Learning, Math, Math Number LIne, number sense

Mathematical Clotheslines

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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.

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Learning, Math, Number Talks, Teaching and Instruction

Number Talks- A Routine for Reasoning

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The word routine is defined as a sequence of actions that are regularly followed so that they become a habit.  In the classroom routines are often thought of as classroom management procedures that support students in making more effect use of classroom time and to transition more efficiently from one activity to another.  Classroom routines such as how to sharpen your pencil, clean up your materials, come in from recess etc. are explicitly taught, and practiced early on in the school year.  As these routines become habits they help the classroom community run more smoothly, save valuable learning time, and create a predicable, safe space for learners and learning.

Routines can also be powerful tools for mathematical thinking and reasoning.  “Like the management routines, these “mathematical thinking routines” also have a predictable set of actions that students learn and then practice repeatedly until they are second nature.” (Kelemanik, Lucennta, and Creighton, 2016, p.18)  Number talks are one such reasoning routine.  As you use Number Talks in your classroom you establish a routine of actions which the students come to expect and become familiar with.  These actions form a habit and in so doing free up cognitive energy so that the brain can focus not on the routine but on the mathematics.

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Think of a routine as a container.  The container does not change, it is a constant, it is solid, it is reliable.  You can count on the container to hold what you need it to hold.  When the container is well established for students their cognitive energy can shift from focusing on the container to focusing on the contents in the container. This is the power of an established and predictable Number Talk routine.

The routine of a Number Talks has 5 main steps that students come to expect.  During a Number Talk they will:

  1. View a problem/ task.
  2. Think and solve it.
  3. Share their answer.
  4. Defend their solution.
  5. Compare and connect their reasoning to the reasoning of others.

The benefits of adding this promising practice to your instructional routines are numerous.  Besides building more confident mathematicians, Number Talks increase students number sense as they require students to become more flexible and strategic thinkers.  Number Talks also, increase students ability to articulate their thinking and refine their mathematical communication skills.  As we work to increase our students computational fluency Number Talks have become one of THE most promising practices we can add to your professional repertoire.

If you would like to learn more about other Routines for Reasoning check out these books: