The Three Essential Math Experiences: Number Routines, Word Problems, and Games

Transcript

Welcome fellow Recovering Traditionalists to: The Three Essential Math Experiences: Number Routines, Word Problems, and Games

In this episode I’m talking about my 3 favorite activities (or I like to call them Experiences) students should be having with math: Number Routines, Word Problems, & Games. Before we get started, I wanted to let you know that as a gift to all you listeners for my 200th episode, I’m giving out a Google file that has examples of all 3 experiences that you can use and modify for your students.  You can request that file for free over at the show notes page BuildMathMinds.com/200 or if you are already on my email list, check for my email today about the podcast, it has a direct link to the file.  If you don’t see that email you can email us or go to the show notes and request the download.  

Back when I started TheRecoveringTraditionalist.com, I was hesitant to do a podcast because I want to encourage you to make math visual for students and how can I do that through audio??  I thought it had to be in blog or video format, but here we are 200 episodes in.  

So thank you for listening (or watching over on YouTube). I just checked the stats on the podcast this week and as of Wednesday, April 30, 2025, there have been 696,295 downloads of the podcast.  With 199 episodes, that’s an average 3,499 downloads for each episode.  

If we also include the video views of podcast episodes (which I’ve been videoing the episodes consistently since episode 149) there have been 77,618 views of the podcast episodes.  So combined, 773,913 times someone has listened to one of the Build Math Minds episodes.  Is that Big or Small?  Depends upon your perspective…I think that is big.  Each of those listens means some teacher out there is building their math mind and that’s happened over 700,000 times because of this podcast. Crazy.

Big or Small? is actually a favorite Number Routine of mine.  You give kids a number and then ask “when would this be big?” “when would this be small?”  So for me 773,913 is big when it’s how many times my podcast has been listened to…it’s small if that was the amount a major league baseball player was getting paid for a 10 year contract.

Speaking of routines, let’s get into the math ideas and this week is about something that hasn’t changed over 200 episodes: the three types of math experiences I believe all kids should be getting in your classroom.

As I talk about the 3 experiences, I’m going to be referencing the Institute of Educational Sciences (IES) and the What Works Clearinghouse (WWC) practice guide for Assisting Students Struggling with Mathematics.  Even though these recommendations are geared towards students who are struggling, they apply to all students.  I’ll link to the 2021 guide and even the 1st one from back in 2009, which is the document that started my obsession with the 3 experiences to begin with.  The practice guide does NOT say to use Number Routines, Word Problems, & Games but after reading the document I kept coming back to those three because they help you do the items they recommend. You can find those links at the show notes page BuildMathMinds.com/200 

Number Routines

Number routines give you the opportunity to provide systematic & explicit instruction, which is supported by strong research evidence from the IES and the WWC. Number Routines help make “implicit” math concepts “explicit” for struggling students through teacher modeling and structured student sharing. The systematic nature comes from carefully selected problems that highlight specific strategies and concepts. Number Routines allow teachers to hear students’ thinking processes, which is crucial for identifying misconceptions and understanding how students approach problems. They also help students build flexible thinking about numbers and allow them to see multiple approaches to solving the same problem.

In the free download to celebrate 200 episodes, you get some samples of the routines we have made for teachers who are members of the Build Math Minds PD site.  You get one example of Big or Small?, Make It, Quick Images, Disappearing Act, and Number Strings but our Build Math Minds Members have complete files for each of those routines (and more routines) with over 100 slides for each routine that have them pre-made for number sense/addition/subtraction/multiplication/division with whole numbers/fractions/decimals.

Word Problems

The IES/WWC guide shows strong evidence that building understanding of story problem structures is effective for students struggling with mathematics.

Story problems/Word Problems/Contextual Problems help students understand the conceptual structure of operations rather than relying on keywords. It’s about structure not teaching students to pull out numbers and look for keywords. One of my favorite ways to do that is through Bet Lines (revealing one line at a time) because it engages students who might otherwise be intimidated by story problems, drawing them into predicting what comes next.

Word problems help students see math as connected to real contexts rather than isolated operations and when used purposefully with the number routine component, contextual problems allow students to apply the strategies they just discussed with similar numbers but in context. By using story problems, you are addressing the fundamental understanding of mathematical operations rather than just mechanical calculation.

Inside the Build Math Minds PD site we emphasize using Bet Lines, Numberless Word Problems, Context-Less Word Problems, and pictures from your daily life to get students engaged in math in context. We have trainings on them and resources to help teachers do them in their classrooms.  In the download you will find some Bet Lines and Context-Less word problems along with some pictures from my life this past week that you can use or just to inspire you to see math in everyday life.  

Some of the pictures I included in the download are my car’s trip odometer.  I have 4 kids in baseball & softball right now and living in rural Idaho we have to travel a lot for games.  Our high school has two schools in their league that are a 4 hour drive, one way.  So I decided to keep track for one week…technically it ended up being 8 days, Friday through the following Saturday.  In those 8 days I traveled more than 1900 miles and my car was running for over 50 hours!!  That doesn’t even count the hours I spent at the ballfields watching or being the bookkeeper for the games. 

So if I don’t get back to you during the spring/summer it is because I spend more time in a vehicle than work. Anyways, I took a picture of my dash almost every day that week and there is so much math you could ask kids using those pictures.  Those pictures are in the download along with some other pictures we got while on the road.  Again you can use these with your students, or use them as inspiration…what can YOU grab pictures of from your life (or your students’ lives) and use them to put Math in Context.

Games

Practice is an essential part of math.  Practice & repetition help us retain information. However, most practice is boring. Games make practicing math engaging rather than tedious.  In the 2021 IES/WWC guide, one of the recommendations with strong evidence is to “Regularly include timed activities as one way to build students’ fluency in mathematics.” Did you catch that….ONE WAY…not the only way.  It goes on to say that we should “Add timed activities once students have been working on a concept over many lessons. Do not use timed activities to introduce and teach mathematics concepts and operations.”  Also, did you notice they say “timed activities” not “timed tests.”  

Games can serve as a “timed activity” to practice a component after the conceptual understanding is built through number routines and story problems.  Even though students are not timed on how long it takes for them to give a response while playing a game, they do have limited time to play and they naturally work as fast as they can because other students are waiting on them (unlike when they are working on a worksheet on their own for 5 minutes)…PLUS many games have a natural speed element built in because you have to answer faster than your opponent.

Games can be a pain because you have to take the time to teach kids how to play the game and usually that takes longer than the time they actually get to play it.  So quite a few years ago I made a template of what I called Evergreen Math Games.  They are evergreen because they are always relevant.  The template shows the game in one math context but you can modify these games to use any math concept.  Plus once you teach them how to play the game you don’t have to re-teach it.  The directions of how you play don’t change, just the math content within the game changes.  Those templates for the Evergreen Games and directions for each game are in the download you can request over at BuildMathMinds.com/200 

These 3 math experiences help provide a balanced approach to conceptual understanding, procedural fluency, application, and engaging practice.  And if I’m lucky enough to still be doing this in another 200 episodes, I’ll be saying the same thing.  Routines, Word Problems, and Games help Build Math Minds.

Until next week, my fellow Recovering Traditionalists, keep letting your students explore math, keep questioning, and most importantly, keep Building Math Minds.