Multiplying Fractions: A Desmos Area Model

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 is a compilation of the 3 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.  DOne-third of a square is shaded redraw 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 OA square sectioned into 12 pieces.N.
    • 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. one-fourth times one-third is one-twelve
    • 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.

A square where 1/3 is shaded red. A second square where 1/4 is shaded blue.  a square representing where 1/12 is shaded purple.      pic12

Figure 1                                          Figure 2                                  Figure 3

 

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Google Slides: Disguise a Turkey

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 Title slice for the Disguise a Turkey activityon 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.

    Three turkey heads waiting for their costumes.      A picture of a panda, pig, goat, dog and ghost costumes for the Disguise a Turkey activity.

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

Slide showing the writing prompt: Write about your trio of turkeys.

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.

A picture of the Redlands Unified Instructional Tech Team

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.

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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.

A two dimensional net of a rectangular prism

Slide 1 from the activity showing a 2-dimensional net for a rectangular prism.

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.Red rectangle: 2 units by 1 unit. Blue rectangle: 3 units by 1 unit

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.

Image of Slide 4. The title of the slide is, "What happens who you move the black dot? Enter your observations below."

Explanation:  The black and red rectangles expand one while you move the black dot but the blue square between the black rectangles moves but doesn't expand.

 

The black and red shape gets longer. The blue shape stays the same size and just shifts.

 

 

 

 

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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.

Picture of a computer, day planner, binder and a composition book

**

Red Binder

 

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.

 

**

Orange Binder

 

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.

 

 

 

Blue composition book

The blue composition book holds:

  • Questions that I have to follow up on
  • Comments that I have to relay back to the department
  • Requests made
  • 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
  • Interesting pieces of information that I want to learn more about, etc…

**

laptop

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!

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First Day Plans: Chips & Salsa

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.

A picture of the Redlands Unified Instructional Tech Team

The Team: Me, Caleb, Jorge & Nicole

Our PDs included:

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

 

First Day of School 

Chips and Salsa

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. 🙂

 

Math Twitter Blog-o-Shpere blogging logo

 

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2017 – 18 Goal: Empower Teachers

 

I’m highly goal oriented.  It’s normal for me to be working towards a variety of goals – Personal,Tweet announcing MathTwitter BlogoSphere's blogging initiative 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

  • answer their questions
  • address their concerns
  • make their wishes a reality

***

My next step … READ

Screen Shot 2017-07-31 at 7.09.48 PM

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.

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Desmos Graph: Adding Positive & Negative Fractions w/ Dynamic Labels

Inspiration

A picture of the mixed number 5 thirds

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.  A picture of the mixed number 5 thirds

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.

Positive fractions are blue      Negatives fractions are red

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

 

Toggle off and on the common denominator feature.
Toggle off and on the common denominator feature************************************************************************************

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

Positive 4 thirds added to negative one halfScreen Shot 2017-07-07 at 8.27.41 AM

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

negative 4 thirds added to negative one half              Negative 4/3 added to negative 1/2

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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!!

 

 

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Diving into Google Sheets: Adding Integers & Pixel Art Multiplication

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.

Level 1: Google Certified Educator badge

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.Book: Teaching Math with Google Apps by Alice Keeler and Diana Herrington 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.

Alice, Me, Jorge, Caleb and Jen H.

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Google Sheet Math Activities

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.

Picture of the Integer Activity

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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.

Multiplication Question #1 on Google Sheets

Multiplication Question 2 on Google Sheets

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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.

 

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Desmos Polygraph: The Periodic Table

A list of elements from the periodic table

Images from the website, The Dynamic Periodic Table.  http://www.ptable.com/

 

Picture of Heather Wingo

Heather

Desmos is not just for math teachers. To support this point, I created a Polygraph activity using elements from the Periodic Table. Eager to field test the Polygraph, I reached out to a few 8th grade science teachers.  Heather Wingo took me up on my offer.

 

A Desmos Polygraph is run similarly to the games, Guess Who and 20 Questions.  The program randomly pairs up students.  In the pairing,

  • Partner A selects an element
  • Partner B tries to figure out the element by asking yes and no questions.
  • Partner A respond to the questions by pressing the “Yes” button or “No” button.
  • For confusing questions, Partner A may respond with the third option, “I don’t know.

I’ve lead multiple Polygraph activities before but this experience stood out for 2 reasons. First, the type of questions students were not what I had expected.  Second, the conversation with Heather gave me insight to improving the activity.

The Questions

Parts of an element, atomic number, symbol, name, atomic mass and energy levels

Since students studied the periodic table months ago, I provided the pictured reference sheet.

Prior to the start, I set the condition. Students were not able to eliminate an element based on color.

When one student pushed the boundaries and asked, “Is your element blue?”  His partner responded by selecting the, I don’t know, option. This made me laugh.

I then began noticing unanticipated questions, such as

  • Is your element used in making a light bulb?
  • Is your element a metal?
  • Is your element a gas?
  • Is your element in group 1?

Eighth grade science teachers reading this maybe giggling at this point.  Or, saying, “Duh.”  Did I take into account the categories such as solid, liquid and gas, metals, nonmetals etc… , when designing the activity?  Yes and No.

There’s a strategy to creating a balanced Polygraph. My design decisions where based on using the symbol, name, atomic mass, atomic number and energy levels to eliminate elements.  Although I did feel states of matter would be another elimination category, I didn’t strategically incorporate that standard into the design.

