# Inspiration

For the past 3 years, my district has offered a back to school PD summit.  Various people from inside and outside the district present. Since I’m Instructional Tech TOA, I presented. My sessions focused on Desmos and BreakoutEDU*.  The activity shared today was born out of a collaboration with one of my BreakoutEDU attendees, Candace.

She wanted to create a Breakout styled activity for a series of class openers. The questions were a mix of review problems, one topic being percents.  As I started working on the project, I felt strongly about building an interactive model that students could use when working on the percent problems.  A model that would strengthen their conceptual understanding of percents. A model that could be linked to the question set or class website allowing students to use it whenever needed.  I put the BreakoutEDU activity on hold while I went to work creating the Desmos AB.  This post discusses the result of my work.

*Side note:  I baked in a Desmos piece to the BreakoutEDU activity during the summer PD summit, but that’s for another post.

# The Percent Model

The Activity Builder is sectioned into three groups where each group addresses one of the 3 types of percent questions, finding the part, finding the whole and finding the percent.

### A:  Finding the Part

The first screen, within a group, sets up the problem.

Screen 1 – Figure 1

Screen 1- Figure 2

Screen 2:

The second screen is designed to support student thinking.  Students can use the sketch tools to annotate the picture and test values.  In this example, a student divided the textured region into three sections in order to identify 10%.

Screen 2 – Figure 3

When 4 is entered into the answer box, an error message displayed.  Four is not the answer to the original question, however, this step confirms that 4 is in fact 10% of 40. This information can be used to calculate the actual answer, as shown in Figure 5.

Screen 2- Figure 4

Screen 2- Figure 5

The graphics and student annotations carry over to the third screen in the grouping.  Students now reflect on their process and communicate their thinking to classmates and teacher.

Screen 3 – Figure 6

## ——————————————————————————————-

### B:  Finding the Whole

The second grouping, Finding the Whole, works similarly to the first.  Students enter either teacher provided information or their own part and percent.  Then they determine the whole.  In this version, the animated bar needs to fill the entire rectangular section (as shown below). The final step is to explain their process.

Screen 6 – Figure 7

Screen 6 – Figure 8

## ——————————————————————————————-

### C:  Finding the Percent

The last type, Finding the Percent, follows the same structure as the two previous.  Students enter in information, determine the answer and reflect.  The expected answer is a percent and students are asked to round their solution to the tenth position (Figure 10).

Screen 8 – Figure 9

Screen 8 – Figure 10

# Classroom Uses

When developing this Activity Builder, I envisioned two different uses – Independent and Teacher guided. As mentioned in the Inspiration section, the original plan was to create a percent model for students to use when working through independent problems.  If percent problems are integrated into a spiral review like my colleague is doing, then placing the direct activity link on a class website gives students access to the model at any time needed.

You will find the activity link by first clicking on the 3 vertical dots in the upper right-hand corner and then clicking on Share activity.  This method takes students to the activity’s “home” screen (Figure 12).  They can open the activity two ways, either by clicking Student Preview or clicking on one of the displayed screens.

Figure 11

Figure 12

If using the model as a part of a lesson, then it’s best to create a class code.  It should be noted that class codes last a couple of weeks before archived.  Once students join the activity, teachers can use the conversation tools (Figure 13) to pace the screens depending on the desired intent.  For more information on the Anonymize, Pacing and Pausing features, click here.  I suggest preparing percent problems that naturally allow for various paths to a solution and then use the sketch and reflection screens to cultivate mathematical discourse.

Figure 13

# Inspiration

I’ve created several hidden number pictures using the conditional formatting feature within Google Sheets. One of the teachers I work with wanted to learn how to create her own designs.  This activity is the result of the training session.

## The Hidden Picture

When you click to make your copy, this snapshot is what you’ll see.  A framed box holding the hidden picture is on the left and a question and answer section on the right.  When a correct answer is entered the reddish color turns green and the corresponding cells begin to reveal a picture.  Click here for your own copy

## Inspiration

Recently a colleague expressed dismay regarding one of her classes.  Her students were not engaged and she was looking for ways to pique their interest. I had an idea. This post outlines the equivalent ratios activity created for her students.

