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]]>The 2020 CMC (California Math Council) South Conference – usually held in Palm Springs) is going virtual like all conferences this year. I attended my first conference there last year and it was amazing. This state math conference attracts amazing presenters from all over the country. If there is one state conference you should attend (other than MN’s) – it is this one. The fact that it is virtual this year makes that easier for you. More INFO here. Recorded Sessions will be available until January 1, 2021.

**My session at CMC South is titled ‘Safe Prompts for Entering ‘Math’mathical Discussions’. This session is similar to one I did for this summer’s Building Math Minds Workshop, but I’ve made it more K-12 vs 6-12. **

My session will go live at 1:00pm Pacific Time (that’s 3pm Minnesota or CST). The link to access my PowerPoint and all the other resources will go live at 1 pm as well. Come back to get access to resources from this session.

Click HERE to be connected to a Google Folder of Resources and LinksJon Orr and Kyle Pierce have put together an amazing FREE 1-week virtual conference for the last several years titled the ‘Make Math Moments Virtual Summit’. This year is no different. For one week you will have access to watching sessions from over 20 math presenters from all over the US and Canada. This year’s conference begins this Saturday, November 7th and runs free until November 13th. **Visit HERE** to register and get more information.

**My session titled, ‘Creating Discourse through Math Language Routines’ goes live Saturday, November 7 at 2:00 pm Central Time Zone (3pm eastern, 12 noon Pacific). **You can watch a recording of the session afterward until the 13th if you can not make it live.

I am excited for this session. It is a new one for me -but I am speaking about things I’ve been doing in my own classroom for the last 20+ years. I hope you can join me for this session.

I will be posting my PowerPoint and other resources from this session HERE as soon as the session goes live on November 7th.

Click HERE to be connected to a Google Folder of ResourcesNOTE: My PowerPoint is not in the folder yet….It will be later today (Nov 7)

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]]>The post The 100 Number Task – during a Pandemic (Is it possible?) appeared first on Sara VanDerWerf.

]]>The 100 Number Task WAS a favorite week 1 activity….but then the pandemic hit.

Our world was turned upside down. Would our favorite math classroom routines, tasks and norms still work during the era of ‘Distance Learning’?

No one has a playbook for our new norm and how it will work. What I do know for sure is this…

- If I was passionate about something before March 2020, I am still passionate it now.
- If I think hard enough, and collaborate with other educators – I can figure out how to do anything in a digital setting.

**I believe anything that I could do during in-person learning, can be replicated (maybe it will look and feel a bit different) in distance learning. Really – I believe this….and I’m willing to put my energy into figuring this out for the things I am the most passionate about. The 100 Numbers Task – is just one of these things. **

Let’s start at the beginning. Why am I passionate about using the 100 Number Task? If you don’t know why you use this task – how can we re-imagine it in a different setting. Creating a digital version of this task starts with us knowing WHAT we are re-imagining. So take a moment – before reading further – and brainstorm…

**WHAT you love about the 100 Number Task?**

**WHY do you use the 100 Number Task with your students?**

**Here is my list…**

**It’s fun. Week 1 of school I want to do something that is engaging.****It’s easy. It has a low floor and invites all students to the table. It’s easy to implement and easy for students to figure out.****Student’s Enjoy it.****Students TALK to one another.****Students LISTEN to one another.****Students work together.****Students Collaborate.****This task has a**PATTERN – it reinforces the definition I share with students week 1 about what math is.**Students work with their teammates to improve their work (beat their previous score) – Models self/team improvement.****It creates powerful, positive feelings for math work. Students love this task and often ask to do it again the next day, week or month.****With very little direction from me, students start working with their teammates (group members). They heads and bodies are all in on this task.****It sets up a discussion on what great group work looks like. Students will tell me what group work looks like rather than me.****I love the part where I take photos of each group. They don’t even notice and this sets up a great conversation about groups focusing.****I reference these photos all school year (hang them on my classroom wall).**

So the next challenge is…Can we accomplish all of this in a distance learning setting. My answer, after trying this with teachers and talking to teachers who have used this with students is YES – to most of the items above. The only item that will still be a bit tough is #11 – the photos I love to take.

So, what are my recommendations to you? Read on…

In early July I was communicating with my friend Morgan Stipe. Morgan is a Middle School math teacher from my neighboring state of Iowa. This summer she started working as a Teacher Leader/Coach for Open Up Resources. (OUR). I noticed Mogan referencing the 100 number task via twitter and I messaged her about it. She and I were on the same page. We both thought perhaps the 100 number task might work virtually using ZOOM breakout rooms & JamBoard – a google version of a collaborative white board.

So…..Morgan and I invited Math Teacher Leaders to join us for a practice session in July via ZOOM. Lots of things went well and other things not so well. At the end of our session though I was convinced that many of the aspects I loved about the 100 number task while in-person – would work virtually using JamBoard.

**Thank you to Morgan Stipe and all the other teachers that added their thoughts to using the 100 Number Task virtually.**

**Note:** There are other platforms to do what we did using JamBoard and ZOOM breakout rooms. Several teachers have used Google Slides instead of JamBoard. I’ve included resources on this below. Many have said to me…”My district uses Google Meets, not ZOOM.” (or Microsoft Teams) “Google Meets does not have breakout rooms!” If you do not have a way to meet synchronously using ZOOM, you can still create the idea of breakout rooms by setting up multiple Meetings. Google Meets has a Chrome Extension you can download to do Breakout rooms. Google Meets will also be coming out with breakout rooms soon. (I’ve heard October)

The 100 Number Task can be just as FUN & USEFUL to starting discussion and group work norms if you use Jam-Board & ZOOM Breakout Rooms. This task will still be fun. It will still be engaging. It can still set up a great discussion about group norms. The only thing lost (although this was a favorite of mine) is the ability to take pictures while students work without them noticing.

**Jamboard** is G Suite’s digital whiteboard that offers a rich collaborative experience for teams and classrooms. Jamboard currently limits the number of people who can sign-on to anyone document to 50 people. Since most classes are 35 students or less, this is not an issue. You will need to make a separate Jamboard (make a copy like any other google doc) for each of your classes. **ProTip** – I’ve learned to make a document I call ‘Original’ and make copies for my class from this. Currently, Jamboard only allows for 20 pages to be made. This means the pages must be used collaboratively in a classroom – with at least 2 students per page. In this activity, I have 4 students per page. Lastly, you may experience a short (1 minute) time when everyone signs on at once where a few students are told they don’t have access – just tell them to be patient and sign on again.

To engage students in the 100 Number task, I highly encourage you to teach them how to use JamBoard and its tools using some other fun (non-mathy) task. I would not have student’s first experience with JamBoard be during the 100-Number TAsk. I like to have a JamBoard Practice Session first.

You can introduce JamBoard to your students using any fun task you want. I might introduce it by showing my students the important tools and telling them…

- I am going to send you to a ZOOM Breakout Room with 3 of your classmates (4 students total).
- When you get to your Breakout room, you may want to split your screen so you can see your classmates (Ideally Camera’s are on, even if it is just part of your head). Show students how to have 2 screens open on their computer at the same time.

- The link for the JamBoard you will be using is in the Chat Box on ZOOM.
- When you open JamBoard. Make sure the page you are in on JamBoard matches your Breakout Room Number. (see purple arrows below)

- Tell Students about the Pen Tool…Tell them to each select a different color and write their name below the post-it note (or ‘stickies’ if you are not from MN).
- Tell students that all 4 of them can write at the same time.
- Tell students to then draw a picture of anything they want with their pen tool using the number below their post-it note.

- Tell students to tell (talk out loud – have them practice un-muting themselves in the chat room) why they drew the picture they did.
- Send students to the chat room to practice using the tools for around 5 minutes. While students are in Breakout Rooms – you can see what they are doing by scrolling through the pages on Jamboard. Its’s amazing to see all your students collaborating in real time. I also like to go into a few breakout rooms and listen in.

- When your students return from the practice round (bring them back from the breakout rooms) you can call on a few students to talk about their pictures as you display the JamBoard Screen for the entire class to see. Ask your students if they explored any of the other tools in JamBoard. Students will talk about using the eraser tool, they will say if you want to type, you pull up a post-it note and type. Some students will even realize they can upload pictures to Jamboard.
- Talk about how important it is to talk to one another as you draw in the breakout room. If necessary (I do this lots) – give your students sentence stems (frames) to support their discourse in the breakout rooms.
- Morgan Stipe made my original practice board look better. You can download her version using the BLACK BUTTON at then end of this post.

Either on the same day as your practice session or a day or two later, Have your students do the 100 Number Task in JamBoard and ZOOM Breakout rooms.

I like to start things out with this GIF and say…”Good news students, to do today’s task, you only need the ability to count. Let’s all practice counting together…’One, two, three, four, five, six…'”

Before sending students to breakout rooms – remind them that their breakout room number should match their jamboad page. (see purple below). Remind Students to use the Pen Tool (each student a differnt color) and write their name before anything else. Tell students that each student must take turns finding the numbers one to 100. Only one student can circle a number each time. They MAY choose to use the spotlight tool to help their group members find the next number. Tell them they will have 3 minutes (you, the teacher, will close breakout rooms after 3 minutes forcing them back into the main room).

When students return to the main room. Tell them you are going to send them back to the Break-out rooms for 3 minutes to talk about Round 1. Tell them to each open a post-it note and write something their group did well or something they noticed helped them find numbers.

Bring students back together in the main ZOOM room. Have a class discussion about what they noticed. Note to Teacher: If you have students write what they noticed on post-it notes – you can have a discussion you can select students to talk (since you can see everything by scrolling the Jamboard pages) when they are back in the main room.

Have students do Round 2 of the 100 # Task using what they learned in a fresh new JamBoard Page. See if students can get further than round 1. (TIP, if you have not read my original post – go read it now – there is a pattern to the 100 number task)

Bring students back to the main room and have them talk about what good group work looks like. Ideally, your class list may look something like this…

Use this list to inform how you as a teacher will enact the 100 Number Task using JamBoard and ZOOM Break-out Rooms. What teacher moves can you do so students say the things above and not you, the teacher?

In the past I’ve used the 100 Number Task Week 1. Many teachers have told me this is their favorite first day of school activity. **During Distance Learning, my gut says to wait until week 2 or 3 to use this task. ** Use Week 1 to set norms around using technology, meeting together online and building a community within your classroom.

If you are doing In-Person Teaching or Hybrid Teaching this fall – we still need to keep our students 6 feet apart. Honestly, I feel like **In-Person learning is still distance learning**. I highly recommend using JamBoard on Devices IN-PERSON this fall too. Students do not need to get close to have a conversation together. Another teacher suggested taping the 100 Number Board to the wall and students do this while standing and only one student can approach the board at a time.

**I don’t tell my students to use different color markers Round 1**. If they do – so be it. If they don’t – that is cool too. The pattern is more difficult to see if students use the same color marker. Consider having everyone start with the same color marker.

There are tons of ways you can mix up this task. You can have students start at 100 and count backward. In my **original post** I have lots of versions others have created for this task to make it more difficult or at least different.

Morgan has used the 100 Number Task using JamBoard and Breakout rooms several times. Here is what she said… “100 Numbers was a hit this week with the JamBoard activities. As a team, we thought if you have a group of 3, it worked to have the group act as person 4 and find the numbers for the missing teammate. If you had groups of 5, one teammate could use the laser and help find numbers!”

Shawna Viet has used this with other adults. Check out HER version on JamBoard.

From Shawna…

“I set up multiple boards and used different colored post-its to help teams find their second board easily. I demoed the Jamboard using the marker instead of the pen, so the pattern would “pop”. They were instructed to add their names to the post-it in order so we could debrief.”