My Conversation with Heather 

During the debrief, Heather addressed her curriculum in conjunction with the activity. Her points:

  1. Students need to know the states of matter (solid, liquid and gas)Students referencing a periodic table while playing the Desmos Polygraph: Periodic Table
  2. Students need to know which elements are metals, non-metals
  3. Students need to know which groups on the period table contain alkali metals, transition metals, halogens and noble gases
  4. Students need to know how to read, understand and identify parts of a periodic table

The activity I presented addressed point 4. She wanted to scaffold questions to include a discussion of points 1 – 3.  Our solution was to create a second Polygraph focusing on the states of matter, and the various types of metals and non-metals.

Closing Thoughts

This was my first time field testing an activity in Heather’s classroom.  As in every field testing situation, I walked away with more information that I walked in with.  I enjoyed listening to Heather share her content knowledge,  expectations of students and ideas for improving, or in this case creating a complementary activity.

 

 

 

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Desmos Marbleslides: 10 Frame Addition

Inspiration

Many many months ago, I saw an intriguing tweet. Kristin, @mathminds, had made a Desmos AB focused on 10 Frames and was inquiring about the possibility of an interactive one. Challenge excepted.  I viewed her inquiry as a chance to broaden my skills while providing a service.

After a few interactions with Kristin, I gathered enough information to begin, however without a way to count the number of dots within the frame, I couldn’t finish.  Thanks go out to Luke Walsh, @lukeselfwalker, who gave me the counting method needed to complete the activity. Here’s the AB:  Exploration: 10 Frame Addition.

I like giving students time to explore, observe and discuss what they notice AND I like having specific tasks for students to complete. Exploration: 10 Frame Addition, addresses the exploration.  My field trip to kindergarten provided the experience needed to build the challenge based activity, Marbleslides: 10 Frame Addition

 

Jenn working on the Prowise computer

Working on the Prowise touchscreen

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Field Testing

Picture of Camille and Jenn VadnaisBeing a middle level teacher for over 20 years, I’m solid with grades 6 – 8.  Primary grades, especially k- 2, are a mystery.  It was time to head to kindergarten and conduct some research.

I partnered with Jen (elementary math TOA ) and Camille (kindergarten teacher).  We split the class in half.  Jen and I worked with one group and Camille the other.  Then after 25 minutes, we switched.  Students scanned QR codes on their tablets to reach the website, student.desmos.com, easily

 

 

Expected Outcomes

  • The zoom feature caused a learning curve.
  • Once students learned how to navigate the zoom feature, they enjoyed moving the dots and creating number sentences.
  • They were eager to share their number sentences.
  • They were able to find more than one number sentence for a specific number.
    • 4 + 4 = 8
    • 2 + 6 + 8
  • Camille wanted an activity that would provide immediate feedback for students

Unexpected OutcomesTwo 10-frames displaying the number sentence, 6 + 1 = 7

  • One excited student, showed me his example.  When asked to read his number sentence,  he said, “3 + 3 + 1 = 7”. His response caused a flood of observations and questions.
    • He was only focused on the dots, not the symbols.  Who else is doing this?
    • Where there other students who focused only on the numbers & not the dots?
    • Which students are connecting the dots and the numbers?
    • What questions can I ask to help students connect dots and numbers?
    • He’s not subitizing the number 6.  Who else is not subitizing larger numbers?
  • When a second student showed me his tablet and joyfully said, “2 + 2 + 1 + 1 = 7”, I knew I needed to formulate follow up questions.
  • Two 10 frames showing the equation, 5 + 2 = 7

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Follow up Questions

Although asking questions is a favorite strategy of mine, I felt unprepared when responding to kindergarten students.  This experience caused me to reflect on my interactions with students and develop a line of questioning that would benefit both students and teachers.   Here are a few possible follow up questions.

If a students says, “6 + 1 = 7”

  • Will you show me your 6 dots?Two 10-frames displaying the number sentence, 6 + 1 = 7
  • How do you know that group of dots is 6?
  • Will you point to the symbol 6?
  • Where is your 1?
  • Explain how to make 7?

If a students says, “3 + 3 + 1 = 7”

  • Will you show my your groups of 3?
  • Will you count all of those dots for me?
  • What do your 2 groups of 3 make?
  • Will you point to the symbol 6?
  • Where is your 1?
  • Explain how you know the dots make 7?

 

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Closing Thoughts

I’ve come to rely on field testing my activities – especially when I hit designer’s block. By highlighting areas of need, my kindergarten experience gave me the direction I was looking for.  I had to address the zooming action and create an age appropriate challenge based activity that incorporated immediate feedback.  My observations and conversations with students guided my future design plans.

Desmos’ marbleslide lab technology addressed all my design needs.  Marbleslides uses a fixed screen which fixed the zoom issue.   If the launched purple marble passes through the stars, then that trial is successful.  Therefore the marbleslide technology allowed me to create challenges that could be immediately checked by launching the purple marbles.

Teacher tip:  Camille requires her kinders to record their number sentences on a separate sheet of paper to draws their attention to corresponding symbols.

Desmos Activity Builder 1:  Kindergarten: Making 10 with Ten Frames

Desmos Activity Builder 2:  Exploration: 10 Frame Addition

Desmos Activity Builder 3: Marbleslides: 10 Frame Addition

 

 

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