The Email

This past week, I received the best email.  Michelle, a 7th grade math teacher and District Google Cohort member, shared with me her Google slide presentation on solving equations.  I immediately solved the first problem, snapped a picture of my work using the Google’s camera feature (formally known as “Take a snapshot”), and inserted the picture into the presentation.

Since learning of the camera feature, I’ve been waiting for this moment. The opportune time to connect a tech feature with a teacher’s lesson.   It’s one thing to promote  technology during a district training, it’s another to introduce a tech feature when it seamlessly integrates into a planned lesson.

I followed the above screenshot, with a brief set of instructions and a screenshot of where to find the camera feature.

The Lesson

I was able to stop by Michelle’s room the day of the lesson.  The classroom energy was positive.  A buzz of excitement fulled the room.  Students were solving problem after problem, taking snapshots of their work and inserting them into the slide presentation.

It was a minimum day which means shorter class periods.  When Michelle asked students to start cleaning up, students groaned.  When she assured her students that they’d continue the activity tomorrow, they cheered!!

Students solving equations on a white board, and then taking a picture of their work to insert into the slide presentation. Bottom left: Michelle and I. I’m on the right.

Added Bonus – Mini Student Presentations

Michelle assigned this activity through Google Classroom.  When in Google classroom, a teacher can open and view students’ assignments, in this case their slide presentations.  Within a few clicks, Michelle has access to all the inserted pictures displaying student work.  She can check progress, prepare for a class discussion or select a few students to discuss their strategies.

Posted in equations, Google, google apps, mathematics, Uncategorized | | 1 Comment

INSPIRATION

My last post, Multiplying Fractions: A Desmos Area Model, blended conversations from the same lesson run in two different classrooms. Although the lesson flowed similarly in both rooms, there was one student who viewed the presented problems differently.  Gabe has an artistic eye and his method of working through the math problem was unique to both classes.  On the other hand, Gabe’s mood was quick to change.  One misstep would cause frustration and self doubt to settle in.  These characteristics  provided me an interesting challenge.  How do I honor his method while reducing his frustration level? (All names have been changed)

Situation 1

MeDraw a square and shade in half of it.

I didn’t want to influence how student’s shaded their square, therefore I waited until they finished before displaying the Desmos model.  Gabe was the only student to draw a diagonal line. (Pictures have been recreated).

Gabe’s picture

Gabe’s picture

MeWhat fraction does the circled section represent?

Up until I asked this question, Gabe was smiling and seemed to be having fun.  My question uncovered a misconception in Gabe’s thinking.   His answer was 1/3.  One piece was circled out of the 3 sections. When he realized that 1/3 was not the correct answer, he became upset.  His lighthearted demeanor turned heavy.  I heard his group talking about equivalent fractions.  My attempted to connect the group conversation to his picture was not successful.

Since this was my first time teaching this class, I stepped away.  Gabe needed a chance to regain composure and I needed to check in with other students.  After circulating, we regrouped whole class.  Most students had either 1/3 or 1/4 as their answer.  The class discussion addressed two points:  1) How someone would conclude the answer of 1/3 and 2) The need for equivalent sections (which generated the answer of 1/4).

I kept my eye on Gabe as we worked through the second situation.  His unique viewpoint intrigued me and his frustration level concerned me. I challenged myself to make Gabe  smile before class ended.

Situation 2

Me:  I found 1/4 of a pan of brownies in the office.  Draw a square and shade 1/4 to represent the remaining brownies.   Most students, including Gabe, drew the same picture.

Figure 1

Me:  I decided to give 1/2 of the remaining brownies to Ellie. Highlight, circle etc… the section given to Ellie

Whereas the majority of the class drew the version shown in Figure 2, Gabe sectioned his picture differently (Figure 3).  Gabe was still visibly upset but continued to be an active participant.

Figure 2                                                                                   Figure 3

Me:  What is the fraction size of the brownie given to Ellie?

This time around, students, who had the answer of 1/3 before, remembered our discussion of equivalent sections.  I watched them add more details to their pictures leading them to an answer of 1/8.  This included Gabe.  Even though students arrived at the same answer of 1/8, their strategies differed.  If you’d like to read about the various student strategies click here.