Shawna Shared a Video of her using this task with her teachers. I love what she said about the adult use of this task in JamBoard…*“some numbers having two colors because one of the guys admitted that he was “helping” others and not following the rules.”*

Gina Anderson attended the test session Morgan & I did. She created a facilitation guide for her teachers explaining the process.

You can find Gina’s Facilitation Guide and all the other resources by clicking the BLACK BUTTON at the end of this post.

Megan Heine and others have used Google Slides & Breakout rooms successfully doing the 100# task. Check out Megan Heine’s Twitter thread on this.

I’ve included Megan’s version of the 100 number Task on Google Slides and others shared with me that you can get by hitting the black button below.

Tip from Sonja Twedt on Twitter – HERE is Alice Keeler’s Post on how to push out slides to each of your students/groups.

Although I addressed this above – I am getting this question a lot online. “Sara, I use Google Meets and they don’t have Breakout Rooms.” The answer is Google Meets does not officially have Breakout Rooms YET. They are coming. Until then, search ‘google meets breakout room extension’ and download it and use it…..OR… take Kendra Newman’s advice to someone who asked. (note – this would work with Microsoft Teams as well)

After posting this blog, Debbie Hurtado commented on Twitter about using the 100 Number Task with Pear Deck. I asked her to talk about how….(more coming soon)

Here is the twitter thread where she explains using Pear Deck

If you would like to get copies of the JamBoards used, Google Slides and a Powerpoint ….Click the BLACK BUTTON below and you will be connected with a Google Folder of Resources.

**NOTE – To make the items in the folder your own, simply ‘MAKE A COPY’. All documents are set to ‘view only’, but you can edit them if you ‘MAKE A COPY’. Best. **

One last reminder! Go back and (re)read my original 100 Number Task Post. This post has lots of different versions of the Task you can adapt for a Distance Learning setting. Enjoy.

If you try the 100 Number Task with students in a distance learning setting – I’d love to hear from you. What worked? What did not? Comment Below or Tweet me @saravdwerf or find me on Instagram @saravanderwerf or LIKE my Facebook Page @saravanderwerf I’d love to update this post with ideas from all of you.

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]]>The post Math Fails 2020 Set #6 – using #mathfails to create mathematical discourse. appeared first on Sara VanDerWerf.

]]>My favorite way to use **#mathfails** is to post them in the hallway outside my classroom with a sign saying ‘Can you find the **#mathfail**?’ or ‘Math Wall of Shame’ and watch all year as it is a continual source of enjoyment for students and adults. Nothing creates discourse around mathematics like a **#mathfail**. (NOTE: I wrote this paragraph before the start of the pandemic and distance learning. At the end of this post I address how I would use #**mathfails** during our current state of education)

My second favorite way to use **#mathfails** is in my classroom to engage students in discourse. Here are several ways I would use images from this year’s set to engage students in discourse.

**IS IT A MATH FAIL?** …or just a typo…

What is a **#mathfail**? The definition I’ve used to curate a large number of **#mathfails** in the last 6 years is ‘a mathematical error based on a misconception’. Often **#mathfails** are created by using in inaccurate representation of the numerical value or it happens due to a miscalculation. If I am honest – in the set of over 500 **#mathfails **I’ve collected – my guess is several – particularly those from stores are typos and not created because the creator struggled with a mathematical calculation or concept.

I think using photos that skirt this edge of **#mathfail **and typo are great for creating discourse.

Denis Sheeran posted the following image on twitter during Thanksgiving 2019. Take a look at his photo and select one of the following statements from the orange box.

- The image below is a
**#mathfail**(a mathematical error, misconception) - The error below is simply a typo, a mistake – perhaps the person making this was working too quickly.
- There is nothing wrong with this sign. It is correct.
- The ‘save 1.00’ represents poor communication.

Here is another image. Is it a #mathfail or an honest mistake?

How could you use this image to create mathematical discourse? I see opportunities for proportional reasoning. What is the cost per ounce? What is the cost per pound? If the 6 oz portion is really $5.99, what should be the cost per pound? If the cost per pound is really $95.84, what would be the cost of a 6 oz portion? ….etc…etc….

**Is this a math fail? Part 2. ** from March 2020 (Shelter in Place time)

This one was posted by MN math leader Ben Orlin. (Thanks Martin Joyce for tagging me) during the need for blood during the beginning of the COVID-19 shelter in place era. I love what Dan Finkel suggested via twitter – this is where the discourse comes in…

**Is this a math fail? Part 3. ** from March 2020 (Shelter in Place time)

Jessica Strom (another MN rock-star math leader) sent me this one during the beginning weeks of our time locked away in our homes in March. This was the time math was featured everywhere in the news (flatten the curve, growing exponentially….). This graph is great for discourse in your students. Why or why not?

Check out the graphs at the world meters Coronavirus page.

CAUTION: The content of this graph may trigger some students, so think about the timing of using it.

**Is this a math fail? Part 4. ** from Late April/Early May (during the stay-at-home era of the pandemic)

In Late April 2020, news stories turned to talking about what it would take to reopen schools. During this time, the CDC released guidelines for what that might look like.

What size would a classroom or a school need to be to assure students have the space they need to be six feet apart at all times?

**IS IT A MATH FAIL?** …or are we centering USA notation?

Take a look at this pic I was tagged in with the #mathfail hashtag. Is this a ‘math fail’?

If you look closely at the measurements of this drop cloth, you will see an interesting conversion. Eight feet is equivalent to Two thousand four hundred thirty eight meters! What! There is no way that a measurement 2 feet taller than myself can be the same as more than 2 thousand meter sticks. If so – this drop cloth, when opened, would cover _________________, much, much larger than a typical sized room in our American houses. This is a great problem for discourse. If this drop cloth really is 2,348 meters by 3,657 meters (or 8,915,766 square meters) – what size space would it cover.

But wait….perhaps the labeled measurements are correct and I am reading them wrong.

**2,438 m in most of the world is 2.438 meters where I live. **

This could be a great photo for opening up your student’s world past what we consider ‘normal’ in the US.

**Empowering Students – Discourse in the community.**

The **#mathfail** to the right came from my home state and my friend, Greta Bergman. Greta spotted this sign at her local Sam’s Club. What I love about this math fail is that Greta heard from a student’s parent that he was going to offer up ONE PENNY to pay for the sundae. Greta’s twitter thread said that the student ‘convinced management’ to give them a Sundae for a penny using their mathematical reasoning and communication skills. So empowering for students to see math at work. Love it! Would you be bold enough to do what this student did?

Here is another Greta Bergman find from February 2020 at a Target in MN

Greta had posted the same signage from Target in 2017. Still no changes in Target’s future. I loved how the #MTBoS community responded. This would be a great visual as you begin talking about inequalities.

** THE POWER OF A DECIMAL POINT**

Article: Decimal point error costs Catalina Foothills School District nearly $2 million

**POSTSCRIPT – CHANGE CAN HAPPEN** (way to go Denis Sheeran & Harry & David)

For the last several years Denis Sheeran has been on a #snowflakesarehexagons rampage during the holiday season – tagging companies on Twitter who are using non-6 sided snowflakes in their advertising and design. Last year (see #mathfail set #5) Denis went after Harry & David (the company) for thier misuse of snowflakes. Check out what happened this year… CLICK to read the thread of comments.

**IMAGES speak words**

The images we select to represent words matter. These images are great for the “What do you notice?” “What do you wonder?” routine.

**Love this one for next Valentine’s Day. Yes Molly!**

**Is Zero Negative?**

Laura Wagenman and Annie Forest both posted pics like this in January. What a great question and chance for discourse with students. Is zero negative? Why would the phone app do this if not? Could the temperature perhaps be -0.5 degrees and it rounded up?

**#UnitChat discourse**

This **#mathfail** image comes from my friend Molly Daley from Washington State. Molly posted it as an interesting #unitchat pic, but I think it would make a great **#mathfail **to inspire mathematical discourse. Check out Molly’s tweet.

Check out the hashtag #UnitChat on twitter for more great ways to add discourse.

https://twitter.com/hashtag/unitchat?src=hashtag_click

**more**

https://www.c-span.org/video/?468552-1/senate-impeachment-trial-day-7&vod

**Oh Stanford University!**

March 2020, during the time CORONA-19 shut down the NBA and all schools across America, Stanford grads started receiving a magazine that includes this add. Do you spot the problem?

**My favorite COVID-19 era #mathfail**

This image was first shared in March 2020 from locations all over the world as signs posted to remind us to ‘socially distance’. This image needs to be part of all Geometry classes this fall. If you teach 8th grade and will introduce the Pythagorean Theorem this fall – then this fail is for you. Give your students the challenge to ‘Fix this Fail’ and make a new sign for us to display outside.

Update August 2020 – I love that Chrissy Newell is ‘Fixing’ these signs in her sphere of influence! Check it out.

I also love Benjamin Dickman’s extentions to this sign…

**Billions and Millions**

Super Tuesday in March saw Michael Bloomberg drop out of the democratic presidential race and it brought us another #mathfail. It all started with this tweet…

Then came the ‘saddest clip in tv’ from Brian Williams on MSNBC commenting on this tweet.

You can see a whole article on the clip HERE.

**Rectangles and Squares – Via a 1st Grade Textbook**

Dr Kate Owens got us thinking about preciseness in our mathematical definitions in March of 2020. Check out her tweets about the definition of a ‘rectangle’.

**More with ‘Squares’**

This is the newest math fail in my collection from Lauren Johnson. Is this a fail? Why or Why not?

Is it a square if you don’t include the zipper portion of the bag? Perhaps you could get out a bunch of bags and investigate.

**The NY Times Crossword has a #mathfail**

The May 13, 2020 NYT Crossword had a mathy clue for row 50a

You can read about the solution to this puzzle HERE.** FIBONACCI SERIES**

**Scaling & Place Value Fail**

There are lots and lots of #graphfails in my 6 years of collecting #mathfails. This one found by Amie Albrecht is a new favorite for discourse. This fail has a really common math misconception related to place value. Show your students this graph and ask, ‘What do you notice?’ and start a discussion as a bell ringer some day.

**UGH – this might be one of the worst. Check out the horizontal scale.**

The state of Georgia’s Department of Public Health released this graph on their website May 2020. So many things are wrong with this. Yikes.

The original tweet with this graphic has been taken down, BUT comments to it are still up FOUND HERE in the thread to the original post..

The thread had many users who changed the graph above to look better. Here is a favorite. It may be a great “What is the same? What is Different?” graph pared with the #mathfail graph. The possible discourse has the potential for empowering students to create graphs that communicate accurate information.

**Fixing TURDs**

My friend, Christopher Danielson, coined the term ‘T.U.R.D’ for ‘Truly Unfortunate Representations of Data’ at his website years ago. During the Pandemic Era it has resurfaced online in the #MTBoS due to all the graph fails. If you love #mathfails – then also look out for #TURDs online. I love that Andrew Gael will be putting together a ‘Fix That Graph’ unit for his students. Think of all the great discourse that could happen in a unit like this.

**Line of Best Fit**???

If you are teaching a unit/standards on ‘Lines of Best Fit’ – Check out this graph. In fact check out the entire Twitter Thread below and look at the source and all the comments that would deepen your student’s exploration of this graph. Amazingly bad…

The Twitter Thread above is full of other cool stuff like this MEME…

**What is the Same? What is Different?**

July 2, 2020

This is my most recent #mathfail for Set #6. It is another COVID-19 #mathfail. This one is perfect for the ‘What is the same? What is different’ math routine. Asking students to discuss the differences is a safe way to foster discourse. These 2 graphs have the potential to talk about data manipulation and the how mathematics can be used within a political agenda.

**How to use #mathfails in Distance Learning**

I can’t end this blog without addressing the BIGGEST educational paradigm shift in our lives….the pandemic and the move to Distance Learning. Many places this fall will start school with distance learning as part or all of a students learning experience.

