain tracking sheet and a task sheet for an individual standard.  The idea is for students to move the green smiley face over when the task is completed.  We will then meet check the Seesaw feed and meet with them to fill in the date met or provide additional instruction if it is not met.

We will begin using this tracking system first for numeracy in the next few weeks, so look for my reflection coming soon!  We are excited to see how it plays out in the classroom!

As always, please provide comments and feedback as this is a continual process for us and we need all the input we can get!