My time as a guest teacher was wrapping up. Although, I didn’t have enough time to discuss a different situation, I did have enough time to present the class with a related challenge.

As mentioned earlier, I had been keeping tabs on Gabe waiting for a chance to positively reinforce his work.  The opportunity presented itself when I observed Gabe sectioning his drawing into eighths. He, again, had a unique solution.  I asked him if I could show his picture to the class and he replied, “yes”.  Still no smile.

Me:  I’d like to show you a picture one of your classmates created.  I drew Gabe’s pre-sectioned picture on the white board. Question, how would you create equivalent sections for this picture?

The class liked the challenge and got right to work. Lot’s of hands raised, including Gabe’s, in hopes of providing a solution.  I called on Gabe.  He applied his solution to the white board drawing proudly and walked back to his desk smiling.

Closing Thoughts

Now that I’ve stepped out of the classroom to be an Instructional Technology TOA, I use guest or co-teaching opportunities to maintain and hone specific skills, such as (but not limited to):

1. Incorporating different strategies into the class discussion
2. Finding connections between different strategies
3. Tinkering with question types that require students to do more of the thinking.
4. Inviting all students to the math party

With Gabe, I focused on #1 and #4.

1. Incorporate different strategies into the class discussion

Once I introduced the Desmos area model (pictured on the right), most students gravitated towards that arrangement.  Gabe didn’t.  He continued to section his square differently reinforcing his individuality and making highlighting his approach a priority. Exposure to different strategies not only honors student thinking but also provides students with references for future problem solving tasks.

4.  Invite all students to the math party.

I first heard this belief at a Dan Meyer workshop around 3 years ago.  The Low Foor- High Ceiling idea was a prevalent theme throughout the series of activities.  Math should be inclusive.  It’s up to the teacher to design a lesson that allows every student entry to the task regardless of their mathematical level. (link to Dan Meyer’s Ted Talk)

The frustration Gabe exhibited wasn’t productive struggle.  He was starting to withdraw or leave the party.  To his credit, Gabe never left, however he wasn’t fully enjoying himself.

At a party, the host touches base with all the guests, makes sure they feel welcomed and connects them with other party goers.  The teacher is the host of the classroom party.  As the guest teacher, it was my responsibility to make sure Gabe felt welcomed and connect him with his classmates.  By being attentive to Gabe’s progression through the second problem, I found my opportunity to draw him back into the party.

INSPIRATION

I’ve been tinkering with area models for awhile, storing countless versions in my teacher.desmos.com account.  A few of my area models support the conceptual thinking of multiplying fractions.  Recently, I was approached by a coaching colleague, Crystal, to teach a lesson using one of the models.  I was thrilled to put a model in the hands of students.

Prior to teaching, I presented the classroom teacher, Mrs. Barnes, with two different fraction area models.  The first is a commonly used model that’s also promoted in her textbook.  The second was a pared down version of the first. Mrs. Barnes selected the version not promoted in her textbook, for two reasons. The pared down version was

1. less cluttered.
2. easier to apply with word problems.

In total, I ended up teaching three lessons in two different 5th grade classes using both whole class and a rotation format.  This post embodies the essence of the collective experiences.  The area models are in the Desmos Activity Builder found here.  I used the first slide only.  For each new problem, students would reset the area models by moving the sliders to 1.  Students revisited the activity builder to complete the word problems.

The Lesson(s)

• I walked into the office and saw a cake.  About 1/3 of the cake was left.  Draw a square and shade the amount of cake left.
• We circulated the room checking pictures.
• I recreated the picture using Desmos.
• When I reached the front of the room, I continued my story.
• I grabbed the cake and decided to share it with a couple of students.
• Teacher tip:  I asked for students who have a December birthday to raise their hand.  One student, Ellie, raised her hand.  Ellie was now worked into the situation.
• I gave Ellie 1/4 of the remaining cake.  In your drawing, circle the piece of cake given to Ellie.
• We circulated the room checking pictures.
• I called on students to guide my Desmos representation
• They first told me to section the red region into 4 parts.
• Then shade in one of the smaller pieces and circle it.
• I instructed them to label their circled part as Ellie’s piece.