My favorite way to use math fails is to display them in the hallway outside my classroom. If I’m not in my classroom, what will this look like? I would be using #mathfails in a variety of ways…

- I would be making a VIRTUAL Hallway using google slides or a free website or….perhaps I would delve into a ‘bitmoji classroom’ type of thing. I would hang up many of the math fails from the last 6 years so I can have a ongoing display of #mathfails I can reference.
- Asking students to identify why something is a #mathfail is a safer question for most students. Rather than having to talk about their own mistakes, talking about mistakes of others invites more students into the discussion. For this reason, I would use one #mathfail each week (Maybe #mathfail Friday) and have students write about the math fail.
- I would use #mathfails as starters synchronously in an online class. I would have it displayed as students are signing on – giving them something to do as others join us.
- I would make #mathfails part of asynchrounous Choice Boards. (note: I don’t think you can do enough things that give choice to students during this time) Students could select a #mathfail from your virtual #mathfail hallway (number the math fails) and write about why it is a fail or why they like this fail or how one could fix the fail or have them record and upload a video talking about the fail. PRO TIP – Create an expemplar an annotated #mathfail visual with a short paragraph describing the fail and how to fix it to model for students what their work could look like.

You can find my previous 5 sets of Math Fails at the links below.

Set #5 – new summer 2019 112+ images

Set #4 – new summer 2018 87+ images

Set #3 – new summer 2017 93+ images

Set #2 – new summer 2016 72+ images

Set #1 – the Originals collected on or before January 2016 80+ images

**To download the 2020 set (#6) of over 100 new math fails, press the orange button below.**

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]]>The post Resources from my August 3rd Building Math Minds Virtual Math Summit Session appeared first on Sara VanDerWerf.

]]>The (free) Building Math Minds Virtual Math Summit 2020 is happening now through August 10, 2020. Have you signed up to attend yet? If not change that by going** HERE **to see who all the presenters are and register. Seriously, go do it now.

I will be speaking at this conference and communicating live on Monday, August 3 at 2:00 Central Time (that’s my time in Minnesota!) or 3pm Eastern or 12pm Pacific.

There will be so many other great speakers speaking over the Summit too. Please check out as many as you can.

My session is titled ** Safe Prompts for Entering ‘Math’ematical Discussions**. How can I motivate my students? Why aren’t my students engaged during mathematics? These are questions educators wonder silently and at times out loud. The answers to these questions are connected to building positive mathematical identities in all students. This session will explore ways educators of students at grade levels can practically structure their lessons to provide safe spaces for students to engage in discourse and mathematical reasoning. To prep for this session, google ‘babies eating lemons’, click ‘videos’ and as you watch the numerous videos as yourself, ‘What does this have to do with mathematics & your students?’. (or watch this session to find out)

You can read more about what babies eating Lemons has to do with ‘Math’ at my blog post entitled ‘What is Math?’ – This is a must for all K-12 math classrooms week 1 each fall.

For LINKS from my August 2020 Building Math Minds Virtual Summit Session on ‘Safe Questions for Entering ‘Math’ematical Discussions’ – including my PowerPoint – click on the button below to be connected to a Google Folder of Resources.

One last note. I am currently (August 2020) Reading, **‘Stamped from the Beginning’ by Ibram X. Kendi.** I highly recommend it. What I know for sure is I do not know a History that is not whitewashed well. I have lots of learning to do. If you are reading this too – I’d love to connect someday. Join me. Also – there is THIS VERSION of the same book written for Middle School Students.

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]]>The post green (REFERENCE) sheets appeared first on Sara VanDerWerf.

]]>**Why did I start making ‘GREEN SHEETs’?**

I am passionate in my pursuit to assure all my students, regardless of the skills and background they brought with them, make growth on grade level mathematics. If I am teaching Algebra 2, then all my students – even if some test says they are not ready for Algebra 2 – will be supported in making growth on Algebra 2 standards. I am a big believer in heterogeneous grade level classes for all. I support NCTM’s ‘Catalyzing Change’ books with recommendations like ‘Dismantling structural obstacles that stand in the way of mathematics working for each and every student.’ Specifically, I am against taking students out of grade level courses and putting them in courses that slow down the curriculum. I am against teachers teaching ‘7th grade math’ and only covering 60% of the curriculum because they feel their students are not ready to go faster. I believe that all students in my mathematics courses can grow and learn grade level material.

Challenging my beliefs my entire career has been a large portion (more than 50%, at times much higher) of students enrolled in my courses each year that are not academically ready to be there. Each year I have large percentages of students who arrive – due to EL status or homelessness or _____________ – with gaps in their education – due to no fault of the own. I have large numbers of students that are not proficient on our state exams. Regardless of this, I know that all of these students can do grade level mathematics. BUT – they can not do grade level mathematics unless I have a plan to support them in filling the academic holes/gaps they arrive with AND to do this with minimal time lost to grade level work.

It is so tempting to slow down my pacing and teach the things I know many of my students missed out on prior to the courses I teach. I don’t do this for 2 reasons. One, slowing down means that they will not have time for grade level work and this will put them further behind. Two, it is not fair to the students who are academically ready for the course they are enrolled in. (& again, as I said above, I refuse to create separate courses for students who are ready and those who are not for grade level work.

SOOOOOOOOOOO……….I created a plan to support all students being able to do grade level work in my courses. This plan has lots of parts. Green Sheets are just one of them. Green Sheets alone will not solve your challenge of supporting students who are not academically ready – but they will give you a tool that can be part of a larger overall plan (and they may be a great way to start). Sooooooo…….

**What is a ‘GREEN SHEET’?**

Simply, a ‘green sheet’ is one sheet of paper reviewing mathematical concepts, connected to current learning, for students to use in the math courses I teach. I call this one-pager review sheet a ‘green sheet’ because it is printed on green paper, specifically green card stock. Why green card stock? Have you ever tried saying, “*Students, please get out your review sheet on ‘solving systems of equations*‘. ” and then watched students spend 5 minutes digging through their folders looking for the right sheet only for 1/2 of them to get out the wrong one? I reserve the color green in my classroom to only be used for the 1-2 review sheets I make for students each unit. When I say, “*Everyone, please get out your green sheet on solving systems of equations*“, it takes moments for the entire class to have out the correct sheet. Saying ‘green sheet’ led to nearly 100% of students being successful with my request. It also allowed me to look across the classroom and see if all students had a green sheet out.

‘Green sheets’ are one of several ways I support the academic needs of my students who arrive in my courses with academic holes that cause them to struggle with grade level mathematics. For example, an Algebra 2 Unit on Solving Systems of Equations assumes my students are proficient already at solving systems of linear equations with 2 variables using a variety of methods (graphing, substitution, elimination and others). I know many of my students are not proficient with this yet. To support students I created a ‘green sheet’ reviewing multiple ways to solve systems of linear equations. A common green sheet I use at the start of each year, because I know students struggle with this is on using the ‘Order of Operations’. Each unit I create 1-2 one page review sheets on topics connected to the learning in the current unit.

**How I create ‘Green Sheets’. **

In preparation for each unit I teach in a course (6-8 units per year), I read through the goals of the unit. I read through the mathematical standards students are expected to master. I make a list of mathematical vocabulary for the unit. I ask myself, ‘Why might my students struggle with this unit?’. Ultimately, I ask myself…

I make a list of the prerequisite skills/concepts/vocabulary and then prioritize the ones I think are most important for success in our new unit. I assume many of my students will need support with this list, so I create a ‘green sheet’ reviewing these items.

For example, in my Algebra 2 unit ‘Solving Systems of Equations & Inequalities’, I knew that to be ready for the mathematics my students needed to have flexible skills for solving systems of equations with 2 variables, so I created a ‘green sheet on this’ skill.

After using these sheets in my classroom for over a decade, I have found that ALL students find these green sheets useful. If I don’t have one of these sheets in a unit – students often beg for me to create one. Students don’t find these useful though unless I help them to find these useful. Keep reading to find out how I do this.

When do I use ‘Green Sheets’ in class?

I pass out a unit’s new green sheet on the day of the previous units end of unit assessment. The new green sheet is usually the homework the night of the assessment. Students pick up the green sheet AND a one page set of practice problems. For example. If the topic of the new green sheet is ‘order of operations’ then students will pick up the green sheet pictured to the left. I will ask them to review/read it for 5-10 minutes first. (note: we’ve modeled & discussed ‘how to read for understanding’ prior to me asking them to do this). In addition to the green sheet, I give students 6 problems to do. The problem set includes ‘hints’ and ‘solutions’ to each problem. I ask students to spend a maximum of 20 minutes working on these problems. I do NOT teach them how to do each problem. I have selected problems that will draw out common mistakes that students will make with the topic.

Students arrive to class on the first day of the unit having looked at the new green sheet and attempted a few problems. (Note: 95% of my students arrive to class each day with complete homework – but that it another post on how I get such high percentages of homework completion). When the arrive in class I hand them an annotated answer key I’ve made of the 6 practice problems. I have modeled for students how to use ‘answer keys’ to maximize learning. Most of my students find the 5 minutes I give them to look over the answer keys extremely valuable. Many students take photos of the answer keys (I totally allow this) and I often find them pulling up these photos later on to study from.

**How much class time to I give to reviewing previous learning?**

Somewhere between 50-80% of the students in each class I teach arrive to my course with small to huge academic holes that get in the way of their current learning. If I were to slow down to fill all these holes, I would never have enough time to teach the grade level standards outlined in the courses I teach. To assure I can teach all grade level standards well, I have given myself a budget of TIME for each unit to spend reviewing. ** This budget is ONE 55-minute class period per unit will be used to review previous learning. **ONE and only one class per unit. My students often need way more than this, but I limit myself to 55 minutes. I may split this 55 minutes into 30 minutes one day and 25 another, but I force myself to prioritize the most important ‘stuff’ to review for each unit.

Most of my one day is spent reviewing prior mathematics learning needed for success in the upcoming unit. This review is always connected to the new ‘green sheet’. I believe if you don’t consistently use the green sheet with your students, they will never use it on their own.

**How I teach students to use their ‘green sheets’. **

At the start of each unit, I give students one (at most two) green sheet for the unit. Simply giving students a ‘green sheet’ does not mean they will use it. In fact, most papers I pass out or share with students are never read or used. If I want students to use the ‘green sheet’ then I need to TEACH them how to use the ‘green sheet’.

One part of doing this is to give students a small number practice problems they can do with the green sheet.

When students do problems side by side with their green sheet they start to see a usefulness to the green sheet. In the case of the green sheet above on ‘order of operations’, students work on the 6 practice problems independently (given hints and solutions). The next day in class I start class by saying, “Everyone get out your ‘green sheet’ on order of operations (I wait until I see every student with a green sheet out) and your set of 6 review problems – even if you did not complete them.”. I then give every student an annotated answer key with all my work shown to the practice set. Students independently review this answer key for 5 minutes. Then I take questions. Usually most students have very few questions at this point. I at most cover one of the 6 problems to review together.

Practice sets for new green sheets don’t all look the same. For example, in Algebra 2 my students needed to review ‘how to solve a systems of linear equations’ – past learning from 8th/9th grade Algebra. The green sheet had 8 different ways to solve a system of linear equations. I knew that my students may be overwhelmed with this working independently, so the first ‘practice set’ was just built to give students choice. I asked them to review the new green sheet and select 2 problems only to solve using any method they preferred.

In class the next day I said, “Everyone, get out your new green sheet.” and together we used this green sheet to solve 1 system of linear equations 6 different ways (graphing, substitution, elimination – 2 ways -, desmos…..). Student’s homework that evening was to do the same thing with a new system of equations using the green sheet. The next day they arrived in class and had a few minutes to look over an answer key. This was our one, and only one, day of review.

“** Everyone, get out your green sheet!“** – Modeling the use of Green Sheets in the classroom.