## Challenge Creator

Desmos has many activities that utilize their challenge creator technology.  Typically, students are lead through an AB and end with a challenger creator.  Lately, I’ve been tinkering with the idea of the AB is only a challenger creator.

The Challenge Creator technology allows the author of the AB to provide students with targeted choices that result in a personalized task aligned with the content standard.

## The Activity

Screen 1 – Choice 1: Students had to select which items to compare.

Screen 2 – Choice 2: Students had to pick one of the two selected items. This choice, unbeknownst to the student, dictates which variable will corresponds to the x-axis and which corresponds to the y-axis.

Screen 3 – Choice 3: Students had to move the point to the desired location.  This screen determines the ratio to be used for the challenge.

Screen 4 – The Created Challenge:  Each choice had a part in creating the final task. They are presented with the opportunity to create equivalent ratios using the context of choice.

Notice that the Submit Challenge button is not activated. Students have to solve their personalized challenge correctly before submitting it to the Class Gallery.

Built-in Feedback: Students are clever.  We have to be one step ahead of them.  After a few failed challenge creator attempts, I’ve learned to build in checks and balances.  For this task, students can’t get away with entering the same ratio.  If they try, a feedback message will pop up ask them to create an equivalent ratio.

Students can use the graph to determine which ratio is incorrect.

The Submit Challenge button will only activate if the two ratios are equivalent and the Check Ratio button is pressed.

## Class Gallery

Once a student submits a challenge, she gains access to her classmates’ challenges.  Students can click on a peer’s challenge and create equivalent ratios for a new situation. In most classes, I ask students to record their work on a sheet of paper.  It allows me to better assess learning as I circulate the room.

Warning:  I’ve run Challenge Creators with and without anonymous mode.  Lately, I’ve been leaning toward anonymous mode.  I’ve had a few instances where students were hyperfocused on how many people were attempting or not attempting their challenge.  The focus was clearly moving away from the math and negatively affecting student learning.  During the 2 lessons where switched midstream from student name to anonymous mode, I addressed my decision with students (gr 4 and 2).  They understood.  Since I’m a guest teacher, I’m not able to do the required work necessary to establish long term understanding and acceptance of class norms.  Therefore,  I now start in anonymous mode.

Reflection Screen:

The last screen asks students to reflect.  Here are some of their thoughts.

What stood out to me:  The students

• knew more about ratios at the end of the period than at the beginning.
• enjoyed themselves
• felt more confident about ratios
• still, question their future understanding of math.

Positive:  My colleague’s students loved creating and solving their own challenge.  The next day, when I wasn’t there, her students asked to do it again.  Students who are not typically engaged in math were asking to create and solve math problems.  That’s a win!

Here’s the activity:  Equivalent Ratios – Challenger Creator.

Acknowledgments:

Thanks go out to fellow Desmos Fellow, David Petro, for helping me refine this activity.  He blogs at ontariomath.blogspot.com.

## Inspiration

In the spring of 2018, I introduced Desmos to a couple of 4th grade teachers.  After running, Ordering Fractions on a Number Line and Polygraph:  Geometry Basics, they were hooked on Desmos.  During the last days of the year, they asked if I had any Desmos activities that focused on place value.  At the time, I didn’t.  But now I do.  🙂

## Polygraph:  Place Value

Polygraph: Place Value

The first time I ran this Polygraph, it bombed.  I was not expecting such a beloved platform to cause so much distress.  Just last year, I ran Polygraph:  Geometry Basics in multiple 4th grade classrooms with great success.  Then it hit me.  This former middle level math teacher quickly realized that 4th graders in August are very different than 4th graders in May. A lot of maturity and growth happens in the months between August and May.

## My Light Bulb Moment

Using the teacher’s computer, I signed in as a student.  When the computer assigned me a partner, I hit the pause button.  I explained that, as a class, we needed to run through a game together. It would be the most efficient way to address all their questions.

To run through the practice game, I had to unpause the activity.  Student computers now had the potential to become a distraction. My solution was to ask all students to turn their computers, so the screen faced away from them.  We quickly brainstormed a list of reasons why we had to reposition our computers. The brainstorm helped students buy into pausing their individual games and playing as a collective group. They were now willing to give their full attention.  Time to play.

My partner picked a card.  The rest of the class and I were tasked with determining which card she picked.  I facilitated the process.  Students provided me with yes or no questions, told me which cards to eliminate and explained why.

