MCTM 2018 5 ways Elementary Teachers can Support the work of Secondary Math Teachers RESOURCES

Hello you all!.  My friend Laura Wagenman approached me 6 months ago and asked me to co-present for her at the 2018 Minnesota Council of Teachers of Mathematics State Conference in Duluth on May 4th, 2018.  Laura is a District TOSA/coach who works with K-5 mathematics at a large suburban district in my state.  I said, “Laura, you know I am a HS math teacher – not an elementary person – right?”    She smiled and said  “Of course, but Elementary teachers need to hear that we are way more similar than we are different.

I agreed to present with her (though I was crazy scared that I would be perceived as being that HS person that would blame earlier grades for the ills of math).  In a week, I’ll fully blog what we shared – but until then I am posting the resources we shared with Elementary math teachers in our state.  If you are not in MN – feel free to check these out too.


60+ Elementary Math Resources for FREE!  (a google doc linked with tasks, videos, PD….etc)  We will add more to this page – If we are missing a great resource let us know.  The resources are grouped in the 6 big areas we talked about in our session.

Our Google Slides (powerpoint)

Thanks to Laura for writing most of this up (several weeks ago) – I am now (Memorial Day) getting around to giving you a taste of our joint session at the Minnesota State Math Conference (MCTM) in Duluth in early May…..enjoy….

Those of you who submit session ideas and tiles to state and national conferences know our pain when you are submitting an idea at the last minute to speak on something 6 months to a year later.  If you are like us – the idea of what you will speak on that far out in the future makes it tough to submit a well thought out title and session summary when the session is just an idea in your head.  There are a few of you weirdos out there – we see you Robert Kaplinsky – who have their sessions completed (and practiced) a year a head of time – but we suspect most of us are like Laura and I and are submitting titles and session summaries on sessions yet to be fleshed out.  That was the case with Laura and I when we wrote our title “5 Ways Elementary Teachers Can Support Learning in Secondary” and our session description: What 

are 5 things elementary teachers can do to support the mathematics their students will see in high school? An elementary and high school math teacher will share these 5 things with the goal of building confident, successful, sense-making mathematicians.’  We had ideas of what we might share 6+ months later – but it was mostly in hour heads and a napkin of notes we scratched out.  

When Laura and I sat down to plan the session – our ‘5 ways’ became ‘6 ways’.  We decided to start our session by introducing ourselves to you so you could get as sense of our shared values as educators.


This is the image Laura and I selected to represent our introduction to you. When you look at this image –  and think of Laura and I – THINK…

What is the same? 

What is different?

(Note:  One goal Laura and I had with our mostly elementary audience was to leave them with tons of resources they could use in their classrooms & planning – here is an example of our first FREE resource – ‘What is the Same and What is Different? images and questions are curated on the Same or Different website as a way to support mathematical argument in the elementary classroom.)

As a way to introduce ourselves we wanted to share our believes and values through some true/false statements.

True or False?  Laura & Sara believe students learn through play.

True!  In fact, this is a picture of a pattern created in Sara’s High School Classroom at her play table.

True or False?  We have both taught in another state.

False!  Sara has taught grades 7-12 in MN for 25+ years.  She spent 5 years as the K-12 Math Lead in Minneapolis Public Schools.  Laura taught in California.

True or False?  Both Sara and Laura have taught 7th grade math.

True!  Sara’s favorite grade she has ever taught is 7th grade. Despite currently teaching HS, Sara’s heart is in middle school.  Laura also taught 7th grade…

True or False?  We are fans of speed in memorizing facts.

False.  Laura and Sara both are committed to removing a culture that values speed in the mathematics classroom.  For example, Sara has eliminated hand-raising from her classroom.  We both know that many students self-identify as ‘bad at math’ simply because they are not as fast as other students in class.  We both know that thinking stops on the classroom by many students when they think others have solutions (hand raised).  Our goal is to change the culture of our rooms so that students don’t believe that being good is math means being fast at math.

True or False?  Paper assessments are the best way to monitor student progress.

Mostly false – but saying this does not mean we don’t value paper assessments.  Both Sara and Laura know that we know a lot about our students thinking and understanding of mathematics by listening to what they say.  We are committed to finding ways for every student to speak out loud about mathematics every day in our classrooms.  We get information about students understanding by listening to them, looking at their work via paper and many other modes.  Everything our students do and say informs our work with them.