Using the ‘green sheets’ with students in my one day of review is NOT enough for students to continue using them independently. Students who most need to use the green sheets, will not use them. This is for a couple of reasons.

- They don’t know how to use the green sheets.
- They don’t want to use the green sheet and reveal they are not prepared (their is a sense of embarressment in some)

For these reasons, I feel it is important to teach all students how to use these sheets AND normalize the use of the sheets. One of the ways I do this is to make it mandatory for myself to use the green sheets in class, with all students, at least once every day the first 4-5 days of the unit. It sounds like this….

I then wait & watch until I see everyone taking out their green sheet.

I wait until I see everyone pointing at right box. Then I ask them to interact with this information in some way, like… *“Turn to your neighbor and tell them what grouping symbols are – hint there are more than 1 or 2 things to say, go”*

I have found that all my students, both those academically ready for the course they are enrolled in and those who are not, love using the green sheets. My students, of all types, love these green sheets. I have also found that using a new green sheet 3-5 days in a row is enough for most students to use them on their own the rest of the unit. Later in the unit, if I know that the green sheet would benefit some students, I will again say, “EVERYONE, get out your green sheet and….” – again, normalizing their use.

**How students feel about ‘GREEN SHEETS’**.

My students loved, loved, loved the green sheets I made. Not some students, but all. I have lots of evidence of this.

Students asked to use green sheets (review of previous learning) on assessments in my class. At first I leaned towards not letting them use them – but I decided to allow it. It turns out that the green sheets were like Linus’ blanket – it was a safety thing for them. They had it near by if they needed it, but 95% or more of the students never used it during the assessments. I found it relaxed their testing anxiety to have it nearby.

I would see my students using green sheets outside of class. My classroom was on 2nd floor, near the commons space that overlooked the lunchroom. During lunch, I would often see students doing homework and would have their green sheets out as part of this work. Our school had a ‘Math Center’, staffed by a math teacher, open all day that students could stop in and get help. The teachers in this center reported that my students always had their green sheets out, without prompting, while working on math. They even would loan them out to students from other courses, without green sheets, and use them to tutor other students.

At the end of each unit, my students would clean out their folders. I recommended saving their green sheets (along with a couple of other items). At the end of the year, my students had 8-12 green sheets and 6-8 yellow sheets (review of current learning – but that is a different post) that they could use to study for and use on the year final. Again, I found my students loved having these, but almost never took them out during the final. The pre-calculus teachers, the students next course after their course with me, reported seeing green sheets used the next year.

What I found is that if I made green sheets useful to them in class and normalized their use by everyone, students would use them, over and over again on their own.

**Making your own ‘GREEN SHEETS’**

I get asked all the time to share ALL my green sheets. If you are a reader of my blog, you know that I am willing to give away for free what I create. At the end of this blog I will share several green sheets I’ve created with you. My plan is to clean up green sheets I’ve created in the past and also create NEW green sheets on math topics I wish I had when I was teaching. Anything new I create I will share with you. My goal is to create about one new sheet a month for the next year to share with you. I will send new green sheets out to all those who have entered their email at my site (either on my ‘About Me’ page or by downloading any resources at my blog).

When I create green sheets, as mentioned above, I have two guiding questions.

I assume many of my students will struggle with the items I made answering the questions above. I create green sheet(s) to support students learning. My goal is to teach them how to learn. I create my green sheets based on what I know about my students. They are designed to support the students I teach. Because I’ve personally made all green sheets I use with students, I know them inside and out and it helps me use them with my students. If I used green sheets others created, I am not sure they would be as effective.

For this reason, if you want to use green sheets I’ve created, great. BUT if you plop them in front of your students – they will not be as effective as creating your own to match the needs of the students you teach. For that reason I HIGHLY encourage you to go through the same process I do. Before every unit you teach, ask yourself, “What does this unit assume my students already know how to do?” Make a list of every concept, skill and/or vocabulary term students should know. Then use the green sheets I’ve made as exemplars of possible ways for you to create your own green sheets. Make your green sheets to match the needs of your students. I know this takes time – but do it anyway. Make it a goal next school year to create your own green sheets for at least 1 or 2 of your units. The next year make them for other units. After a few years, you will have them for all units.

I am sharing my green sheets below as editable word documents. Feel free to take what you like of what I created and tweek it to make even better green sheets for your students.

I promise to continue adding new green sheets to what I am sharing today. If you create one you would be willing to share with other teachers, send it to me and I will add it to the folder of resources. (giving you credit).

Although I plan to create additional green sheets – the very best green sheets for your students will be created by YOU, not me. I encourage you to make your own green sheets.

**I’d love to hear from you. Do you have a topic you’d like to see me create a green sheet on? ****If so, let me know by filling out this quick google form.**

**A resource for creating ‘GREEN SHEETs’ **

Ultimately, a green sheets is a review of previous material that is connected to the new learning. Some curriculum resources come with pre-assessments that test this previous material. One FREE resource that I work with is Illustrative Mathematics. You can find the FREE versions at Kendall Hunt’s site (6-12) and at Open Up Resources (6-8) site. At both sites if you register with a teacher email, you can obtain access to all assessments. One way to create a green sheet if you are new to them is to use the unit pre-assessments at these sites to help you craft a new green-sheet. There are 2 ways to do this…

**Number 1 – Use ‘Check Your Readiness’ pre-assessments as is…**

Even if you do not use the IM curriculum (it’s great, by the way), you could use their pre-assessments (they call them ‘check for readiness’). Find a unit with topics similar to what you are teaching. Print out the pre-assessment. Give the pre-assessment to your students as a homework assignment with the directions, “*Spend no more than 20 minutes on this assessment. Try every problem. Show your thinking on each problem. I am more interested in your thinking than the answers. Circle the 1-2 problems that are the most challenging for you*.” The next day give students an annotated copy of the pre-assessment with solutions printed on green paper. Have them spend 5-10 minutes reviewing this. Take 1-2 questions from the class. Have students keep the green answer key and find ways to use it every day for the next 4-5 class periods so that students find it useful.

For example – Here is an assessment item from an Algebra 1, Unit 2 IM pre-assessment. This unit assumes students can solve 1 & 2 step equations. I would have my student’s try this item on their own and then the next day give them an annotated copy of those same assessment items printed on green paper (AKA – their new ‘green sheet’). Look at my annotations below. What do you notice? How might this be helpful to students? How could I improve this?

Here is an Algebra 2 assessment item. Think about how you might make an annotated answer key for this item. What could assist your students in understanding this previous material without you having to reteach this item. My attempt is below. I don’t think it is perfect and honestly I prefer creating my own green sheets as they are more organized , but in a pinch, this is better than nothing.

The Geometry Pre-assessment had items asking students to do constructions. In order to make an annotated answer key, I did a photo shoot of myself doing a construction to explain my steps. It looked something like this:

The geometry ‘green sheet’ also included a glossary to support students.

This glossary will only be used by students if I model it’s use in class. For example, every day you will hear me say, “Everyone, get out your Unit 2 green sheet. Put your finger on the ‘types of transformations’ box. Turn to your neighbor and tell them 4 types of transformations.”

**Number 2 – Use ‘Check Your Readiness’ pre-assessments to inform how you write assessments.**

I much prefer making my own ‘green sheets’. I want them to be at most one piece of paper front & back. In my ideal world they would be one sheet with only one side. Remember from above the 2 guiding questions I ask myself when I prep a new green sheet?

The great thing about using IM’s ‘check your readiness’ pre-assessments is they have done the thinking on these questions for you. The items on these assessments can give you the ideas for the content of any green sheet you may want to create. Don’t try and create ‘green sheet’ content for every single item on the assessments, Be selective. Which item(s) are most crucial for your student’s success in the upcoming unit?

**How would I use a ‘GREEN SHEET’ in the era of COVID-19?**

As I write this, everyone’s classrooms look different due to the pandemic. We are meeting virtually with our students. I can’t simply look around the classroom and make sure students have their green sheets out. What I do know for sure is that now, more than ever, our students need support for their learning. If I were teaching during the pandemic I would still be using ‘green sheets’. Here are a couple of thoughts on how I would be doing this…

- At the start of the unit I would still give out a green sheet. In the virtual sense I would share a document in a shared google folder or via my district’s LMS. I would encourage students to print this out. Knowing that many of my students who need this sheet the most would not have the ability to print it out, I would work with my school to print out the ‘green sheets’ and find ways to get them to students. (Even if I had to drive to students houses to deliver them myself – that is how important this is to me).
- When I meet with students virtually in a class meeting, I would normalize the use and say, “Everyone hold up your ‘green sheet’ – even if it isn’t green and show it on camera.” I would say, “point at _____”. I would normalize it’s use virtually, just like I would in class.

- For the many times I am not meeting with my students via ZOOM or other methods, I would write into the daily directions things like “Step 1: Prepare yourself for today’s work. Take out your green sheet and….”. If I were using Desmos, I would put in statements like, “Take out your green sheet.” into the directions. I would include pictures of the green sheet to normalize it.
- I would create a short 1-3 minute video for families introducing them to the green sheet and talking about how it can support their child.
- I also would be flexible with students not having it printed out and using electronic copies. If this were true, I would have them bookmark where their green sheet was, or download it as a document onto their ipad or….anything to make it easier for them to find and use.

**You ask, “***Sara, How can I get copies of all the green sheets you have created***?”. Let me tell you how!**

As I said above, I get asked all the time for copies of the green sheets I’ve created for my own students. Making your own green sheets for your own students will always be best, but I want to give you several copies of green sheets and practice problems I’ve created so that you can use them as potential models (although I know you can create even better content than I) for the ones you create for your students.

By clicking the orange button below, you will be connected to a google folder of green sheets and practice problems (all the ones above and more). I will be adding to this folder over time. If you are subscribed to my blog (clicking the button below does this) I will send you emails when I create new green sheets. My plan is to create one new green sheet (hopefully with practice problems) a month for the next year.

**One more note on ‘green sheets’**

I mentioned this in what I wrote above, but it bears repeating. I use green sheets as one of many supports for my students who arrive to the courses I teach not academically ready for the course. I have found that ALL students find green sheets helpful – but only after I have taught them how to use them and also normalized their use in class.

But……

If you think green sheets will magically make your students who struggle, to not struggle, you would be wrong. Green Sheets alone are not a magic bullet. Green Sheet’s are though part of the solution.

I am on a mission to build a classrooms where all students will grow mathematically, feel safe and empowered. A classroom where positive mathematical identities are built. I have 11 specific things I do to support students that arrive academically behind thrive in a grade level math class. Green Sheets are just one of these things. In my blog, I’ve written about other things I do. I’d love for you to use Green Sheets – but alone they will not magically make all students successful.

I’d love to hear how you support students in your courses. Comment below or tweet at me @saravdwerf. Until next time….

The post green (REFERENCE) sheets appeared first on Sara VanDerWerf.

]]>The post Modeling E-Learning (distance learning in the era of COVID-19) appeared first on Sara VanDerWerf.

]]>**Ultimately, this post will ask you to NOT assume your students know how to learn in an E-Learning environment and give you one thing you can do to help them as they transistion to learning from videos.**

Just so you know, I have never taught students virtually. For the last year and a half though I have led many virtual tranings for teachers and leaders ranging from 15 minutes to 3 hours. Like all things, I’ve gotten better at my work in this arena the more I’ve done it. Also, one year ago, I co-presented at my state math conference on ‘* Best Practices for the Math Flipped Classroom*‘ with an amazing teacher from St. Cloud, MN named Elise Morell. In prepping for our session, I interviewed tons of teachers, read lots of research and learned a ton about students learning at home.

Before I type the rest of this post though, please give yourself and your family permission to PAUSE before you even think about jumping back into education. Your emotional health is more important to me than anything in math. Find ways to connect with your family and with others – even if it virtually. Take time to catch your breath and tap into your JOY. When you are ready for it – read the rest of this post.

