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. 

Wednesday, April 10, 2019


Going Google with Hyperdocs

The agony of leaving your class with a substitute for the day is gone when you "Go Google" with Hyperdocs. A Hyperdoc is a digital google document that contains links and directions to student learning activities in a colorful and playful way that get's your kids excited about showing what they know about subject matter. Think about a table in your document where each section has an activity and instructions on what to do and how to do it. It's like you are right there in the classroom telling them what to do, except your really not there and hopefully on a fun tropical vacation. 

Creating a Hyperdoc is easy with Google Docs.  Just create a table where each section includes short and sweet instructions (i.e complete the Desmos activity) and what to do to show they have finished  (we call this "evidence").  Your evidence might contain a screenshot of their score or a reflection of what they learned.  The fewer steps and the simpler the better.  

 As a Hyperdoc is simply a Google Doc with a URL you share with your students be sure your "Share" settings are in "View Only" this forces the reader to "Make a Copy" and work on their own. Did I ever tell you about the time when I left my Google Doc in "Edit"? Oh the places your kids will go, and yes they went there ( I work with 6th and 7th graders). I always include this directions on the top of my Hyperdoc, and to "share" with me so I can see evidence of their work.  

Hyperdocs are perfect sub activities because you can allow your students to work autonomously and encourage them to "be on task" all the while you are tracking their performance with digital tools and online websites.  Some of my favorite webtools such as FlipGrid, Desmos and Khan Academy include a teacher dashboard where I can see how my students are performing and where they struggle.  Check out my Google Doc on Webtools for lots of resources for online tasks.

The key to a successful Hyperdoc is differentiated activities with a "low floor" and high ceiling".  What I mean by that is creating increasingly challenging activities that begin with tasks that all students can do without any support.  This might be watching a video about a concept, or playing a game and recording their score.  Thinking about how tasks can become increasingly challenging are easy with a framework such as Bloom's Taxonomy.  
Your first few tasks should promote students in "remembering" the concept and big ideas and "understanding" how things work to make sense of the skills and strategies they are learning in class.  Once you've activated prior knowledge then students can "apply" the skills and strategies in a context that requires more cognitive demand.  Finally your students should reach the highest level of Bloom's by creating a product of learning that shows mastery of the standard.  This might include "creating" an Educreation video that shows how to perform a task, or a Digital poster with a tool such as Canva that allows them to synthesize big ideas.  

Want to see what this looks in action for a 6th Grade Math Standard on Equations and Expressions? Check out my video below and be sure to Subscribe to my channel to receive a copy of this Hyperdoc so you can start creating your own.

Join my Facebook Group Teacher Prep Tech or Making Math Connections for more freebies and best practices in teaching with digital tools! 


Friday, March 15, 2019


Creating Open-Ended Math Tasks

Regardless of your class size, designing instruction for everyone’s ability is a complex endeavor, students come into the classroom with different funds of knowledge, experiences, and beliefs about themselves as a learner. Despite these differences, you must prepare students to meet grade level standards and access state adopted curriculum.

While traditional math textbooks often provide the structure for students to practice procedural skills, they often lack the flexibility to scaffold instruction based on students' needs and interests.  Just like a doctor needs to focus on the patient's needs, lifestyle, and symptoms, so must the teacher individualize instruction based on their students. This is where designing open-ended tasks for your students can move your instruction from "why do we need to learn this" to "when can we work on our task." 

There are two main types of tasks: close-ended and open-ended tasks. Close-ended tasks are predictable, focus on one way of thinking, and have a single right answer. In contrast, open-ended tasks are unpredictable, provide students with opportunities to explore ideas more broadly, have multiple solutions, and incorporate many ways of thinking and decision-making. There is often ambiguity in open-ended tasks, as such they are frequently referred to as ill-constructed questions or problems. Open-ended tasks require more cognitive effort from students and therefore engage them in higher levels of thinking and learning. Students must draw from their knowledge in broad ways to figure out potential solutions.

Another difference between open-ended and close-ended tasks lies in the type of thinking required when determining a solution. Close-ended tasks often draw on narrow ways of thinking that rely on procedure or previously memorized information, while open-ended tasks draw on students’ broad conceptual knowledge (Stein & Smith, 1998). The path to the solution of an open-ended task requires effort, multiple steps, and application of broad conceptual knowledge, rather than rote memorization.  