• Here’s my question:  What is the fraction size of Ellie’s piece?
• We circulated the room, listening to student conversations and asking additional questions. I heard 1/4, 1/6 and 1/8
• When I’d hear, 1/12, I’d ask:
• Where did the 12 come from?
• Student responses
• “We need equal parts.”
• “I drew imaginary lines.”
• “If you extend the lines, to create equivalent pieces, you get 12.”
• “The first row has 4 sections.  I counted 4, 8, 12.”
• “The first row has 4.  There are 3 rows, so those rows need to have 4 sections too.  You multiply 4 by 3.”
• Being a middle level math teacher for 20 years, I was unfamiliar with 5th graders. I didn’t know what to expect.  Needless to say, I was blown away by their responses, especially the last two – which were explaining the algorithm.
•  At one table I noticed a student with the answer of 1/6.  When I asked him how he arrived at 1/6, he pointed to the 6 sections.  His table-mate immediately added, “You need equivalent pieces!!”
• Once back at the front, student shared their thinking.
• From our discussion, we seem to agree that Ellie received 1/12 of the whole cake. I’d like you to slide the black dot from OFF to ON.
• Student responses
• “I knew it!”
• “I was right”
• “Yes!”
• Overall excitement
• Their response was completely unexpected and a pleasant surprise.
• Lastly, we connected the algorithm with the visual.
• 1/3:  The original cake was divided into 3 sections, one of which was left.
• 1/4:  The remaining cake was divided into 4 sections, one of which was given to Ellie.
• Multiply numerators:      1 section of  1 section =  Ellie’s portion    1
• Multiply denominators:  4 sections x 3 sections = total sections    12

The Textbook Version

Earlier, I mentioned presenting two area models to Mrs Barnes.  The post outlines the structure of the pared down area model.  The other model, found in the textbook, uses an overlapping approach (shown below).  One-third of a square is vertically shaded red.  One-fourth of a square is horizontally shaded blue.  When the two squares are combined, the overlapping region represents the area.  Both models area found in the Desmos Activity Builder found here.

Figure 1                                          Figure 2                                  Figure 3

Posted in desmos, fractions, Uncategorized | | 1 Comment

Inspiration

During our last Google Cohort Meeting, my colleague, Nicole, shared Eric Curts‘ Google Slides activity, Build a Jack-O-Lantern with our elementary cohort teachers.  Students and teachers loved it.

The computer skills focused within the activity are:

• Copy
• Paste
• Creating custom shapes with the polyline feature
• Inserting shapes
• Changing the fill color

I had the opportunity to co-teach the activity in a couple of first and second grade classes.  A few students nearly jumped out of their seats when they pressed control – v and saw the copied feature pop onto their screen.  Pure joy!!

Our Turn

After the success of the Jack-O-Lantern task, we searched for similar activity focusing on Thanksgiving.  Our first move: check Eric Curts’ blog, Control Alt Achieve.  Eric has a great Build a Snowman Google slides activity, but at the time we didn’t find any Thanksgiving related posts. 😦   Second move:  Create our own!

The Disguise a Turkey task was a joy to make – A collective effort resulting in a lot of laughter.  Since the premise is to create a disguise for the turkey,  we provided various outfits and costumes. To use a costume, students will need to know how to move an object forward.  A gif showing the keyboard combinations is included in the slide deck.

We continued the model Eric established by including a writing piece.

In the time we created Disguise a Turkey, Eric posted 2 Thanksgiving tasks.   Build a Turkey created by Beth Kingsley (@bethkingsley13) and another Disguise a Turkey created by Kelley Costa (@costasecond).  You can find them here.

Conclusion

Jorge, Caleb, Nicole and I hope you and your students enjoy this activity has much as we enjoyed creating it.

The Team:  Me, Caleb, Jorge and Nicole

Happy Thanksgiving!