For a long time I’ve been planning on blogging on something all of us Math Teachers need to do more of in our classrooms. Sixteen years ago this ‘thing’ I am advocating for was given a name when I attended ‘Responsive Classroom’ training for my new school. At the training they said ‘* Teaching the social part of education is just as important – if not more important – than teaching the academic part.*” This means that as a math teacher, of course I need to teach mathematical concepts – but unless I am also teaching students how to do school, how to be in a community of math learners and teaching my students how to connect – I will never be teaching students mathematics effectively – teachers need to teach both content (academics) and how to be a student an function as part of a community of learners in our classroom (social).

An important aspect of teaching the social part of teaching is to **not assume student knew how to learn in a math setting**. Instead – anytime I do something new in class, **I should MODEL (teach) this new thing**. For example, if I plan to use markers for the first time in a school year, I should model the use of markers in a math classroom. If I want my students to discuss a math concept – I should first model how to discuss. In my own classroom I ultimately model anything that bugs me. If students are not doing homework, I model how to do homework. When I’ve done this my homework completion rates immediately went up. (someday I’ll blog about this and video how I model these things) If it bugs me students don’t how to take notes, I model it. When I hear other teachers saying things like “*My kids are so lazy this year – they won’t _________________________________*” – I am always thinking in my head when I hear this….”*This teacher needs to model _______________________ for their students*“. Modeling is something I do regularly and it has changed the culture of my classroom for the better.

**SO, WHAT IS MODELING?**

Since I’ve learned about modeling- I’ve modeled EVERYTHING. I’ve used exemplars. I’ve done think alouds. I’ve modeled all new things and asked my students to tell me what they noticed, observed & saw. **Modeling is basically modeling what you hope students will do and having them name what they say you doing. **(Note: You can read about how the people behind Responsive Classroom & how they define ‘Interactive Modeling’ HERE. It looks a bit different in my HS classroom – but many of the elements are the same.)

For anyone that has followed my blog, you know that my classroom planning goal is to create classroom experiences where ‘s**tudents will SEE it before I show them and SAY it before I tell them**.’ I always ask myself, “* How can I help students see what I want them to say?*“. Modeling fits perfectly into this goal. I show students how I hope they will do something and ask them to name the things they saw me do – ultimately my students name the things they should be doing as they engage in learning mathematics..

One example of this, that is the #1 most read post on this blog, is how I teach students to work in groups – specifically using the 100 number task. (read about it **HERE**) The goal of this task is to get students to tell me what great group work looks like (vs. me telling them). After students engage in the 100 # task – they say all the things I want them to say. Below is an example of what my students say – not what I said – good group work looks like. By modeling quality group quickly, students identify how all of us will look/sound and fell like every time we engage in group work.

So – as we engage in the brand new world of E-Learning, I am going to ask you to NOT assume your students, your children know how to work in this environment. I am asking to you ask yourself, how can I model this new environment for my students. How could we get our students/children to say all the things about how to best learn in an E-Learning environment before we ever tell them how to do it. The rest of this blog is on one way you can MODEL this new environment.

In this post, I am going to give you a way to **MODEL** for your students how to learn while watching videos. Many of us will be creating videos for our students to watch OR asking students to watch & learn from videos at sites like Khan Academy. One of the fears I’ve seen many expressing online is will students learn in an online, virtual environment. My answer to this is YES! – but only if you model it for them first. **They will learn in this environment if they can name, before you even tell them, the things they need to do in order to learn from a video. So how do we do this?**

**This is where my friend Elise Morell, a math teacher from St. Cloud who has been flipping her classroom for several years, comes in. She advocates that you start with having students learn how to do something non-mathy from a video first. For example, have them learn to juggle from a video and then have students name what they did in order to learn from the video. **

**Here is what this could look like in your e-learning environment. (Parents, you can do this too!)**

- Give students a choice of several videos to select from (see above). Each video should be between 3-15 minutes in length.
- Ask students to select a video of something they do not know how to do YET.
- Tell students to learn this new task using this video. Don’t tell them much more than this at this point. Tell your student they will perform this task soon.
- Give your students a timeline to do this. I recommend between 1-3 days.
- After 1-3 days, have your students perform their NEW skill. Teachers if you are meeting together virtually with video, do this as a show & tell. If you are not meeting together virtually, have your students perform their new skill for a family member and have their family member sign off on it. (or take their word for it).
- THEN –
**Ask your students to name how they used the video to learn this new skill. What helped them?**Things they might say are…

Who knows what else students may say? The list above is amazing. What if they brought the ideas from above to Math Videos? Follow up the conversation of what they notices by typing up a list of things your students/children will do as they begin learning from math (or other educational) videos. Below is an example of what that may look like. **Ultimately, whatever you give students should NOT be what I (Sara) typed up below. Give your students a list of tips using their words (note mine).**

**ADDITIONAL TIPS & NOTES FOR MODELING HOW TO LEARN FROM VIDEOS.**

**TIP 1: ** Don’t ask your students/children to learn something from a video until you have learned something first from a video. Seriously, learn something new first. You will do a much better job with your students if you first pay attention to how you learn when watching videos.

**TIP 2: **Give your students choice in the video they will watch. Down below you will see a few videos I recommend, you can also get a copy of my task with these links by clicking on the button down below. Although these videos are good – this is a perfect time to give your students choice in something they will learn. If you read my task sheet, you will see I let students select one of the videos I linked OR one they want. I did ask them to select a video with a length between 3-15 minutes and clear their choice with me first.

**NOTE #1: ** I highly recommend starting your new distance learning/E-Learning environment with your students with something that is NOT math. We are all a little overwhelmed. Start your journey together with something you can all laugh at as you do it. Start with something where students have choice. Learning something new together with your online classmates will build community and connect you with them in ways math sometimes struggles to do.

**NOTE #2:** I know that many students do not have easy access to watching videos at home. This post is not saying that your home/E-Learning environment must include videos. Not at all. This post is simply to say that if videos are part of your online curricula, then please MODEL how to learn from them.

If you would like a copy of my task sheet for learning from videos (shown above) OR a link to the PowerPoint Elise and I used in our session on flipping the math classroom (with links to other resources) – C**lick the button below and I will link you to these resources. ** As always, If you have ideas for me or would like to learn more on this topic, comment below or tweet me @saravdwerf.

**UPDATE March 19, 2020 – My friend and former MS/HS Science teacher, Jon Peterson, recorded a PODCAST connected to this , so if you prefer to listen to this topic, check it out HERE: ** https://www.buzzsprout.com/285701/3061270

**UPDATE SEPTEMBER 1, 2020: I am loving seeing teachers using this as a way to start their school year. Check out a couple of Twitter Threads with their results…**

Below are some of the videos your students may select to learn something new. If you are the adult reading this, you do the same thing. Pick a video below and learn something new. As you are learning, pay attention to how you learn from videos. What helps you learn? If you have a video you think I should add to my list, comment below with a link or tweet at me @saravdwerf.

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]]>The post Defining Circles appeared first on Sara VanDerWerf.

]]>There is a High School in the district I worked in for my entire career that is notorious for putting math content questions on their list of interview questions if you are interviewing to be a math teacher there. A favorite question of this type for many years (until word got out that they used this question) was, ‘**What is the definition of Pi?**‘. Off the record and according to several people who were part of these interviews, more than half of all secondary licensed math teachers who applied struggled with this question. They could talk about the number pi (3.14159….) & that this number is irrational. They mentioned ‘Pi Day’ and named formulas for the circumference of a circle and the area of a circle, but when pressed for more they could say little. How sad that so many math teachers struggle with a basic concept in mathematics.

I would say I was surprised by this lack of understanding, but I have my own evidence of math teachers lack of understanding of mathematical concepts. We are addicted to teaching skills – we can talk all day about how to use pi in formulas, but we struggle to see and talk about it as a ratio (circumference to diameter) or anything else like this. 11 years ago I started a job at my district office as the K-12 math lead. On a visit to a local alternative middle school I noticed a new math teacher hired was given room 314. I said to her, “Lucky you, you got the Pi room”. She looked at me and said, “What is pi again? Is that the golden ratio?” UGH!!!

Since I’ve learned of the HS’s interview questions and seen it for my eyes – math teachers lack of understanding of circles and ‘pi’, I’ve been on a mission to make sure my students would never have the lack of understanding some math teachers have around ‘pi’ and circles.

As you know, I believe our students are way more engaged when #mathMovement is a part of our classes. My students move every single day. I’ve written about numerous ways students move on my blog.

This post is about how I incorporate movement and mathematical discousrse into how I introduce the concepts of circles, pi and all the vocabulary connected to circles. I use these same ideas if I am reviewing these concepts. I’ve used this in Middle School when students first learn about pi and in High School Geometry and Trigonometry. I would also use these ideas with elementary students.

My goal always to create the experiences in my classrooms so that students will SEE what I want them to SAY. Below are THREE videos describing how I used movement to support my students mathematical discourse around circles.

**Video 1** is about students defining circles!

**Video 2** is about how you make the ratio of the circumference to the length of a circles diameter come alive! (Hello Pi!)

**Video 3** is about how I help students develop a circle vocabulary.

**One word of warning – this blog post is a bit different. To get all the information – you need to watch the videos below. **

Watch this first video to see how I have all my students move to form a circle without ever using the word ‘circle’!

Watch this 1st video to learn about a really cool ‘Math Language Routine’ from the University of Stanford that incorporates **#mathMovement**!

Watch this video to see how students engage in discourse to build a definition of a circle.

I have a love/hate relationship with Pi Day! The hate part is seen in this tweet thread from Dan Meyer.

EVERY DAY EXCEPT MARCH 14: "Math isn't about memorizing random bits of information."

MARCH 14:

"PRIZES FOR ANYONE WHO MEMORIZES 500 DIGITS OF PI"— Dan Meyer (@ddmeyer) March 9, 2020

Too much of how Pi Day is celebrated is connected to low level memorization and not the beautiful relationships in Pi. There are so many other wonderful things you could do on March 14th – than just memorizing digits of Pi. If you need one small way to start this – Check out video #2 where I have students start to build an intuitive idea of Pi – you could expand the ideas in this video to really do something special with Pi.

In Video #2 you will see why having rope/yarn of 3 different colors can quickly help your students see the relationship between the circumference and diameter of a circle.

In Video #2 – it is all about ratios and comparisons! Check it out….2 great ideas for building the beginning ideas of ‘pi’.

Since most of my career has been teaching lots of Immigrant students and many others who have a low academic vocabulary – Video 3 is set up to connect Circle Vocabulary with Movement & Discourse. The goal the entire time is for students to say the definitions for all kinds of circle words way before I say them.

**BONUS** – my favorite #mathFail is in this video. It is one I got from the amazing Greta Bergman!

I hope, after watching these 3 videos, you have lots of ideas to build into your practice #mathMovement, having students engage in discourse (they say it before you do) connected to concepts – and in the case of this blog – the concept is ‘CIRCLES’! If you like adding movement connected to mathematical concepts into your classroom and want more ideas – comment below and say ‘Sara, I want more!’. I have more ideas for you on lots of other topics.

When you start getting ready to teach circles – make sure you are using resources that are conceptually rich. I love, love the Illustrative Mathematics Materials. Check out 7th grade Unit 3 and Geometry Unit 7 on Circles. See the button below to download links to rich curriculum. I also included an oldie but a goodie and connected you to the IMP curriculum’s resources on Circles – again, click the button below for more.

Here is one small curriculum teaser for you. IM has a movement activity on day 3! It is similar to my videos above but for defining ‘perpendicular bisectors’….so, so good. Check it out HERE: Illustrative Mathematics (IM) HS Geometry, Unit 1 Lesson 3 Activity 2 – Human Perpendicular Bisector (as found at Kendall Hunt website)

If you would like the power point I used in the 3 videos above – or resources on ‘Math Language Routines’ or get links to conceptually rich curriculum for Circles – **CLICK the button** below to gain access to a Google folder full of resources for you!

