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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Kindergarten, Learning, Math, Reggio Inspired

Provoking Exploration in Mathematics

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Provocation can be defined as the act of causing someone to feel, think or begin to do something.  In the Reggio Emilia approach to learning they involve the teacher creating invitations/ displays that provoke students to begin to explore an idea or concept with materials that spark thinking. Provocation materials can be loose parts, natural items, children’s literature, photographs, inquiry questions or all of the above.  The goal is to find something that sparks curiosity and leads to new learning.

Within mathematics, provocations can lead to inquiry and discovery of mathematical concepts and initiate mathematical thinking.  I am currently working with a group of four exceptional kindergarten teachers to develop opportunities for our elementary teachers to explore the idea of using provocations as a tool to provoke mathematical inquiry, creativity, and discussions.  Together we initiated the first ever Kindergarten Mathematics Learning Community in which kindergarten teachers come together to discuss ways to provoke their young mathematicians in thinking and growing mathematically.

Our first provocation focused on the question How do Numbers Help Me Tell My Story?  This question and the materials we deliberately put together can serve as a starting point for developing a deeper understanding of numbers and counting concepts in Kindergarten.

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Some of the Big Ideas of Counting that can be explored through this provocation are:

  • You say one and only one number for each object (one to one correspondence)
  • The last number spoken tells how many. (cardinal principle)
  • You can represent a number in a variety of ways.
  • The quantity of a group does not change if the objects are rearranged. (stability)
  • There is a consistent set of counting words that never changes. (stable order principle)
  • You say one number name for each object tagged. (synchrony)

Our How do numbers help me tell my story? provocation included a variety of loose parts (shells, buttons, rocks, glass beards, pipe cleaners etc.) as well as tree cookies with numbers printed on them and wooden numbers.  We used felt squares to delineate the space and added round cork pot holders.  Looking in the mirror students could study themselves to recreate what they see using the loose parts.  They can also think about numbers that connect to themselves and represent those numbers using the loose parts on the counting place mats as a guide.

 

Using high quality children’s literature to connect mathematical concepts, and cultural perspectives is an important consideration for us in every provocation we design.  The Colors of Us  was our inspiration for our How do numbers help me tell my story? provocation. Other literature connections can include The Best Part of Me,  and Every Buddy Counts.

 

For those of you wanting to provoke the thinking of our young mathematicians I am including a freebie to get you started.  Here are the counting mats I created in French and in English as well as the Number Formation Cards.  Enjoy!!

This exploration of Provocations in mathematics is has become a wonderful learning journey for me.  I am so honored to have an opportunity to learn with some fantastic teachers within my school division and around the world.  If you are looking for inspirations from leaders in this area make sure to check out the work of Janice Novakowski. 

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