True or False?  We have taught tricks to our students to make our students proficient.

It is (sadly) TRUE that both of us at times in our career have taught tricks to our students.  We know better now and choose NOT to teach tricks to our students anymore.  We value student understanding of concepts over quick tricks that feel good at the time.  Sara has written about this a ton HERE.  In our list of resources we recommend every teacher downloading the FREE ‘Nix the Tricks’ book and working to eliminate tricks from their own classrooms.  We’ve also included a great NCTM article on eliminating teaching ‘rules that end’.

My guess many of you reading this are like Laura and I and are either currently teaching math tricks to your students or use to teach tricks to your students.  Laura and I don’t want to shame you.  We don’t want you to feel bad.  We both have this quote near our work spaces.  Always in our career as teachers we are looking to do better.  This gives us comfort.

True or False?  Allowing students to share their thinking encourages equity in the classroom

TRUE!  TRUE!  TRUE!  This may be the one that Laura and Sara want to scream out to anyone who will listen.  Our goal in lesson planning, in selecting tasks for the math classroom and in what we want our classrooms to look like is things that value students to make their thinking visible.  Not just some students – but all students.  We are on a mission to find math resources that make this same value easier for teachers who want to do more of this in their own classrooms.

True or False?   We are fans of Pinterest & Teachers Pay Teachers. 

Mostly False!  We are never going to be against these resources and know many of you find them super valuable – we just know there are so many other valuable resources out there for FREE.  There is no need to pay anyone for great material.  We also are fans of all teachers valuing great content in resources over the ‘cute factor’.  Don’t get us wrong – we love ‘cute’ – we just love great mathematical concept development even more.

Laura and Sara find most of their resources for own math classrooms by being part of the online math community on Twitter.  If you want to join us there – start by following us @saravdwerf and @laura_wagenman on twitter and search the hashtages #MTBoS (math twitter blog o’sphere – the name of the online math community – anyone can join in the conversation – anyone) or #Iteachmath.

For those of you who don’t want to (or can’t) join Laura and Sara on Twitter – we’ve put together over 60 FREE resources just for Elementary teachers – these are some of our favorites!  They are grouped by the 6 ideas we will share below for how Elementary Teachers can support the work of Secondary math classroom teachers.

Sara – a HS math teacher – and Laura – an Elementary Teacher Leader – are way more similar than we are different.   That said – for some reason in education many people look at Sara as having some authority to speak about mathematics over Laura simply because she teaches higher levels of math and uses words like logarithm and trigonometry regularly.  What they don’t know looking at Sara – is that she views the learning of mathematics in K-5 as much more important than the work she does in HS.  Sara knows how smart and valuable Elementary Math teachers are.  Teaching students how to have a flexible understanding of the base-10 number system can not be underestimated.  Sara believes that every HS math teacher should be signing up for a 1 week PD this summer on how to teach elementary mathematics.  If they do, it will radically change their work at the HS level.  Sara knows we have much to learn from Elementary Math teachers and hopes we can see each other as peers who both have expertise that the other needs and not as peers where someone knows more.

Sara and Laura are on a journey to learn from one another.  What you will find below is the 6 areas Elementary mathematics gets right that supports the work of Secondary Math Classrooms.  In this post we hope to show you just a taste of what Elementary does well and how that plays out in the secondary classroom.  While we have our differences, we are very similar and look toward each other for best practices and leverage each other’s assets to learn and grow.



If you had been at our session, we would have had you do a STAND & TALK (a favorite of Sara’s) to get you talking to another teacher.  Before reading any further – talk out loud (really do it out loud) about how you would answer this question…

Think about how you solved this task and how you would want your students to solve this task before reading further….

This task is one that changed Sara’s practice 10+ years ago when she looked at the student work of her students from a pretest she was asked to give her 7th grade students at the start of the year.  Here is a copy of one students work on this problem.   What do you notice?

This student got the problem correct.  (although it took me a lot longer than I would have liked to figure this out).  Despite their correct solution – look at all the arithmetic this student did to figure this out.  Think of all the places they could have easily made a small error that would have resulted in them getting this wrong.  As a HS math teacher – Sara looks at his and thinks about this student on the ACT where they have 1 minute per problem to answer questions – Is this really the quickest way to answer this problem?  Is this way efficient?  Does this work show a depth of understanding of fractions?

