Rethinking Hands on Math with Understanding by Design

This quarter for our class EDTC6102 we had to create or modify a lesson that integrated technology in a meaningful way using the Understanding by Design model by Grant Wiggins and Jay McTighe. After being assigned this project, I knew that I wanted to pick an upcoming unit that is apart of the school districts curriculum for math. I wanted to explore ways to enhance the math my students were already receiving. The unit I decided to revamp using the Understanding by Design model is Composing and Decomposing numbers to 10.

Understanding by Design Process

Stages of Backward Design

Stage 1- Identify Desired Results

Stage 2- Determine Acceptable Evidence

For this unit I wanted to create performance tasks that allows for students to show their understanding in multiple ways including using technology.

Performance Tasks:

-Students will create visual representations of decomposition patterns and will record the corresponding addition sentences. Students will use unifix cubes to show the different ways to make a number (example: the number 8). Then students will create a visual using colored squares to represent the cubes. Once students have shown their patterns, they will write the addition number sentences to represent their decomposition. Students can choose an number 2-10 to show decomposition patterns.

-During math rotations students will use the classroom SMART board to solve decomposition problems. Students will show work using a different colored pen per student.

-Students will use to create an interactive whiteboard to teach others about part-part-whole relationships. Once students create their interactive whiteboard they will share it with the teacher.

Other: Students will also complete an end of topic assessment, along with quick checks throughout the lesson to check for understanding. At the end of the entire unit students will complete a self-assessment of their decomposition visual using a rubric. Students will then ranking their understanding using of the topic. To see an example click here.

Stage3 – Plan Learning Experiences and Instruction

Digital Citizenship-

When introducing technology to students it is important for students to become digital citizens before interacting online. With my students being only in Kindergarten, I am usually the first person to teach them technology standards. ISTE has seven student standards. Standard 2 Digital Citizenship is stated as “Students recognize the rights, responsibilities and opportunities of living, learning and working in an interconnected digital world, and they act and model in ways that are safe, legal and ethical”. Before teaching my Rethinking Hands on Math unit, I first need to teach my students about being safe on the internet, especially if they are going to interact with the site With our discussion on digital citizenship students will become aware of their role with safe, ethical, positive, and legal behavior when using technology.

Six Facets of Understanding-

  • Can explain—via generalizations or principles, providing justified and systematic accounts of phenomena, facts, and data; make insightful connections and provide illuminating examples or illustrations. 
  • Can interpret—tell meaningful stories; offer apt translations; provide a revealing historical or personal dimension to ideas and events; make the object of understanding personal or accessible through images, anecdotes, analogies, and models.
  • Can apply—effectively use and adapt what we know in diverse and real contexts—we can “do” the subject.
  • Have perspective—see and hear points of view through critical eyes and ears; see the big picture.
  • Can empathize—find value in what others might find odd, alien, or implausible; perceive sensitively on the basis of prior direct experience.
  •  Have self-knowledge—show metacognitive awareness; perceive the personal style, prejudices, projections, and habits of mind that both shape and impede our own understanding; are aware of what we do not understand; reflect on the meaning of learning and experience. (p.84)

During this unit students will be hitting all 6 facets of understanding. When making their visuals and creating interactive whiteboards to teach others this concept they are explaining what decomposition is, they can interpret their work to make it personal and available for others. Students will apply when creating their interactive whiteboard to teach the class this concept. When their interactive whiteboards are shared among the class they have perspective and can empathize. Finally, students will have self-knowledge when they complete their self-assessment of their visual and overall understanding of the content.


The Understanding by Design model was first introduced to me when I was studying for my undergrad. While I practiced using this model in college classes, I got away from using it during full time teaching. When this current course brought Understanding by Design back into my life I remembered how great it really is. Using this model allowed for me to step back and really think about the content I was teaching my students. I felt like I was often just using the curriculum assigned by the district rather than looking at what I wanted my students to get out of the lessons I was teaching. With knowing the desired results of a lesson or unit helps make these lessons/units more meaningful for students and allows for them to know the purpose of each lesson.  I really liked how this process allowed for me to integrate new learning opportunities for my students by using technology. I also really appreciate how this model made me think about what I wanted students to produce to show their understanding. In the past students have complete math magazines for each lesson, now I have allowed the students to demonstrate their learning in a personalized way. I love this simply because I am able to connect with all of the different learning styles my class has to offer.

Sources- (2017) ISTE Standards for Students. (Retrieved on 2018, March 17) from:

Wiggins, G., & McTighe, Jay. (2005). Understanding by design (Expanded 2nd ed., Gale virtual reference library). Alexandria, VA: Association for Supervision and Curriculum Development.

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