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


Learning, Math, Math Number LIne, number sense

Mathematical Clotheslines


A Mathematical Clothesline is a great visual tool to support students in reasoning proportionally with numbers.  Students can work cooperatively to place a set of concept cards (various representations of number) on the line in a position that makes sense proportionally.  As students place the cards on the line they need to consider the card they have, the cards left to position, and any benchmark numbers (numbers that assist in estimation and tend to be multiples of 5 or 10) that are already present.  Mathematical Clotheslines differ from a formal number line in that cards are not placed in a measured and scaled sequence, but simply displayed in a specific order.

I have seen many clothes line activities online in recent months but only recently this activity for younger students.  Janice Novakowski recently created this post which inspired me to explore her idea to use this tool with younger students.  I expanded on her idea by adding in number words in English and French as indicated by our grade one curriculum outcome.  I have also created a fraction version.

In both of the Mathematical Clotheslines below students have multiple representations of numbers to work with.  Not all representations need to be introduced and used at the same time.  As students expand on their understanding of different ways to represent numbers and fractions pictorially more and more representations can be added to the activity and become a topic of discussion in the classroom.