Laura and Sara look at this work and it challenges us to do better.  We want students who look at the original 4 fractions and have the ability to compare them to benchmarks.  We want our students to say things like “5/12 is slightly less than 1/2”.  There was no use of benchmark fractions, estimation, any sense making. 

Our #1 wish for Elementary (and HS) mathematics is to value Estimation and Sense Making in the math classroom.  So how can we do this?  

What can we do, starting in elementary, so students are estimating and sense making? A favorite resource of ours is Estimation 180. (Thank you Anderw Stadal!) There are 300 images that help build estimation and sense making skills through real-world, engaging pictures.  Think about how using visuals like this can increase student discourse in your classroom.  Think about how these pictures can be used to increase opportunities for students to estimate and develop number sense in your classroom.  


Think about how using a photo like this can help students build on their concept of ‘volume’.  How many cans are in this cart?

SIDE-NOTE:  For obvious reasons you can’t use the following photo Jessica Strom posted on Facebook this week in the classroom- but imagine what great questions you could explore with this photo.

High School Math Teacher, Megan Schmidt recently spent a lot of time in Elementary Math Classrooms and blogged about her experiences HERE.  Laura and I love this quote from her blog:

Our goal is to have mathematics classrooms that value ESTIMATION and SENSE MAKING. 

In the secondary classroom Sara uses this prompt towards the beginning of the year to look at the sense making her students bring to the classroom.  She says, “No Calculators – calculate this as quickly as you can.  Go.”

What Sara finds year after year – is that students rush to remember how to add fractions.  They work furiously to get common denominators – many students make arithmetic errors along the way.  Most students struggle to figure this out quickly.  After 60 seconds Sara says “STOP.”.  She then points at the number and asks a student to read the expression out loud.  As they read she points at a place value chart she keeps in your room.  

As she points at this chart – students explain “OH!” and quickly work to write an answer.  She then talks to students about how our classroom will value sense-making over speeding to do a calculation with rules you have to remember.

One of the tweaks teachers can make in their classroom is to replace the world ‘point’ with the word ‘and’ every time they (or students) read a decimal out loud.  

For elementary math teachers – in addition to using resources from Estimation 180 – we totally recommend using a teaching technique we learned from Brian Bushart.  If you don’t know who Brian is – you need to visit his blog.  He is AMAZING.  We asked Brian to say a short greeting to MN Elementary Teachers so you could see he is a real person doing the same great work you are.  Check him out & listen to what he says about sense making.

Check out this problem we would present to students.  What do you notice?  What do you wonder?

Are you are wondering what the question is or what you should figure out?  We purposely removed the numbers and and the question from this problem to create what Brian and others call a ‘Numberless Word Problem’.  Think about what students will notice and make sense of before they rush to answer a question and how that may change how they interact with the mathematics in this problem.

As students ask for it – we reveal information to them.

Again – we will often delay giving the question for a bit allowing students to make sense of the information they have.  We have found that removing numbers and questions in our classroom has invited many more students into the problem solving process that in the past did not engage.  They were allowed to make sense of information before the ‘race to solve’ the problem began.

Later in this post we will talk about this task again….but until then – we encourage you to value and build number sense in your classroom by learning about Numberless World Problems and using them in your classroom.  They are game-changers.


5.28.18 2:30pm….I am stopping for now – but more resources are coming soon….









Closing Thoughts


60+ Elementary Math Resources for FREE!  (a google doc linked with tasks, videos, PD….etc)  We will add more to this page – If we are missing a great resource let us know.  The resources are grouped in the 6 big areas we talked about in our session.

Our Google Slides (powerpoint)

Sara VanDerWerf

I am Sara Van Der Werf, a 24-year mathematics teacher in Minneapolis Public Schools. I have taught math in grades 7-12 as well as spent several years leading mathematics at the district office. I currently teach Advanced Algebra at South High School and I'm also the current President of the Minnesota Council of Teachers of Mathematics (MCTM). I am passionate about encouraging and connecting with mathematics teachers. I'd love to connect via twitter.  Join the community.  Tweet me @saravdwerf.

Click Here to Leave a Comment Below 2 comments