The first round was the longest.

• Our question:  Is your number odd?
• Response:  No

There are 16 cards and we talked through whether to eliminate each card.  The process of understanding which cards to keep and which to eliminate can be challenging.  It’s important for students to understand how to maneuver the elimination step.  Sixteen different students verbalized their thinking.  This process moved at a snail’s pace at first, then, as students solidified their understanding, it sped up.  Believe me, this is time well spent!!

To exposed students to varied questions and to expand their academic vocabulary usage, I guided their questions.

Examples of question types:

• Is there a 4 in the hundreds place?
• Is your number 5 digits long?
• Is your number greater than 1000?
• Is your number less than 10,000?
• Does your number have a digit in the millions place?

Each round moved faster due to a combination of fewer cards and increased understanding of how to play.  When we discovered our partner’s number, the class cheered.  I love to hear cheering during math class.  Music to my ears.

Student were given the signal to turn their computers around and continue playing their individual rounds.  Students were more independent and far less frustrated.

Over the next two weeks, I ran the activity with two more 4th grade classes and a 3rd grade class.  Each time, I ran the activity whole class before letting students play individually. Each time, the individual games ran smoothly afterwards.

## Side Note – Third Graders

In my opinion, due to typing skills, the youngest grade I’d use Polygraph with is third.  Any younger, the ability to type hinders the questioning process.

Polygraph: Place Value

# Inspiration

RandomGenerator is one of the functions within Desmos’ computational layer.  As I explored the feature, I began to see the benefits of random generated tasks.  Many experiments later, I’m publicly sharing my first random generated (RG) series.  This one focuses on slope and y-intercepts.

This AB would not have been possible without the help from Jay , Suzanne,  Jocelyn, Serge and last but not least, Eli. Each person either added CL examples to the Desmos Fellows CL Bank of Wonders (that I adapted or used in complete form) or answered my questions when I was completely stumped.

# My Intention

As I learn computational layer (CL), I often practice writing the code I’m using.  Let’s take Jay’s example, Sketch and Check Random.  Since the example involves features that I haven’t coded with before, I used Jay’s code for practice activity 11.  I’ll now need to go back and learn the code. Study it.  Figure out the purpose of each line and how the various lines connect with components to achieve the desired outcome.  I’ll then work on replicating the code.  It takes me multiple tries to replicate code.  The rewriting process not only helps me understand the CL language, but also helps me become more efficient when creating future activities.

Throughout the school year, teachers offer a variety of experiences.  There’s definitely a need for exploration activities and tasks that build conceptual understanding.  There’s definitely a need to focus on academic language through mathematical discourse.  There’s also a need to practice a specific concept, similar to when I practice the writing of code to gain fluency.

The random generated aspect of the Random Generated:  Determine Slope and Y-intercept  activity builder allows teachers and students to use the activity as often as they wish without the worry of duplicating problems.  A feedback loop is built into each practice activity, therefore regardless of the example, students will know if they calculated the problem correctly.  Listed below are few suggestions to integrate the AB.

Example 1:  After assessment practice.  Mr. X gave his students an assessment and he noticed that the majority of his students struggled with finding the y-intercept when given two points.  The next day, he could project practice slide 6 for a whole class task.  He could also pass out one computer per group and ask a group member to go to slide 6.  Now each group has their own problem to solve collaboratively and since feedback is provided, students will know if they completed the problem correctly.

Example 2:  Collaborative practice.  If you use #VNPS (vertical non-permanent surfaces aka white boards on the wall), pair up 2 students with 1 computer.  Let the partners work through a few randomly generated problems on the whiteboards while you circulate through the room.  Since the problems never run out, some pairs may complete 2 problems where others finish 3 or 4. A follow up activity could require students to reflect on the strategies used.

Example 3Individual practice. Sarah often struggles to determine the slope when the line does not have clearly marked points.  Prior to a test, she could run through a few examples on slide 4.  After she answers the first problem correctly, she can press the button for another example (if necessary). Again, each slide is designed with built in feedback.  Therefore even if Sarah practices at home, she can gauge her progress.