Click HERE to gain access to a Google folder of resources about Circles, Movement and Discourse.

How are you using** #mathMovement** do review or introduce mathematical concepts like ‘Circles’ in your classroom? Comment below or tweet at @saravdwerf or using the hashtag **#mathMovement**. I’d love to hear your ideas and/or questions.

- My favorite way to move everyday! Stand & Talks
- Movement review activity –> Balance Points
- Movement in common Math Instructional Routines
- Movement when reviewing or introducing Circles -> Defining Circles

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]]>The post What is the most important question you should ask in mathematics? appeared first on Sara VanDerWerf.

]]>For my entire teaching career (getting closer to 30 years) I’ve been asked to focus on working on my questioning of students in the classroom. I’ve been given countless sheets with sentence stems for asking good questions in the mathematics room for both me and students. The amount of questions on these sheets are so many that I, like many of you, never ask any of these questions with regularity. The goal of this post is to give you ONE – and only one (type) – question that I want to propose you should be asking every single day in your classroom – over and over again. ** Do you have any ideas what this ONE question may be?** Keep reading.

During the professional development I lead I often reference the one question I ask more than any others when I teach (though this is NOT the question this blog post is about). What I often say is this question is **“What Else? What Else? What Else?”** – a lesson I learned years ago from Annie Fetter from her ‘Ever Notice what they Wonder?’ ignite video. In the video she advocates for asking mathematics students “*What do you notice? What do you wonder?*“. These simple questions are now a common mathematical instructional routine being written into most new curricula and modeled in PD sessions everywhere. WDYN? WDYW? are great questions – but learning to ask, ‘**What Else? What Else? What Else?**‘ is powerful as the first 3-5 things students say are not that mathy – but when you ask ‘What Else?’ several times – students always start saying mathy things they notice. (Note: Do not tell students to not say the first 3-5 non-mathy things – this will only impact their mathematical identity negatively – let them say these things and chart them with everything else. If they see a llama write it down).

I would love it if all math teachers asked ‘notice/wonder’ and ‘what else….’ questions daily – but those are NOT the most important questions a teacher should ask every class period. **So, what is the MOST IMPORTANT question I believe you should ask all the time in mathematics?** First a story. You can watch it in this video or scroll past the video to read the written version of what is in the video.

Several months ago I was observing in a alternative High School with my math leader friend Brooke Williams. The class was full of students who were working on everything from pre-algebra to calculus depending on their background and what they needed for graduation. The teacher had a system for students to work independently. As the teacher was working with other students, a student caught Brooke and my eye. We went over and asked him how he was doing. He was working on problem 4 on a sheet where he was being asked to multiply binomials. This was his work.

The student responded to our question of how things were going by saying, “*This is my work. I think it’s right*.” He had a note of uncertainty in his voice as he said this. As a 6-12 math teacher my mind immediately started diagnosing what I thought maybe he was uncertain of.

I thought, ‘*Maybe he is unsure of how to write variables and coefficients (noticing the ‘s7’ vs ‘7s’ we normally write it as) or maybe he does not know what to do next and does not know how to combine like terms*.’ In my mind I was jumping to conclusions of how to treat what I thought was wrong with him. As I did this I heard my math leader friend Brooke ask him, “**Why did you say ‘I think’?**” The student went on to say, “Well, I am not sure about the sign on 14. I am not sure I am multiplying negative Numbers correctly.” As an experienced teacher, I never once predicted this student was struggling with this as the sign on 14 was correct. If I had jumped in and treated what I though he was struggling with – I would have wasted his time. My friend Brooke quickly had a conversation with him around multiplying integers and quickly gave him confidence he understood this. Moments later, without our help, he recorded the correct solution on his paper.

Brooke with her question, “**Why did you say, ‘I think’?**” had surfaced his reasoning. She was able to support him in what he was unsure with and build is confidence as a mathematician.

The power of the Brooke’s question “* Why did you say, ‘I think?*‘” is that the young man could have said almost anything. He could have said, “

**I believe Brooke’s question, “Why did you say __________?” is the most important question all math teachers should be asking more than any other question in our classrooms. **

I believe the question ‘Why did you say __________?’ – when we as math teachers learn to ask it every class period multiple times – **becomes the best formative assessment we will do in our classroom**. It provides real-time evidence of student reasoning that we can act on immediately.

Max Ray did an incredible IGNITE talk years ago titled ‘*When is 2 greater than 4? A proof by induction.*‘. I call it… ‘**The amazing 2>4 video**‘. If you’ve never seen it – stop what you are doing for 5 minutes and watch it now.

In the video Max talks about how and what we math teachers LISTEN for. He asks, “** Are we LISTENING 4 answers or LISTENING 2 students**“.

I know for a lot of my career, for most questions I asked in the classroom, I was listening for the answers I wanted to hear and as soon as I heard them I would move on. It created a culture in my classroom that was about answer-getting. The culture in my room was not about surfacing student reasoning. (Sidenote: If you’ve never seen Phil Daro’s video ‘Against Answer getting’ – it’s amazing – check it out HERE.) As I began to transform my classroom and devalue the race to the answer and value student thinking I realized one of the first things I had to work on was to really surface student thinking. I had to change how I questioned students and ask about ideas and not answers. Then I had to listen to students and not for the answers. The question that has transformed my classroom more than any other were versions of the one Brooke asked the student in the story above.

August 2015 was the first year of ‘Math On-a-Stick’ at the Minnesota State Fair. Math On-a-Stick is the creation of Minnesota Math Leader Christopher Danielson. At the 12 days of math fun the first year we watched as families interacted in the space with their children. Some parents would let their children play with the math experiences without interrupting them. We also saw some parents jump in and tell their child how to play with things at the table saying things like “*Why don’t you build a patern*” or “*No, do it this way*“. Many times – adults jumping in to interrupt the learning would shut down the child’s natural curiosity and play in the space. Some parents would, as their students as they played, say, “*Tell me what you created*” and we would hear the child excitedly explain to their parent all about their thinking – and the child would create more. What the parents said and did not say had a powerful impact on how they interacted with the mathematics in the space. Christopher wrote about what he observed that first year in a piece on his blog titled “Let the Children Play”.

What I learned the first year of Math On-a-stick to do even more of in my classroom was to give my students the space for them to make meaning and for me to not try and control every aspect of what that looked like. I learned to ask questions that would surface their reasoning. I started asking more “Tell me about what you ‘ve done so far” “How did you get __________” “Where did the number ______ come from?”…..

Check out his recent tweet from the online math community #MTBoS that connected to me of a visual Tracy Zager uses in PD.

You can hear Tracy’s own words about this picture in a Global Mathematics Department titled “How will we know what they are thinking?”. I love her picture of Heidi Fessenden (skip ahead to the 5 minute mark to see this photo) and what Tracey calls ‘the new posture of teaching mathematics’. This is what I need to look like in my classroom. I need to be listening to what students are saying and not listening for just answers.

As a Secondary Math Teacher – I use the visual pattern each fall in the first week with students. I don’t start with it this way though. I start with just one of the 3 images above in a math talk. I ask “*How many white squares do you see?*” I follow this up with my favorite question – the question that will help me surface student reasoning, “* How do you see that number?*“

Check out my nephews above. The spent 1.5 hours like this as my father introduced them to his favorite game and they played with him. I would love it if I could create the conditions in my math classroom so it looked like this every single day. I love using my nephews occasionally to try out mathematics I am doing with students. In order to have them engage in the task above, I got out my square block manipulative. I started by building the first shape in the picture using blue and orange blocks. **One at a time I asked my nephews – ages 4, 6 and 7 – how many blue squares there were.** **I then asked them – How do you know it is 8 blue squares?**

I asked my 4-year old nephew, “*How many blue squares to you see*.” After thinking and interacting with the squares he excitedly said ‘8’. I said, “* How do you know it is 8*?’ He put his cute chubby fingers on each square and counted ‘one, two, three….eight, nine….”. I’ve learned to not interrupt student thinking (my old self would have jumped in and corrected him double counting) and watched as he caught his mistake and started over and pulled one each blue square away from the inner orange square to count. He looks up and smiled at me when he got to 8. As a Pre-K student – his one-to-one correspondence of number to object is totally where he should be developmentally. (proud aunt).

I then asked my 6-year old nephew in the fall of his Kindergarten year – “*How many blue blocks are there?*” He looked at the shape and quickly said ‘*8*‘. Developmentally he should still be one-to-one with number & objects like his brother – but rather than assume I asked, ** “How do you know it is 8?”**. To which he excitedly moved the top 3 blue squares up and said, “

My 2nd grade, 7 year old nephew, also quickly said, “8” when I asked him how many blue squares there were in this shape. I also asked him, “**How do you know it’s 8?**“. To which he replied, “*Well I know the whole thing is 9 and I took the one away.*” After he said this I thought, ‘my 2nd grade nephew is mathematically advanced. It is September and he is beginning to see groups (3 groups of 3) and multiplying’. But instead of assuming this was correct, I asked “** How do you know the big square is 9?**“. The 2nd grader said, “

Later I asked my 2nd grade nephew about how many blue squares were in a larger shape. He did not say, ‘I*t is 15 and take away the 3*“. He did not have this shape memorized and he used similar thinking to his 6 year old brother to determine there were 12 blue squares.

By asking my nephews to not just give me an answer and have me celebrate the correct responses and fix their responses with misconceptions – I’ve instead learned to always ask some version of… “**How do you know _________?” **of them. This question reveals their mathematical thinking. It reveals their assets. It reveals how they see the world. It reveals not just how they think mathematically, but aspects of their humanity. I am am a better aunt to them, when I listen to them instead of assume or direct. This is the attitude I also need to keep as a daily practice with my students. It is a daily practice I need to bring to my work with adults.

In conclusion, I’d love it if you joined me in working to – in the words of Max Ray – ‘**Listen TO our students vs listening for answers’ and to ask questions that surface student reasoning.** My favorite question(s) to ask are some form of the ones below. I believe all 4 of these really are the same question.

I ask you to join me in not assuming we know what students are saying by their words. I ask you to daily follow up student responses with “How do you know _______? and to ask questions that will give us a window into how we can support their learning (formative assessment). If you are like me, it will take some time to develop this norm in your classroom – but when we do we will begin to see more of our students assets and take our focus off of what they get wrong.

**I’d love to hear from you! What questions do you think we should be asking in the classroom? Comment below or tweet at me @saravdwerf. How do surface student reasoning and decrease the culture of answer-getting in your classrooms? I’d love to learn from you!**

**For even more thoughts on LISTENING TO STUDENTS REASONING & the questions we should ask – keep reading to learn from other educators. **

Check out some cool threads on twitter about listening to students and surfacing their reasoning. The online community of math teachers has been a huge support for me to deepen my own practice around asking the questions in this blog.

I am so excited to see this resources from Marilyn Burns fall 2020 – Listening to Learn – check out her website to learn more.

**“ Our job isn’t to fix them **(our students who are stuck)

This thread on surfacing student thinking from Dan Meyer recently is chock full of great ideas from him and so many other educators….

**A final thought – on surfacing reasoning with adults – not just students. What are the most important questions we can ask of one another?**

The questions I am advocating asking students in this blog do not just work with students – I need to use them with adults in my life. For example, I saw this on a teacher Facebook page when I was writing this blog. I immediately started scripting a response to the teacher referenced in this post if she were my nephews teacher. My first thoughts were quite negative. I assumed things about the teacher and what they valued in math education.

