Sunday, September 13, 2020


6 Fun Ways to Go Digital with Number Talks

One of the cornerstones of a solid elementary math block are activities that support students in developing numerical literacy. Developing numerical literacy in the elementary classroom will support students in being confident problem solvers, and engage in mathematical discussions at a higher level.  Number talks are one such activity that builds students numerical literacy and are taking place in classrooms on a daily basis.  

If you are not familiar with number talks here is the gist of it.  The goal of a number talk is to give your students an opportunity to use mental math strategies to solve a problem.  That's right no paper, whiteboards or pens, just solve the problem in your head.  

The conversation that occurs after the number talk is teacher facilitated with students sharing answers and their strategy.  This process supports students learning from each other and teachers assessing students thinking and what strategies they use naturally.

       Teacher says: How can you solve this problem by doing it in your head? Give me a thumbs up when you have a solution!

One thing I love about a Number Talk is students are provided with a problem that can be solved in a variety of ways.  This allows students to be flexible in their thinking and develop a variety of strategies that will support them when they are faced with cognitively demanding math tasks.   

       Get these slides here

One thing that is a struggle with this process is number talks can be incredibly time-consuming if you are in a class with 30 plus students who all want to share how they found their answer.   As a teacher, I want to honor all of my students' voices and give them an opportunity to express what they know, but logistically this is not always possible.   

This is where technology can come in to support you in making number talks accessible to all students and useful as a formative assessment tool to see where all your students are at and give them a chance to share their thinking.  

Here are 6 Fun Ways To Go Digital with Number Talks: 

1. Google Slides: During a synchronous meeting with your students share this slide deck in edit mode for students to record their solution to a number talk problem.  Students can drag the icon to indicate they would like to explain their thinking or to show agreement with another student's explanation.

2. Google Voice:
For asynchronous collaboration post an image and/or your question in a Google Doc.  Students can work with a partner or independently to share their strategy. All you need to do is create a Google Doc and Share with your students.  Then have your students go to the Tools Menu in the Document and click Voice Typing

                                       click here to get this document

If you want to see how quick and easy this process is just check out my 8 year old son demonstrate how to use Google Voice Typing.

3. Padlet: Post your question on a padlet board.  Students can access the board with a URL and automatically post their response by sharing a picture, text or video.  Try this out by responding to my number talk wall below with your response.  If you have fun doing it imagine what you kids will say! 
Made with Padlet

4. Google Drawing: teachers can illustrate student responses using Google Drawing either on their IPAD or computer.  The Scribble tool is a quick way to make illustrations and the student can also illustrate their response using this web based tool .  Google Drawing can also be used inside Google Document and it even features math symbols as images.  
                          Click here to view in Google Drawing

5. Flip Grid: Create a video word problem with a student response system that records students thinking in an instant.  This process can ensure that students voices are heard and recorded. You can also leave feedback for your students with this process.  The videos below were created shared on Youtube

6. Shadow Puppet: This tool can be used by you to make video number talks or by the student to share their response. Students can illustrate their work with paper and pencil then take a picture with an ipad or iphone.  Then they can audio narrate their response.  This can be a center activity that students complete and provide feedback and comments to their peers.   This is an app and not accessible on a computer 

If you are an elementary teacher looking to improve your students number sense than number talks are a must.  This process instinctively allows me to see where my kids are at, who has grasped the concept and who needs some extra nudging and support.  With number talks the nudging and support does not necessarily come from me it can be found in how their peers respond and with web tools I have the power to capture their answers.  

Want a book that can put it all together for you with over 100 digital resources and tools then check out my book on Amazon

Check out these digital number talk images I have collected and be sure to share yours with me. 

How much for one (unit rate)? How much for 13?

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Friday, June 26, 2020


Ratios and Insert Learning

Math Warm Up: Which One Doesn't Belong? 

Look at the Graphic below and decide "which one doesn't belong" 

What justification could you use to say that 8 doesn’t belong?
What justification could Student B say that 64 doesn't belong?
What other justifications could student A have used to decide that 27 does not belong?

How can students A, B, and C all be correct even though they each chose different values?