Example 4Choice boards and Hyperdocs.  If you provide choice boards for your students, then one or two of the practice activities could be used as an option.  A familiar Hyperdoc format is:  Engage, Explore, Explain, Share and Reflect.  Teachers could find interesting ways to integrate the RG practice activities into a Hyperdoc.

# The Random Generator Slope AB

Feedback has been built into each practice activity.

Note:  If a vertical line pops up on a slide where the check depends on a numerical value for slope, then generate a new problem.  Vertical lines are addressed on slide 10.

Slide 1:  Students are asked to acknowledge the individual rise and run and then enter the slope.  The program calculates the y-intercept based on the displayed points and the inputted slope.  Therefore, the line that matches the student’s response is graphed.   If the student enters the correct slope, then the line will pass through the given points. If their slope is incorrect, then the graphed line will not pass through the given points.  Students are encouraged to use the sketch tools.

Slide 2:  Similar to slide 1 but requiring students to calculate slope using 2 points.

Slide 3:  Students practice finding the slope when points are not prominent.  For these examples, the slope values are only integers.

Slide 4Same as slide 3, except the slope values can include fractions.

Slide 5:  Students are expected to calculate the y-intercept when given the slope and points.  In order to generate slope values to include fractions, I had to randomly generate a numerator and a denominator.  This method produces slopes in various formats, like the one pictured, -4/-2.

I entertained the idea of simplifying the slope but then made the conscious decision to leave it as is.  In my experience, students often struggle when a fraction contains 2 negatives, a negative in the denominator or is not simplified.  By leaving the slopes “messy”, students have more opportunities to navigate tricky formats.

Slide 6:  This activity requires students to calculate both the slope and y-intercept.  Students can either determine the slope using rise/run or with the given points.

Slide 7:  Similar to slide 6 but without a grid.  Without the grid, students are encouraged to practice calculating slope using the formula.

Slide 8:  Students enter the linear equation in slope-intercept form.  Sketch tools are available.

Slide 9:  Same as slide 8 but without a grid or sketch tools.

Slide 10:  The same as slides 8 & 9 but with vertical lines.

Slide 11:  Using the sketch tools, students draw the line that represents the given equation.  When the button is pressed, the correct line is displayed.

The activity builder:   Random Generator:  Determining Slope and Y-intercept

# Inspiration

The majority of my posts begin with an inspiration segment.  A few words explaining my motivation to write.  Originally, I was planning to write about podcasts with the inspiration segment focused on Friday Night Lights.  FNL lead me to podcasts. However, as I reminisced about my brief obsession with FNL, it became clear that the story about a town, a team and and a dream needed a post of it’s own.

# Friday Night Lights

It was to be a summer of coding.  I planned on spending my days deep in the world of  Desmos CL (computational layer) and Google app scripts.  I did neither.  And I completely blame Coach and Tammy Taylor, Tim Riggins, Matt Saracen, Tyra Collete and the rest of the Friday night Lights cast.

During spring semester, I started watching Friday Night Lights, the series, and spent my first week of summer break binge watching the 5th and final season.  It took all of 1 hour before slipping into the dreaded show hole.  Not ready to let go of the characters, I hopped onto the internet searching for fun facts about the series.

That’s when I discovered that the series was actually based on the book, of the same name, written by H. G. Bissinger.  Show hole averted.  I drove to the library and checked out the series inspiring book.  Bissinger skillfully weaves the story of Permian Panther football within layers of Odessa, Texas history.  The book’s rawness clung to me making it even harder to shake the entrenched football culture of Odessa, Texas.  My mind scanning both mediums acknowledging the parallels between the book and the series.  I moved onto Friday Night Lights, the movie.  The triangulation of the book, series and movie fascinated me even more.  More connections, more parallels. More Obsession.

