The following task is one of my personal favorites because it uses so much mathematics to introduce a complex idea. Solving equations. Moreover, this task has an enormous amount of flexibility for its use. So, for this task I will:
- Introduce the major concept of the task.
- How to setup with students
- Provide you with an example of how I’ve used it in my classroom
- Create a template for you to use in your classroom.
- Check out some opportunities for ways to engage students in this task that are accountable and equitable.
These examples may be downloaded and used, or provide inspiration.Bags and Blocks Task examples
What is a balance beam task?
Using the concept of a balance beam, student reason through the process of identifying the number of blocks inside a “mystery bag.” In doing so, students are practicing the reasoning of solving an equation, often complex equations using the reasoning of a balance beam.
How do I set it up with students?
I like to start by asking students to consider the meaning of the word “equal.” In general, students reason that equal means fair or balanced in some way. Then I show them a makeshift balance beam using buckets and a meter stick, depositing binder clips into the buckets. Eventually, I want students to determine that there are two ways to make this balanced:
- Adding binder clips to each side
- Taking away bander clips from each side.
Then, I throw out an idea that some binder clips have a lifting force, and suggest that I add one of those lifting clips to one side and then ask groups to determine at least two different options that they could do (knowing they have unlimited resources) to make it balanced. I will select and sequence until students say:
- Add a lifting clip to the other side
- Add another positive clip to the same side as the lifting clip.
At this point, students have EVERYTHING they need to start the task. Some students will not understand the second part of this demonstration, that is okay for right now. Let them play around and explore.
Simple example explaining balance beams: https://youtu.be/5q9wy7G2v5U?t=35
Online interactive balance beam: http://www.learner.org/courses/learningmath/algebra/session6/part_c/index.html
My friend Nancy Ku developed two tasks that she uses in her class, she has allowed them to be shared here:
Copy and paste the items to the left of the slide…
Henri Picciotto’s MathEd.page is one of a kind and has an abundance of resources, I’ve gotten sucked into this site for hours. He invented a similar procedure to Algebra Tiles called LabGear and has published the whole book for free on his website. Learn and use Lab Gear without an investment. https://www.mathed.page/manipulatives/lab-gear.html
Algebra Tiles and Algebra Blocks are products that are valuable for students to learn more about algebra:
- CPM Interactive Algebra Tiles
- MathBits Algebra Tiles (downloads and resources)
- IXL Practicing with Algebra Tiles
- Books to Support Algebra Tile Work