Today's Lesson: Ratios
Ratios are used to compare values. They tell us how much of one thing there is compared to another. For example, ratios can be used to compare the number of cars to motorcycles on the road. If we have a total of 12 cars on the road, where two are motorcycles and ten are cars, we can write that in ratio form as 2:12 (motorcycles:cars). We can also write it in factor form as 2/12. To compare the number of cars to motorcycles, we can simply rewrite our ratio with the number of cars first as 12:2 (cars:motorcycles ) or 12/2.

3 Acts Math Task: World Fastest Dog
What do you notice and What do you wonder?


Monday, August 19, 2019


Are you Teaching Outside the Box with Technology Infused Math Instruction?

Technology that promotes 21st century skills are essential for the classroom today. But if technology use consists of students working in silos while staring at a computer screen they are more likely modeling the 21st century skills seen at Starbucks, than the skills students need to thrive! The opportunity to partake in experiential learning, ask questions, compose an argument and justify your stance, must extend beyond a typical twitter post and exist within the realm of social engagement.
Image result for starbucks everyone on their cell
Learning happens when students' experience a shift in their thinking (scientist call this disequilibrium) and this happens when we collaborate, create, communicate and think critically (the four C’s); notice click was not included. Teachers and peers provide the perfect context to challenge our current ways of thinking so that students can stretch themselves cognitively. Using technology as a means to avoid printing out worksheets for students to complete would be what Dr Ruben Puentedura (founder of the SAMR Model) would say is the Substitution stage. Using technology to “redefine” a traditional tasks and create a novel experience is where we want to go with technology (think of Bloom's Taxonomy and the higher levels of learning). If kids are just using technology to answer test questions, then we are going to turn them off to technology just like teaching to the test turns kids off to school. 

Brubaker image
Image created by Jonathan Brubaker (@mia_sarx)

Is it obvious I am writing this blog post while sitting at Starbucks? If teachers are using technology purposefully and with the intent of having students be co-facilitators of their learning then the future of education technology will revolutionize the classroom and move education beyond the 21st century. 

Technology is a tool for student learning, just like a utensil is a tool for eating and we can still eat without it. As a classroom teacher you need to know your students as well as your subject matter to decide which tool is best for their needs.  Considering how PE teachers are typically outside the class; they can use QR readers and a recording sheet to get kids using technology to support their understanding of a skill, or demonstrate what they can do via video recording is a great way to integrate technology meaningfully.


As a math teacher I love using Google Docs and Google tools to create my own activities for students to play with and explore math concepts.

For example I created a Google Slide show for students to understand the concept of dividing fractions using the shapes tool where students can divide up parts of the shape to find the quotient of 2 divided by 1/4. This is much more meaningful than teaching students the standard algorithm which is multiplying the dividend by the reciprocal of the divisor. None of this makes any sense to students especially if they don't have a conceptual understanding of dividing fractions.

There are a plethora of tools and innovative approaches to utilize technology such as using Flip Grid with students for a video-based response to a questions. Having students create a podcast in your English Language arts or a Social Studies class can be an innovative way to approaching an oral report on a topic as it be shared in your class and beyond.  For math solving a 3 Acts Math Task, or using Desmos can transform student learning into active problem solving and critical thinking. I have curated a list of over 100 free tech tools to use immediately with your students

The biggest tech innovation is the ability to put the technology in the hands of your students which was not the case twenty years ago when I started teaching. I went knocking at company's doors in Los Angeles to get enough computers for my students to have access.  Now that students have access as teachers we need to use technology to create personalized learning for all learners. You can reach and teach all with technology and that's the best innovation of technology. From having students create their own video to explain a concept, to using virtual manipulatives to develop conceptual understanding, innovation comes from the teacher and the choices they make in using the technology to support student learning. 

Filling the gap between math pedagogy, content knowledge and technology integration was the inspiration for my first publication "Teaching Outside the Box: Technology Infused Math Instruction".  I spent three years working alongside math teachers across the K-8 grade span to examine how technology can be used intentionally to support student learning in math and the results were amazing.  
The book focuses on five instructional practices in math: Daily Routines, Open-Ended Tasks, Project-Based Learning, and Problem-based Learning and how technology can be used intentionally across each pedagogy.  Moreover the book specifically focuses on technology as a tool to support English language learners and students with learning disabilities. Most curriculum material focuses on separate activities and approaches for teaching different groups of learners but this book supports real inclusion by making content and pedagogy accessible for all with technology. The book has a ton of resources and examples that teachers can use in their classroom the next day. 

