Computational Fluency, Learning, Math, number sense

Student Inquiry into Computation with Cuisenaire Rods


At our last math community meeting teachers were given an opportunity to explore the provocation shown above.  This provocation was provided to support wonder, curiosity, creativity and multiple opportunities for computation.  Teachers were able to create designs with addition, and multiplication using one of my favorite computation manipulatives…Cuisenaire rods.

I chose this activity and these manipulatives for many reasons.

  • It allows students to explore part-part-whole thinking
  • It provides opportunities for multiple computations in an engaging way
  • It brings creativity, and design into mathematics
  • It allows for collaboration, and conversation
  • Students can discover relationship, and multiple interpretations

After our professional exploration many teachers took this activity back to their classrooms and shared it with their young mathematicians.  Below are some examples of what the students came up with in classrooms.

As a follow up students can bridge the concrete to abstract continuum by recording their computations/designs pictorially and abstractly on a sheet.  Initially, recording sheets could have pictures of coloured rods to match the concrete representations the students created.  As students progress in their level of abstraction they can switch to just marking the value on the rod.  Abstractly, they would record the equation their design represents.

Below are some supports that can help you incorporate Cuisenaire rods into your classroom.

Student Desk Cards

Whole Numbers

Decimal Numbers


Build It! Draw It! Write It! Student Recording Sheet


Math, Teaching and Instruction

Inquiry in Mathematics

In Saskatchewan our provincial curricula are built around one central core…inquiry.  Inquiry is a philosophical approach to teaching and learning that empowers students to explore and discover.  Through inquiry students are active participants in the creation of understanding and knowledge.   They are asked to be curious, to wonder, to question, to reflect, to share and to think

In Mathematics inquiry is often seen through problem solving.  By collaboratively solving and creating mathematical problems students construct and deepen their understandings of concepts, strengthen their strategic competence, and develop their logical reasoning skills.  As students engage in problem solving they need to attend to 4 important stages in the inquiry/problem solving process:

Stage 1: Understand the Problem–  This very important stage is often overlooked in the classroom.  It is often assume that students understand the problem in front of them but this assumption can by costly.  Without a solid understanding of what they are being asked to do, students are often stumped before they start.  Time spent carefully dissecting a problem and ensuring understanding can be critical to success.

Stage 2: Make a Plan– Just like the construction of a building, the construction of a mathematical solution requires forethought and a plan.  Having a carefully considered plan of attack can help students construct their solution successfully.  Problem Solving plans or strategies can include:

  • Acting it out
  • Using a model
  • Drawing a picture
  • Guessing and testing
  • Looking for a pattern
  • Making a chart or a graph
  • Working backwards
  • Making an organized list
  • Using logical reasoning   

Stage 3: Carry out the PlanIn the words of  Nike – Just Do It!

Stage 4: Look Back –  This stage involves careful reflection, checking to see if your answer makes sense, and considering the solutions of others.  Considering the solutions of others and comparing them to your own provides an opportunity for understanding and learning to be collaboratively constructed in the mathematics classroom.

For more information on Problem Solving in Mathematics check out these great resources:

Making Math Meaningful to Canadian Students by Marian Small

Making Math Meaningful

Introduction to Problem Solving by Susan O`Connell