Images used were either free downloads or labeled for reuse.  Many from Clip Art Library and Pixabay.

Collaboration Tip 2: Don’t. Touch. Your. Computer!

The other day, I had the pleasure of running the Desmos Activity Builder, Nets & Surface Area: Rectangular Prisms, with Mrs. Keser’s 6th grade math classes.  I’ve updated the opening of the activity, since I first wrote about it back in 2016 (see previous post). The updated slides add more clarity on how to use the net tool and better prepares the students for the challenges.

An interesting class reaction was the impetus for this post.

Slide 1:  For slide one, students were instructed to enter the dimensions for the blue and red rectangles. When I checked the teacher dashboard, the first three responses where not only incorrect but also very different. The lack of consistency was a serious red flag. Multiple misconceptions were apparent..  Time for a conversation.

As a whole class, we highlighted the given information and clarified the question.  Then I gave the following instructions, “I’d like you to take the next minute and talk with your group members to figure out the dimensions of the blue and red rectangles. Time starts now.”

****

((((

Every single student turned to their computer and started typing!

I interjected, “Stop.  Hands off the computer. Don’t. Touch. Your. Computer.” Once I had their attention, I added, “For the next minute, you are not allowed to type.  You must talk with your group members.  I will let you know when it’s time to enter your answer into the computer. Time starts now.”

Conversations began.  Students pointed to their computer screens while sharing their thinking.  Others tilted their computer toward their group members.  Students leaned in to listen and see up close what their classmate was pointing to.  No one typed. 🙂

After a minute, students were given the signal to enter their responses. This time around the answers were correct.

You may be wondering why I didn’t use the pause button.  I could have but, I wanted students to talk about the image on their screen.  Although the pause button doesn’t black out the screen, it does cause the screen to go gray.  For this question, I didn’t want anything to interfere with the visual – therefore no pause button.

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Side Note – Updated Screens

Slides 2 – 4:  These three slides were designed to help students the take note of the parts of a rectangular prism net, how the parts are connected and how the connected parts influence how a net increases or decreases in size.

Organizing an Instructional Technology TOA

This is my first August as an Instructional Technology TOA and my colleagues and I are off the hook busy.  It’s common for me to start my day at the district office before heading off to 1 or 2 school sites.  My district has recently given all students, faculty and staff Google accounts, which means I field a lot of different questions and requests daily. Some I know how to respond to immediately while others require research prior to answering.

Customer service is a top priority.  As a department, the director, coordinators, office staff and the 4 instructional techs work together to provide a positive customer service experience for all our teachers and staff.  Which is why, I never go anywhere without these 4 items.  They keep me organized and efficient.

**

The red binder holds my yearly planner where all appointments are recorded.  I also record my appointments on an on-line calendar. However, if I’m walking across campus and a teacher asks if I’m open next Monday, there’s not enough time to open up my computer. Instead, I grab my red binder and access my weekly and monthly schedule within seconds.

**

Any technical procedure that I’d have to complete unexpectedly or on the fly are stored in my orange binder. I’ve typed out the steps and stored them in a folder on my computer, but the hard copy saves precious time when at sites.

The blue composition book holds:

• Questions that I have to follow up on
• Comments that I have to relay back to the department
• Trouble shooting steps taken when working out a problem
• Technical steps that I have to write up, store in a folder, then put in my orange binder

**

When I flip back through the pages of my composition book to address the questions, comments and requests, the follow up happens through my computer. The research, the emails, the scheduling – all of it done on my computer.

As the stickers suggest, Google and Desmos are 2 programs I promote.  My district has gone Google, therefore I became Google Educator Level 1 certified. I spend a considerable part of my day either training teachers on Google apps and/or learning how the apps can best be utilized in the classroom.

I’m also a Desmos fellow. Desmos is a dynamic graphing calculator program that allows students to interact with math.  One can find the calculator at Desmos.com.  For me, I spend time on teacher.desmos.com creating activities for teachers from kindergarten to high school.

I love my job.  It’s fast paced and each day brings a different adventure.  If I didn’t have my red yearly planner, orange binder, blue composition book and computer, I would not provide the positive customer service experience my department prides itself on!