If the pictured worksheet were given to my nephew in pre-school and I believe in listening to teachers not just for the answers I assume they will say – My question to the teacher should take a similar form to what i am advocating we ask of our students. For example, I may ask this teacher, “*What were the activities that led up to this worksheet?*” This teacher may go on and tell me all about these amazing Montessori concrete manipulative experiences my nephew may have engaged in before this sheet were assigned or they may tell me __________….who knows what – but what I know for sure is listening to the teacher will further the conversation more than me listening for the evidence to justify my anger at seeing this assigned to 4 year-olds.

This weekend I was hanging out with my nephews again. I got a text from their mom, my sister-in-law, saying they wanted me to bring my ‘pop-up game’. So of course, I brought my old-school game, Perfection, for my nephews to play with me. After one round my 7-year old nephew, the 2nd grader, exclaimed – “*I got 23 pieces!*” To which I asked, “** How do you know it is 23?**” My nephew smiles up at me and says, “

**Side Ending Note:** In this nation we have great messaging for parents around supporting literacy at home. Most parents will say, “I know we should read 20 minutes every day to our kids.”. Let’s start a campaign that families can support mathematics at home by playing games together for 1 hour a week. As we play games, let’s ask kids “How did you know _______?” and listen to their reasoning. In the words of Christopher Danielson, Let’s let our children play and make meaning of the world they live in without forcing our idea of it on them.

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]]>The post How Kobe Bryant challenged me to be a better math teacher. appeared first on Sara VanDerWerf.

]]>Hello friends! In the past I’ve blogged HERE and HERE about this topic – though it was buried in middle of other messages. With the recent passing of Kobe Bryant and his daughter (and several others), I have taken an image I wore around my neck while teaching out of storage and used in it in multiple professional development events I’ve led in the last month. It has resonated with many I’ve shared it with, so I thought I’d re-blog about it so you all can be challenged in the same way I have been by Kobe Bryant and a graphic representing his NBA career. Feel free to watch this short video explaining this OR read below the video link for more.

In 2016, I found the following graphic from an article on the cover of the LA Times the day Kobe Bryant retired.

When I first found this graphic I used it with my students. I removed information and asked them to Notice & Wonder. Here are some of the things student noticed and wondered. (note: I’ve been using this graphic with teachers so some of the notice/wonders are teacher words)

After some Notice/Wonder I revealed that indeed this was a Shot Map from Basketball and that the purple dots represented made shots and the gold dots were missed shots. I revealed that these dots represented every shot Kobe Bryant ever shot in his 20 year NBA career – all 30,699 of them. This graphic was in the LA Times the week he retired from the NBA.

I highly recommend you check out the LA Times version of this graphic because every point you see in the graphic you can hover over and get information on the shot (which game…etc) and you can break apart the layers and see the success of different types of shots and so much more. **Check it out HERE**.

I loved this graphic so much I laminated it and wore it around my neck. My math teacher peers liked it and asked for copies of it too and wore it around their necks. It was a great conversation starter. An elevator message about Productive Struggle and Mathematics. Kobe Bryant missed 55 percent of all the field goals he attenmpted and was still consdered one of the greatest basketball players of all time. In the era of Jo Bolar and growth mindset we used this graphic to normalize struggle in the mathematics classroom. We would say, “*You are not going to get fast answers (purple dots) all the time. There will be times in math you struggle. Sometimes a lot, but you can be considered the most amazing math student of all time even if you struggle. The yellow dot days are just part of your journey to be a great mathematician…etc…etc*”

This graphic was great to use with students. I would hear them say “*I’m having a purple dot day*!” with excitement or sometimes tell their friends, “*Don’t worry. Stick with it, you are just having a gold dot day*.”. Despite it’s success – our (me and my math teacher peers) were using this graphic with the wrong people. Our students were amazing. They are not the ones that need to change the most for them to be successful. We, their teachers, needed to push ourselves to change. We started using this graphic with ourselves.

My A-ha for how useful Kobe Bryant’s Shot Map was for my career came the day I did some arithmetic. Check this out. I calculated how many lessons I might teach in my entire career as a math teacher.

Shockingly, the number of lessons a career math teacher will teach in a career is pretty darn close to the total number of shots Kobe took in his career – 30,669. This mathematics gave me a new lens to bring to this graphic. What if every dot in this graphic represents one math lesson I will teach in my career.

I will have lessons that work (purple dot lessons) and lessons that don’t (gold dots). I could be considered the greatest teacher of all time even if I have more missed lessons than perfect lessons. In this testing era I started using this graphic as healthy self talk for the stresses of my job. In the testing culture, I don’t need leaders, data meetings or others to point out where I am getting it wrong. I am already harder on myself than anyone else. This stress could result in me leaving the profession. To stay in, I’ve had to use positive self talk to quiet the negative voices.

The coolest thing about this graphic for me (and I would argue for other teachers) was found in articles written about Kobe at the time of his retirement. People were arguing where Kobe ranked in the best list of the greatest NBA players of all time. One argument for Kobe to rank high was that his Shot Map was different than many other players. Many players played to their strengths and their dots were clustered to the left (if they shot left) or to the right. Some players maps had dots almost all in the inside. Others only from 3-point land. Kobe was considered dangerous (and therefore GREAT) because he could successfully shoot from all parts of the field. He was a balanced player.

I started thinking about me in my classroom. When I entered teaching I taught from the part of the teaching field I was good at – the part of the field I had found success in as a student. I collected purple & gold dots from only one part of the field – using a “**I do, we do, you do**” teaching motif. One day I took a risk using a radical math curriculum and asked students to make meaning of a rich task. It was bumpy at first but then purple dot days came and I saw students making meaning of math concepts I had not taught them.

15 years ago I met my math teacher peer, Allison Rubin and her students moved/danced in math class every day and were so engaged. Research confirmed that students who move are more engaged in math – yet I hesitated to try this with my students. It was a part of my teacher Shot Map that had ZERO dots. I feared the yellow dots that may come and when they did come I stopped. I never had purple dots on this part of the field because I gave up.

Kobe Bryant is quoted as saying he would get up every morning and shoot 500 shots, eat and shoot another 500 shots. 1000 shots a day. Many gold and many purple.

To diversify our teaching to do what research says is best for students – we teachers need to be like Kobe and take risks and stick with them through the gold dots (failure) to get to the purple dot lessons (SUCCESS!). Luckily, I did this for movement. I started with Stand & Talks – something I’ve done for 10+ years every single lesson and every single student talks about math every day (purple dots galore). I’ve added other #mathMovement activities that lead to discourse like Balance Points and Movement with common Math Routines. Purple dots, purple dots – with a few gold dots.

I have lots more parts of my teacher game to continue working on – places from the field I rarely if ever go due to fear or neglect. I am pushing myself to think about the equity work I’ve engaged in. It has been lots of reading, talking and not enough action yet. I want to be bolder to work to dismantle the structures I’ve established in my classroom that advantage some and not others. I want to learn more, but more importantly do more. I want to use more of Peter Liljedahl’s Building Thinking Classroom work on Visibly Random Groups and de-fronting my classroom and having students work more often vertically. I want to incorporate more math routines like #CthenC or **Contemplate** then Calculate….and so many more things to work on.

I hung Kobe’s graphic by my work space in 2016 (and still have it hanging there) without words to **Challenge Myself that if I want to be considered the best math teacher of all time, I need be be a balanced teacher. I need to work on the parts of my teaching I am not good at yet. It does not come without fear. But am I willing to decenter my comfort to do what is best for students. To do what research says is best for students? **

Kobe Bryant has been making me a better teacher since 2016. He has challenged me to be more balanced math teacher and to work on the parts of my ‘Shot Map’ I’ve avoided or feared. A few days after Kobe’s passing I was scheduled to do a day long PD with HS teachers in Los Angeles. Our training space is in a building downtown on the 18th floor with huge windows overlooking downtown. On that day I looked out he windows to see Kobe’s face and the numbers 24 and 8 covering buildings all over LA. As our PD started I shared this image with teachers. All but one had never seen this graphic of his 30,669 shots. The graphic book-ended our work together that day. I’ve heard from several teachers that this picture challenged them more than anything else I’d shared from my previous visits. My hope is you too will be challenged to use it.

**A note to LEADERS** (principals, coaches, superintendents…): One reason many of the teachers I work with are afraid to change is a fear of disappointing you and the testing culture in our nation. They would love it if you told them that you know ‘Gold Dot’ days will be part of the norm as they implement best practices and together you will work towards ‘Purple Dot’ days.

If you would like copies of Kobe’s graphics/badges and all sorts of things I used with students and displayed inn my classroom, click the link below for a google folder full of resources.

I’ve used Kobe’s graphic above in all the PD I’ve done in the last month since Kobe’s passing with thousands of teachers. At breaks and during lunches I always have teachers come up and ask me how this graphic was made. My response to them is, “*The people with the sexiest jobs in mathematics make these visuals*“.

What is the ‘sexiest’ math job out there? I decided to as the #MTBoS community what they thought and see if it matched what I said. Check out this thread.

I want to make an argument for what is in my opinion the ‘sexiest’ math job a student can pursue right now. Sexy is just my term to distinguish between what is desirable to students and what is not. I don’t think saying to students ‘*you can be an Engineer someday, so pursue mathematics*‘ or ‘*learning math could lead to becoming an actuary someday and there is lots of money in this*‘ is motivating for most students. You know what is potentially desirable for many students (thus the use of my term ‘sexy’) are jobs that can connect our students to their favorite sports team. I believe ‘Sports Analytics’ is the sexiest math job in 2020 and the next several years beyond. One could have zero athletic skill, but excel in math and be in the room where the excitement happens at the highest level if you pursue this career.

The movie Moneyball made this job field come alive. In the last 10+ years – almost all major sports teams (and college programs) have invested heavily in these positions. Anyone who wants to broadcast sports these days invests heavily in Sports Analytics. The number of real-time data nuggets coming out of sports casters during games and scrolling across the bottom of our TV screens all come from this sexy math profession. What sports do your students love? Start finding the data being created for these sports and share them with your students.

Check out this feature on Lakers Genius Data Scientist – Diana Ma.

Read more about data’s impact on sports **HERE** and **HERE** and** HERE** and **HERE**. Also, check out this post on famous Statisticians and this article: Visualizing One Million NCAA Basketball Shots

Sports Analytics has created even more cool graphics like the one I highlighted above from Kobe. Check out this example:

The best NBA players at every spot on the floor

How Mapping Shots In The NBA Changed It Forever

You can finds tons of Shot Maps like Kobe’s at ESPN and other sports sites. ESPN makes real time graphics like Kobe’s. Check out a recent NBA game, January 27th, of my home NBA team, the MN Timberwolves (they are not doing so well – be kind) and the Kings. Check out the game time probability. This game went into overtime – These graphics have the potential in your classroom for great mathematical conversations.

The Graphic I blogged about above for Kobe is pretty darn cool to look at and even more fun to interact with if you go to the LA Times Site. There are tons of graphics like this created every day and week for sports of all kinds. If you want to spice up your math classroom with authentic real time data – start following statisticians and sites that create graphics. Let’s be honest – most teachers never have enough time to teach the entire resource/set of standards they’ve been given and the thing that gets cut the most is the ‘Data & Probability Unit’. Such a shame since data literacy will be a necessary job skill for almost every student you currently teach. What if? What if? **What if you could embed data and probability experiences in your weekly routine with your students?** It is pretty easy to do if you are following on social media (and other places) places that visualize data and make it interactive.

I learned a lot of where to find this data from Jared Engel, a young mathematics teacher in the Milwaukee area. He teaches Geometry and AP Stats. Check out a graphic he used recently with his students.

He found this graphic at ESPN’s site and covered up some of the labels and asked his students to notice and wonder. After doing some notice/wonder he revealed the titles he had covered. As a class they told the story of this data.