That is one thing I learned about being a Math Coach and presenter, is that teachers want something they can use in their classroom immediately and this book does just that.

Want to learn more about how technology is shaping the classroom culture join our Facebook Group: TeacherPrepTech

Sunday, May 19, 2019


Would You Rather: Spark Interest or Keep Your Students Quiet?

By Guest Blogger: Heather Szabo
In my classroom I commonly use “Would you Rather?” questions as a warm-up or an appetizer. Students usually choose an option and are asked to be able to support their argument with mathematical reasoning.
Question: "Would you rather have your weight in pennies or your height in quarters?"
This particularly days question sparked a powerful debate so we decided to explore the problem deeper. Students identified that in order to prove which they would rather, they would need to know the weight of themselves and of a single penny as well as the height of a quarter and the height of themselves. I collected the materials and student table teams explored. In the moment I did not know that a simple question would turn into our whole unit of study on linear equations and writing/solving systems of equations. This lesson driven by students was much better than the storybook problems I have used in the past.
Set Up: Each student in the grouped followed the same protocol and we collected data as a whole class to prove which would equate to a larger value, the weight of a student in pennies or the height of a student in quarters.

Students first weighed themselves using a digital scale in pounds. Students then used a kitchen scale to weigh pennies. Each group weighed a different number of pennies. The mean penny measurement was 10 pennies with a measurement in grams. Students then used conversion facts to calculate the number of pennies that would be equal to the weight of each student.

Once students had a total number of pennies they calculated the value in dollars.
Students used 10 pennies and divided to find a unit rate. Students noticed that they were getting different measurements for weight of the pennies based on the image on the penny. We researched this and found that pennies minted after 1982 have two different weights.

Following the penny/weight measurement students did a height/quarter measurement. Students first measure their height in inches using a measuring tape. Students the converted that measurement to meters. Students measured the height of a stack of 10 quarters and recorded the measurement in mm. Students then used conversion facts to calculate the number of quarters that would be equal in height to each student. Once students had a total number of quarters they calculated the total value in dollars.

After collecting all of the data students realized that for some students choosing pennies would be most profitable and for others choosing quarters would be most profitable depending on their height and weight ratio. We then extended this activity to figure out at what height and weight you would rather choose pennies or quarters. We used this example to cover topics of linear equations and systems of equations.
When finished students asked questions like: What if we chose dimes instead of pennies? Since dimes are smaller but have more value students were interested to see if the outcome would be the same. So we embarked on the same journey led solely from student questioning and facilitated by the teacher.

Reflection: This appetizer turned entree was rewarding for both the students and myself. It truly embodied the five key aspects of project based learning including: real world connection, academic rigor, student driven, multifaceted assessment and structured collaboration

First the question was real to them. They chose to seek the answer out which was the driving force. Second, the rigor was embedded within the lesson. Once students had their own data, they shared it with the class. We then looked to the class data to make predictions and generalizations. We used this time to create graphs and solve systems of equations which is the next chapter of our current curriculum. I let them ask genuine questions and pursue the answers themselves and that is where it led. Some student groups were more ambitious than others. Many groups struggled with the unit rates and conversions so we took time to discuss proportions via a mini lesson in class. The rest just fell together. In this lesson, I was really able to take on the facilitator role and let the investigation be student driven. This is not to say that the lesson was without struggle but the struggles students faced were productive struggles that they persevered through.
When the students asked if this situation would hold true if we used dimes instead of pennies I responded, “I don’t know! Let’s find out!” Due in part to this the finding out became an adventure for students which caused them to buy in more to the lesson itself. 

Saying yes to student ideas in this instance was easy because students were so inquisitive. They wanted to know more which paved the way for much deeper understanding.  

I wholehearted believe that we as math educators are responsible for creating students that are comfortable enough with numbers to challenge and question the authority of numbers. I want my students more than anything to be well prepared to be consumers in a market that is out to take advantage of the mathematically illiterate.

As stated in the video, “without mathematical literacy career opportunities shrink and students become easy prey for credit card companies, payday lenders, the lottery and anyone really that has a dazzling statistic. Because when we aren't comfortable with math we don’t questions the authority of numbers.” I want my students to question and to seek answers and during this lesson that is exactly what they did! 

Heather Szabo is a 7th Grade Math Teacher. She is learning different approaches to math instruction in the course The Math In Our Lives which focuses on designing instruction based on real-world application.