Posted in technology, Uncategorized | | 3 Comments

The Days Leading up to the First Day

Last school year my district created a new department, Instructional Technology and Accountability, of which I am now a member.  We were tasked with preparing 2000 plus teachers for the integration of G Suite.  Over the months leading up to summer break, the department developed a multi-tiered approach.  One tier involved summer training opportunities, which meant the Instructional Technology Team started school 2 weeks before teachers. We organized and led multiple PD sessions for various groups. Although some of the content overlapped, the structure of each day differed.

The Team: Me, Caleb, Jorge & Nicole

Our PDs included:

• New teacher training
• Teacher Tech Summit
• Content TOA Training
• Our District’s Google cohort training &
• Individual site specific trainings

First Day of School

Teachers, excited to meet their students, made their final first day preparations. Administrators set the tone by greeting students as they walked on to campus. And the office staff answered, what seemed to be, an endless line of questions. Everyone was busy and focused on students. The Instructional Tech Team was not in high demand.

After 2.5 weeks of preparing and leading trainings, we were blessed with a day to regroup. Tier 1 – completed. We celebrated the successful “pre-school” training series with chips and salsa.  On the first day of school, we switched our attention to the next phase of the instructional technology plan – Our Google cohort teachers.

Second Day of School

Phones rang. Emails flooded our inbox. Calendar appointments, to assist our cohort teachers, were scheduled.  Our day of downtime was over. School’s now in full swing and our services are once again needed. 🙂

2017 – 18 Goal: Empower Teachers

I’m highly goal oriented.  It’s normal for me to be working towards a variety of goals – Personal, professional, short term and long term. When I came across @ExploreMTBoS‘s tweet about their new blogging challenge, I grabbed my computer and started typing.

The one goal I’d like to highlight for this blogging challenge is to empower teachers.  As a TOA/Coach, I hear a lot about change.  Change that the district wants.  Change that principals want.  All of this “change” typically falls on the classroom teacher.  What do the classroom teachers want?  That’s where I’m starting this year.

Last school year, I switched from a Middle Level Math TOA to a K-12 Instructional Technology TOA.  As a district, we are going Google.  All district teachers have been given a professional google account.  Teachers have access to G Suite which includes docs, slides, sheets, forms and classroom (to name a few of the apps).  A major part of my job will be to run trainings and workshops on google apps.

At times, the job requirements feel overwhelming.  I choose to view that overwhelmed feeling as opportunity.  Since there are 4 Instructional Tech TOAs and over 2,000 teachers in the district, we organized a cohort of 149 teachers.  Thirty-seven elementary and middle level teachers are in my sub-cohort. As their cohort leader, my goal is to empower them.

The cohort models allows for flexibility.  Here are some inquires teachers have already shared:

• Gather data using google forms
• Start the year using the management system, Google Classroom
• Learn how to use the chrome extension Screencastify to create listening stations as well as gather student evidence.
• Use Google sheets to spark conversation
• Use Desmos more purposefully

I’m looking forward to talking and especially listening to teachers.  Acknowledge their questions, concerns and wishes, then problem solve together to

• make their wishes a reality

***

Art of Coaching.  TOAs/coaches in my district go back to work the week before teachers – which means we just wrapped up our first week of the 2017-18 school year.  For me, the week was spent attending a professional development workshop, preparing trainings and leading tech based trainings.

Carolyn, who lead the professional development day, peppered the workshop with a variety of thought provoking activities and protocols.  One activity resulted in this goal. We were presented with a prompt:

The peer coaching structure that I want to build on is  ____  because  ____

We were then asked to choose one of two reading options with the purpose to use the chosen text to answer the prompt.  I chose Aguilar’s blog post describing the framework, Mind the Gap,  Aguilar’s book has been on my must read list for many years and after reading her post, her book will be my next read.

Posted in Uncategorized | | 1 Comment

Inspiration

For the past 15 months, I’ve been working on fraction models.  When I brought the models to students, the resulting conversations were great.  Just what I was hoping for.  The downside stemmed from the behind the scenes “coding”.  My original design coupled with the need to import multiple images required lots of conditional statements and therefore caused the program to run slowly.