• Matt Saracen’s character represented Mike Winchell
• Tim Riggins’ character  represented Don Billingsly
• Smash Williams’ character represented James ‘Boobie’ Miles
• Don Billingsly has 3 children: Landry, Skylar and Riggs.  FNL, the series, has characters named Landry Clarke and Tim Riggins
• Odessa, Texas had 2 high schools, Permian and Odessa.  FNL, the series, introduced a second high school at the end of season 3.
• IMO, Coach Taylor’s phrase, clear eyes, full hearts, can’t lose summarizes Coach Grimes’ speech to his players during the 1988 state championship.
• In actuality, the 1988 Permian Panthers reached the semi-finals not the state championships. The movie adjusted for dramatic effect.
• I could go on, but won’t 🙂

• Upper left:  Garrett Hedlund playing Don Billingsly in FNL, the movie
• Lower left:  Taylor Kitsch’s character, Tim Riggins representing Don Billingsly in FNL, the series
• Right:  Don Billingsly circa 2015 and 1988

I watched the series. Read the book.  Watched the movie.  Still inside the show hole.  Now what?  PODCAST! Yes, there are podcasts dedicated to FNL.  I listened to Binge TV ‘s podcast on Friday Night Lights- all 6 episodes.  That did the trick.  When the final seconds of the final podcast episode concluded, I felt fulfilled.  Done. But now I was hooked on podcasts.

## Closing Thoughts

The post on podcasts never materialized. Instead, I added the fifth medium – blogging.  I watched, read, listened and finally blogged about a heart wrenching story of Texas football.  My next post will pick up where this one ends. The baton officially passing from Friday Night Lights to the academically minded podcasts discovered thanks to my FNL obsession.  Until then, clear eyes, full hearts, can’t lose.

## Inspiration

Toward the end of the school year, my colleague Jorge and I, had a regular gig co-teaching in Mrs. S’s 4th grade class. Jorge had been working with Mrs. S throughout the year on various projects. I joined the duo during the last quarter to show Mrs S how to integrate Desmos into her math lessons.

On the day in question, I was scheduled to lead a 1 hour lesson using the Polygraph: Quadrilateral Attributes. I was prepared and ready to go when Jorge’s text came through reminding me that I was scheduled for 2 hours.  What?  Wait… How did I miss that detail?  Dang! I needed to restructure – and fast.

## Necessity is the Mother of Invention

The text scrolled across my phone minutes before leaving my office.  I had the  3 mile drive to conceive plan B.  For a couple years, I’ve demoed or co-taught various Polygraph lessons and then, during the debrief, shared ways to build off the experience – Never getting the chance to run with any of my suggestions.  This day was different.  On this day, I was granted time to extend the Polygraph lesson.

Once in the classroom, I assisted with the transition to math.  Students turned on their computers, logged into Google Classroom and clicked the Desmos link.  Polygraphs aren’t new to this group of students.  Their first experience was playing Polygraph:  Geometry Basics.  When all students had logged in and the activity norms were recapped, students were free to play and plan their questioning strategy.

Now that students were focused on guessing their partner’s selection, I sat down to create the post Polygraph task.  The task linked below is a cleaned up version. Time was limited and the original version valued substance over aesthetics.  Yes, the students were familiar with this type of activity, but circulating the room, listening to conversations and interacting with students is crucial to the activity’s effectiveness.  My charge was to whip up the task and get back to the students ASAP.

My district jumped onto the Google Classroom train this year and I’m thankful for the flexibility it brings.  Once in drive, I created a new Google slide presentation, copied the pictures from the Polygraph activity and started writing questions.  One question per slide.  The task was placed into Google Classroom using the create assignment feature and the option, Make a copy for each student.

Title Slide

The main purpose of a Desmos Polygraph is for students to experience and understand the need for academic vocabulary.  When used at the beginning of a unit, student questions are often constructed with informal language.  As the playing continues, the teacher plays a key role in helping students infuse academic vocabulary into their questions.  Click here to read a post outlining one method of integrating academic vocabulary as students are playing a Desmos Polygraph.  Many teachers use the same Polygraph activity at the end of a unit with the expectation that academic language is used in every question.

For this lesson, the Polygraph activity focused on math symbols. Students based their questions on the various symbols displayed in the given images.  For the post activity, student needed to work with the vocabulary and symbols differently.  The post activity required students to explain the meaning of each symbols as well as physically create quadrilaterals based on the given criteria.

The camera feature built into Google Slides is wonderful.  Students really like taking pictures of their work.  More information on how to use the camera feature can be found in this blog post.

## Resources

Desmos has 2 quadrilateral based polygraphs, linked below.  I created a third one after speaking with a handful of elementary teachers and coaches in different parts of the country.  I asked them which geometry concepts their students struggle with the most.  Their common response:  Quadrilateral Attributes.  With their response in mind, I built a polygraph that focused on the symbols used to differentiate the various quadrilaterals.  Once students are confident with their understanding of the symbols, I suggest upping the ante by moving onto one of the Desmos Polygraphs.