When I asked Jared where he found this graph to make his graphic he said, graphs like this are made, in real time, for every basketball game at ESPN’s website. Check out this LINK for a Marquette & Xavier game (remember Jared is in WI). **CLICK** on ‘**Gamecast**‘ at this site to see the graph. Find the ‘game flow’ graph and **CLICK** on ‘**Win probability**‘ How might you use graphs like this in your classroom to tell the story of basketball games? What other graphs might you find at ESPN’s site you could steal and use?

On famous Statistician in the US is Nate Silver. Nate gained fame during Obama’s first election when he out predicted others down to most counties across America. As a result he made the cover of Time Magazine and the NYT’s gave him his own company to fill with other statisticians. If you are not following FiveThirtyEight – stop what you are doing and do it now. FiveThirtyEight is a website full of sports, political and so much more data and visualizations. 538 is the number of electoral votes needed to with the presidential election. Why wouldn’t you pay attention to this site in an election year?

Collin Malaney is a young math leader in Minnesota. He is the secondary math lead for St. Paul Public Schools. Collin connected me with the site ‘**Chartr’ – A data storytelling site**. (seriously good tag line – a ‘STORY TELLING’ site – data can tell a story – what if math class looked like this?) Enter your email to receive free charts sent to you. How might you use these in a class to tell a mathematical story?

Here is the graphic that popped up when i went to ChartR right now…

What could you cover up in the graphic above to make an interesting discussion in your class? Here is another graphic…

Data People to Follow on Twitter:

- ChartR
- Five Thirty Eight
- Data is Beautiful
- What else? Where do you find data and visualizations you can bring into your math classroom?
**Comment below or tweet at me and I will add your selections to this list.**

If you think sports analytics is just for the pros – you are so wrong. Check out this small town Minnesota High School (Pine City HS) who was featured in the Wall Street Journal a couple of years back on how the use of Sports Analytics (the coach was the HS math teacher) transformed their game (I’ll give away the ending…they only shoot 3-pointers and lay-ups the entire game as they have the greatest potential, using mathematics to get points). **Check out their story HERE** at the WSJ and HERE with a video from our local news staion.

Check out the coach presenting at a Coaches Conference.

OK – I am done now. This post was way, way longer than I set out to do. Crazy. One day I’ll work on my blogging Shot Map and start working on writing concise informative blog posts. When I do – even when I have yellow dot blog posts – perhaps someday I’ll be considered among the best education bloggers out there. I am not done learning yet. I have lots of practicing to do. Hopefully you will find some purple dot nuggets in this blog post you can bring into your own work. Go be amazing, my friends.

The post How Kobe Bryant challenged me to be a better math teacher. appeared first on Sara VanDerWerf.

]]>The post #mathMovement ideas with well known Math Routines appeared first on Sara VanDerWerf.

]]>There are so many amazing math routines, many with websites full of resources. These math routines, when implemented well, will increase student mathematical discourse. I would argue that many of these routines are even better when students are standing and moving. Check out a few of the routines I think benefit from a bit of **#mathMovement**! Try these out with your students. **Students need to move every 25 minutes each and every day. ** Below are some ways you can use to add **#mathMovement** to your daily routine in class.

#mathMovement with **Open Middle**

The **Open Middle website** is a curated set of K-12 challenging math problems worth solving. Robert Kaplinsky wrote about implementing ‘open middle’ problems in his 2019 book ‘Open Middle Math’ from Stenhouse. Open Middle Problems are perfect to do while vertical. Ideally have your students work in groups of 2 or 3 on an Open Middle Task at #vnps Vertical (standing) Non-Permanent (white boards…) Surfaces.

If you are not yet at a point where you have enough ‘non-permanant’ stations around your classroom – do what I use to do. A lot of the ‘Open Middle’ tasks ask students to manipulate the digits 0-9 to solve a math challenge. Have students pull out 10 post-it notes (stickies) and place the digits 0-9 on each.

Go to Open Middle and look for a task to use.For example check out this task from Graham Fletcher:

This task only uses the digits 1-9, so get rid of your post-it note with zero on it. Write up the form of this task on chart paper (or photo copy the frame of the task on paper to tape to the wall) I transformed Graham’s original task to write the ratios in fractional form. I made boxes for each digit and when I drew them I made each box approximately the same size as a post-it note.

So….the next time you do an OPEN MIDDLE task with your students – do it vertically. Get your students up and moving.

#mathMovement with **Which One Doesn’t Belong?**

I will always be a fan of ‘Which One Doesn’t Belong?’ routine because not only is it a great first win for teachers trying to increase discourse in their room but because it was made popular by people who live within miles of me. I was introduced to this routine by Terry Wyberg (University of Minnesota) and Christopher Danielson (Who wrote a book of the same name). I’m telling you all – we have amazing math leaders in Minnesota.

So, what does WODB look like with** #mathMovement**? One common way that many use WODB, is to give each student a post-it note and then present a problem. For example, this one from the wodb.ca website…

Have students individually select a number that does not belong and record their choice and reason on their post-it note. NOTE: I give students a sentence stem to write their choice **“The number ______ does not belong because…”**

I then have students **ALL** (yes all – everyone needs #mathmovement – even for a few seconds) stand and walk to the board and place their post it notes next to the box of their choice. It would look something like this (though this is a different problem).

I then have a discussion with the class about what hey wrote. Imagine this picture with 30 post-it notes. I usually start with the number with the most post-it notes next to it and have students share their reasons. Sometimes I have a box with no post-it notes and we will brainstorm as a class reasons.

The method above is OK for **#mathmovment.** At least all students move for 30 seconds – but my favorite way to use WODB problems with **#mathmovement** is the following. For most WODB’s I do, I use an EL best practice of inviting more learners into the discourse by using language that most students can access.

Did you know that many students don’t participate in a WODB because they don’t have QUICK language to say things like “The one in the upper left….” or even say “Letter A doesn’t belong because….” I have had teachers excitedly tell me, I put axis through the middle and have students tell me what quadrant their choice is in. When I hear this I think – “Yikes – our classrooms have lots of students with language needs and adding another layer of complexity tends to shut these students down, not support them in their language needs.

What is quick for most students, despite their language needs are colors. You would be amazed how many students will start talking about WODB when you make each quadrant a separate color. All of a sudden students will say things like, “The purple one doesn’t belong because……”.

For this reason – I do all my WODB on a template in a word document – though it could be a power-point template. I simply create a jpeg of the 4 boxes and paste them into the template. I then take a jpeg of this and share this with my students and ask them ‘Which one Doesn’t Belong?”. Note #1 For my color blind students I also label each quadrant with A, B, C, D. Note #2 When students say “The purple one doesn’t belong.” I will re-voice and pair language to build academic language for all “Tell my why the purple, letter D in the lower right does not belong.” – (pairing language though is another post I need to write some day).

SO….where is the **#mathmovement** in this activity? Well, first let me show you my classroom. I squeeze 35+ students into a tiny room and I still do movement. What is on the four walls, way up high, is an 8.5×11″ sign that says ‘WODB’. Each sign is in a different color corresponding to the 4 colors in my WODB template.

I display the WODB for students to see and then I have them stand up and go to the side of the classroom to stand next to their choice. I usually will then stand in the center of the classroom and orchestrate the discussion of why students selected each choice. All of us will remain standing for the discussion. **#mathmovement** with WODB. Excellent.

**Note:** If you would like my templates for creating color coded WODB’s or want to download the 8.5×11″ colorful signs I keep up in my classroom, click the button below to go to a google folder of resources from this blog post.

#mathMovement with **Debate Math**

Debate Math is an amazing math routine incorporating debate language and now a book from my friend and co-presentor on** #mathMovement**, Chris Luzniak. I am not going to say much about his other than to say – click on the links to either the Debate Math blog or book from Chris and read one or both. Debate Math is an incredible routine to increase mathematical discourse in your classroom and get students moving. Check out this tweet from Stephanie Lewis!

#mathMovement with **‘Would you Rather?’**

The ‘Would You Rather?’ website has great math prompts to get your students engaging in discourse around a variety of topics. Check out this tweet/photos from Karla Doyle.

The ‘Would you Rather’ Math Instructional Routine would be another great routine to incorporate #mathMovement. Similar to what I wrote about above for WODB – consider tweaking the resources at the website to have students make a choice between the 2 items by physically moving to one side of the classroom. Hold the class discussion about the 2 choices while all are standing.

Step 1: After selecting an image from the website (or make up your own task of this form)- add it to a color backed template and display for students.

Step 2: Have students make a choice between the 2 options and move physically to the corresponding side of the room.

Step 3: Lead a class discussion having students voice their reasons for selecting each option.

Note: If you would like signs for your classroom or templates for creating a **#mathMovement **‘Would you rather?’ task – click the button below.

#mathMovement with **Estimation 180**

Estimation 180 can become a **#mathmovement **activity with the addition of BLUE 3M Painter’s Tape (3M is a Minnesota product – thus my support of them). All you need to do is create a (semi) permanent number-line in your classroom that you have your students use in a variety of ways. (sidenote: My good friend, Ali Rubin, will write a blog post soon on 10 ways to use a classroom number-line soon – I’ll link to her post her when she does)

The classroom (blue tape) number-line in my own classroom went down the center of my groups of tables.

Then select an ‘Estimation 180’ prompt (or make up one of your own). I selected day 206 – How many cheese-balls fit onto a tray? Display the image provided by Andrew Stadel at his site.

Have students write down their estimates. I recommend using Andrew (creator of estimation 180) Stadel’s template for having students make their predictions – Have student’s not just estimate the number of cheese-balls but also write down a number they believe is too LOW and another number that is too HIGH. Finally, have students record their reasoning.

Now it is time to incorporate #mathMovement with Estimation 180.

Have students work in pairs with white boards. As a class talk about what students think is ‘too low’. Have a student stand up and represent this amount on the number line. For example, maybe this class thinks 20 is too few cheese balls to cover the sheet pan.

Next have a class discussion about an amount that is ‘too high’ and have a student stand up to represent this amount. Write the amount on a white board (or paper) for the class to see. For example, maybe the class thinks 700 cheese balls is definitely too many.

Next have one person from each partnership make their best estimates and stand on the line between the 2 numbers.

Have a class discussion about where students are standing. Are students spread out in proportion to the distances from the low to high number or just standing ‘in order’. Are the best estimates all bunched together or spread out? Why did they select their value. After a standing class discussion, show the reveal.

**Last note: ** Have you checked out Andrew Stadel’s ‘Estimation 180’ podcast yet? If not, take a listen soon and imagine this routine with #**mathMovement**.

#mathMovement with **Clothesline Math**

You can not use number-lines enough in K-12 math to model student thinking. One way of using more number lines (and your the blue painter’s tape number line you now have made (see above) on your classroom floor) that has gotten traction in recent years is ‘Clothesline Math‘.

Chris Shore and his site has lots of information on this routine as well as downloadable resources. Note: Kristen Acosta has lots of Clothesline resources for Elementary. (and check out all the other clothesline enthusiasts linked on Chris’s site.)

Ultimately, you as a teacher print out a set of cards for students to sort on a clothesline. Clotheslines are superior to written number lines in that it is super easy to move numbers as you place them and replace them as you add more cards.

What if you used the clothesline math downloadable cards at Chris or Kristen or Andrew Stadel’s sites and instead of sorting them on a clothesline, you had students engage in a **#mathMovement** activity and had them stand on your classroom number-line on the floor? Think of discussions you could have.

How are you using** #mathMovement** with Math Instructional Routines in your classroom? Comment below or tweet at @saravdwerf or using the hashtag **#mathMovement**. I’d love to hear your ideas and/or questions.

- My favorite way to move everyday! Stand & Talks
- Movement review activity –> Balance Points
- Movement in common Math Instructional Routines
- Movement when reviewing or introducing Circles -> Defining Circles

The post #mathMovement ideas with well known Math Routines appeared first on Sara VanDerWerf.

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