Recently, Desmos released their newest feature – Dynamic Labels!!  This feature is a game changer.  I no longer need to import number images.  I also abandoned my need to separate the parts of the mixed number for a more streamlined look influenced by @Klockmath  and  @nathankraft1 ‘s work.  The two changes reduced both the lines of “code” and the number of conditional statements thereby creating a tool with more usability.  You can find the graph here.

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Positive and Negative Fraction Model

Now, it’s time to update all my old fraction models.  A task, I happily accept.   I began with a graph that visually represents adding positive and negative fractions.  Positive fractions are blue.  Negative fractions are red.  Use the black sliders to toggle between positive and negatives.

One fraction is stationary and the other moveable.  Use the moveable fraction to estimate the answer.

Toggle off and on the common denominator feature.
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For the second picture, I copied the image onto a Google slide and inserted lines to represent the elimination of zeros pairs. Then used the scribble feature to circle the answer of 5/6.

Example 1:  4/3 + (-1/2) = 5/6

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Example 2:  -4/3 + (-1/2) = -11/6    aka        -1 1/3 + (-1/2) = -1 5/6

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Closing Thoughts

I love summer. It’s my time to recharge, spend quality time with my family and work on projects too time consuming to complete during the school year.  That said, I’m excited to for the school year to begin.  Honestly, I can’t wait to get this fraction model into the hands of teachers and students.  Let the fraction talk begin!!

Inspiration

In August of 2014, I stepped out of the classroom to become a middle level math TOA/coach.  After 21 years of teaching, I craved a different challenge and found that challenge with Desmos.  Once I learned how to make AB’s, I was hooked and began creating Activity Builders for my teachers.

Roughly 2.5 years later, I switched from being a Math Coach/TOA to be an Instructional Technology TOA.  My interest in Desmos was the catalyst. 18 Months of creating and testing activities, providing Desmos based PD and participating in the Desmos Cohort lead me down a new path.  The switch seemed inevitable.

Now, I work with teachers K-12 regardless of the subject.  This new position stretches my established tech skills while continually adding more.  The learning is constant and welcomed.

My district is going Google.  Our teachers received their Google accounts toward the end of the 2016-17 school year.  When school starts up again, student accounts will be activated.  Upon hearing the district’s plan for the first time, I began studying for and then passed the Google Certified Educator Level 1 exam.  While studying, Google Sheets became a high interest app.

Members of our Instructional Technology and Math TOA Teams attended a math based Alice Keeler training. Participants received the book, Teaching Math with Google Apps that she co-wrote with Diana Herrington.  Her section on Pixel Art intrigue me. The combination of Google sheets, conditional formatting and math spoke to my creative side.  I had to create my own.

Alice, Me, Jorge, Caleb and Jen H.

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Although I  work with k-12 teachers of all subject areas, math will always be my first love. Designing and field testing math activities is a passion of mine.  My new position takes me out of my middle level comfort zone and broadens my client base.  For now, I can also collaborate and design activities for elementary and high school teachers.

The goal, for my first google sheets activity, was to create a visual representing the addition of integers.   It’s more of an exploration tool.  The open design allows students and teachers to use the tool however it best fits their needs. Click here to make your own copy.

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Imitation is the Sincerest Form of Flattery

– Charles Caleb Colton

My second activity is not original in any sense.  I sat down with Keeler’s book, Teaching Math with Google Apps, read the section on pixel art and used her techniques to create a 4th grade multiplication activity.  The activity contains 3 questions.  1 question per sheet.  Click here to make your own copy.

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Closing Thoughts

As I look forward to our district’s venture into Google Apps and my task of helping teachers of all subjects integrate more technology into their lessons, I feel compelled to state that technology alone is not the answer to increase student engagement and learning. Effective lessons overlap content, pedagogy and technology.  How a teacher uses technology to foster discussion, collaboration and reflection within their subject area is the key to creating engaging lessons and increasing student learning.