The Desmos Polygraphs:

Other links found in this post:

My colleague Jorge and me

## Hidden Picture: Double Digit Addition & Subtraction

The core group of G Suite apps are docs, slides, sheets and forms. All of which I’ve used over the past 2 years.  However, I recently discovered Google Apps Scripts, a hidden gem built into the suite.  Bottom line, I can add another level of customization to my Google creations using Google app scripts.

## My First Google Script Activity

When students open the spreadsheet, they’ll see 21 addition and subtraction problems.  Once an answer is calculated, students enter the sum or difference in the corresponding red box and then press enter.  At any point during the activity, a student can check their answers by pressing the button icon.

Correct answers are indicated two ways. The red box turns green and the hidden picture slowly appears.

The final image

## The Catch (no pun intended)

1.  Since the activity was created using Google Script Apps, students will have give their permission for the coding to run.  Press continue.

2. Select account

3.  Select Allow

Once students click the necessary buttons, they have access to the activity.  Enjoy!

## Kindergarten, Number Bonds & Desmos

Recently, I had the pleasure of teaching a kindergarten class for the very first time! My colleague, CeCe, invited me to teach a lesson on number bonds using my Desmos Number Bond Activity

## The Lesson

The Kinders sat on the rug.  Cece projected the activity from her computer onto her whiteboard.  To start, I stood by the whiteboard and, with Cece’s assistance, ran a mini-lesson.  But anyone who has taught kindergarten before understands, it didn’t take me long before I was sitting or kneeling on the ground.  I spent the mini-lesson “toggling” between standing to address the whole group and sitting/kneeling to listen and ask follow up questions.

• Me:  What do you notice?
• Students:
• I see numbers
• I see dots
• Me:  What color are the dots?  Talk to your neighbor.
• Students: Red, purple, green blue.
• Me:  What’s the difference between the dots?  Turn to your neighbor and talk about the difference.
• Students:  Some are big.  some are small.
• Me:  What else do you notice?
• Students:
• I see, no.
• I see, yes
• And a number bond
• Me:  Let’s talk about all the items you mentioned ….

This simple opener highlighted all the parts of the slide that I needed to discuss prior to using the computer.  We then spent a solid 15-20 minutes discussing

• The vocabulary of a number bond: whole & part
• The purpose of the small and big dots
• The value of the whole (for this example)
• How to move the purple slider to fill in the whole value
• How to check an answer by moving the green slider from No to Yes
• The different messages that could pop up
• How to change an answer when a mistake is made (move the green slider back to No, change answer, then check)

And when I say discussing, I mean there was a lot of

• Pair-share
• I listened to their conversations and then based my questions on what was mentioned. Depending on what I heard, I asked followed up questions with 1 student, a small group or the whole group.
• I say, you say

A smiley emoji pops up when the whole is correct.

A sad emoji pops up when the whole is incorrect.

*****************************************************************

## Computer Time

Students were organized in pairs and used QR codes to access student.desmos.com.

As the students worked through the problems, CeCe (pictured above) and I circulated the room and checked in with each pair. We asked students to explain their thinking and to read the messages that popped up.

A week later, I had the opportunity to run the same lesson with Ana and her students.

## Acknowledgements

I’d like to thank CeCe and Ana for inviting me into their classrooms.  Through our collaboration,

• Students enjoyed an engaging math activity
• Students were introduced to new technology
• The activity was refined
• With your tutelage, I gained new insights into teaching primary grades

# Inspiration

My instructional tech team and I always receive grateful comments from our elementary teachers we share seasonal activities.  Most of the activities we shared were using Google slides.  I wanted to challenge myself and create a seasonal activity on Google sheets.  Here are the fruits of my labor.  🙂

## The Activities

I created 3 different versions of a St. Patrick’s Day Google Sheet activity.  Students have to answer age appropriate math questions. Two actions occur when a correct answer is inputted.  First, an image begins to emerge in the blank rectangle.  Second,  the answer cell fills in with a light purple color.  A wrong answer, as shown below, is left white.

Below is the picture for grade 1. The picture is different for each version.