So are you ready to infuse Open-Ended Tasks into your classroom practice? In this video I am demonstrating how I introduce an open-ended  task of a Scavenger hunt to identify arrays in this second grade classroom.  Students have been working with arrays by constructing models using a variety of manipulatives.  In this activity they are extending their thinking to identify an array in their class. 

The flexibility of open-ended tasks allows students to work in their "Zone of Proximal Development" (ZPD) while providing you with the knowledge of where student understanding lies in an authentic task.  

Technology can also support students in ways of showing and expressing what they know about a concept.  Using free tools such as SeeSaw or Flip Grid students can create a video to explain their thinking.  This type of activity also allows students to create, apply and synthesize learning in a meaningful way.  As an extension of this activity students were required to identify arrays in their home. 

When creating Open-Ended Tasks you must ground the task in students' interests, funds of knowledge and ability.  This will support you in creating a hook, that will capture students' attention and support them in making mathematical connections.  Holiday's and school events are also a perfect way to build on students' fund of knowledge.  In this gift giving guide activity, students were able to select a gift to get ratings from their peers.  The concepts of ratios, percents, and division were all included in this open-ended task.  Once students completed a hard copy of their gift guide they then completed a digital version which was shared with families.  
Ratio Gift Guide

Creating open-ended tasks are a perfect way to keep students motivated to "do the math" and apply the concepts they are learning about in a meaningful context.  When the recess bell rings and kids are still motivated to work on this open-ended task, you know it's worth the investment. Create your own open-ended tasks with this planner and invited Dr. Dickenson to your school for Professional Development in curriculum and design.  

Join our Facebook Group for more Freebies and share your best practices on making meaningful math connections.  


Wednesday, August 8, 2018


Tech Tools for Teaching

Got Technology? 

Can technology help to support your students through personalized learning, visual representations, digital tools, and online activities to support making connections and explaining their thinking?

A meta-analysis of the effect of technology on mathematics achievement showed statistically significant gains across the K-12 classroom (Slavin & Chung, 2013). Students who reported their teachers used computers frequently as a way to demonstrate new topics had higher levels of math achievement (House, 2011). 

Mathematics knowledge was also positively related to the use of multimedia strategies for elementary students (Weiss, Kramarski, & Tails, 2006). These findings suggest the role of technology does make a significant impact in students’ academic achievement in mathematics. 

Moreover the findings suggest the use of technology should not be limited to one instructional approach or methodology. Teachers should vary how they use technology from showing a video clip of a math related concept, to providing practice of mathematics facts and concepts through technology tools and resources.

As a technology advocate, teacher educator, and mother, I want my students and children to know how technology can support learning and instruction.  Dr. Ruben Peuntedura, coined the SAMR model as a way to articulate the level of technology integration across a continuum.  SAMR is an acronym for substitution, augmentation, modification, and redefinition. 

This framework is important to consider when integrating technology, in terms of the level of cognitive demand.  However teachers must also consider the function of technology when designing instruction.  Will technology be used to: assess, present, display, demonstration, create or gamify learning?  

If students are working on a project-based learning task, then digital tools that support students in the creation phase of their project might be useful to consider, whereas teachers who are explaining a concept might need virtual manipulatives to help students construct a model.   

As such I have created a classification of technology tools in relation to mathematics instruction.  Have fun, take a look and share your teaching ideas and technology tools with me.
Click Here for the Google Sheet 

Digital Assessment Tools: understand your learners and what they know, need to know or have learned. 

Blended Learning: personalized and provide additional support or challenge using a blended learning program. 

Calculation Tools:  calculating data and displaying information with pictoral and symbolic representations. 

Creation Tools: express ideas and show what they know via multimedia and video recording. 

Collaboration Tools:  students share ideas, resources and work collaboratively on different devices at the same time. 

Construction Tools:  create a mathematical model using either real world images or virtual pieces. 

Connectivity Tools: share  ideas and/or products of learning, with other people in a virtual space. 

Gamify:  ask questions and provide immediate feedback. 

Math Tasks: Rigorous math tasks that allow students to problem solve and think deeply about a concept. 

Presentation: share ideas in a presentation format. 

Productivity: support you and your students in organizing ideas for self-regulation. 

Video: used to demonstrate a concept or express a related math idea.

Got technology tools, tips, ideas or just want to share an idea? Please leave a comment below, and join our discussion on Facebook