Putting Manipulatives to Work, Part 1: Developing Number Sense in K–5 with Cuisenaire Rods®, Rekenreks & Place Value Chips

Putting Manipulatives to Work is a three-part series of webinars designed to take advantage of manipulatives that are likely to be available in schools and in classrooms. Each session discusses several manipulatives that can be used to support a common topic: number sense (Part 1), geometric measurement (Part 2), and algebraic expressions/equations (Part 3).

The series came about from the questions of educators in the field regarding unused manipulatives they have accumulated in their classrooms. They could have been left behind by another teacher or part of a new program, but the common theme is that these materials are available and should be used. Teachers often aren’t sure how to use them. This series highlights a mix of manipulatives—some old friends like Cuisenaire Rods, around for more than 80 years, and others newer to our classroom like Rekenreks. This webinar answers the question, how can we best use these manipulatives to enhance instruction?

What is Number Sense?

Number sense is a broad term that reflects a deep understanding of numbers – what they represent and how they behave. The Curriculum and Evaluation Standards (NCTM, 1989) describe five key elements of number sense:

  • Number meaning,
  • Number relationships,
  • Number magnitude,
  • Operations involving numbers, and
  • Referents for numbers and quantities.

One of the primary goals of mathematics education in the elementary grades is to build number sense. Manipulatives are a key tool and there are two important attributes to consider. These models can be proportional or non-proportional. They can also be groupable or pre-grouped. Developmentally, proportional models help students understand number magnitude and groupable models help them see number relationships. Over the course of instruction, students should have experience with a wide range of models.

This webinar features Cuisenaire Rods, Rekenreks, and Place Value Chips. We cannot share all the uses of these tools in a single session; the webinar shares examples of activities that are most closely related to number sense.

Cuisenaire Rods

Cuisenaire Rods to teach number meaningCuisenaire Rods include rods of 10 different colors, each corresponding to a specific length. White rods, the shortest, are 1 cm long. Orange rods, the longest, are 10 cm long. Rods allow students to explore all fundamental math concepts, including addition and patterning, multiplication, division, fractions and decimals, and data analysis. Learn more...

Uses of Cuisenaire Rods modeled in the webinar

  • Counting – 1:1 correspondence, one more/one less
  • Subitizing – seeing a number as a whole entity, not a collection of single items
  • Fact Families – how many ways can you make a train of a given length/value?
  • Modeling Operations

Rekenreks

Rekenreks useful for subitizingThe Rekenrek, or arithmetic rack, was developed by Adrian Treffers, a researcher at the Freudenthal Institute in Holland. A common version consists of twenty beads on a frame. The beads are organized in two rows of ten, where five are red and five are white on each row.

Uses of the Rekenrek modeled in the webinar

  • Representing Numbers
  • Subitizing
  • Addition & Subtraction - counting on/counting back
  • Benchmark Numbers - 5 and 10

Place Value Chips

Place Value Chips useful to teach divisionPlace Value Chips are colored counters where each color is labeled with a different place value amount. Green chips represent hundreds while pink chips represent tens, for example. They are used to model numbers and operations, especially with large numbers, where base ten blocks and other proportional tools are not practical.

Uses of Place Value Chips modeled in the webinar

  • Regouping
  • Division - whole numbers

References

National Council of Teachers of Mathematics (NCTM). Curriculum and Evaluation

Standards for School Mathematics. Reston, Va.: NCTM, 1989.

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Webinar Information

Topic: Number Sense
Grades: K to 5
Recording Date: 6/2/2015
Length: 58:02
Supporting Documents:

  • Presentation Slides
  • CE Quiz
  • Chat Log

Manipulatives Used in the Webinar

 
 
 

About the Presenter

Image: Dr. Sara Delano Moore

Sara Delano Moore, Ph.D., Director of Mathematics and Science, hand2mind

Sara Delano Moore is the Director of Mathematics and Science at hand2mind. Dr. Moore earned her Ph.D. from the University of Virginia in Charlottesville, and also holds degrees from the University of Oxford (United Kingdom) and The Johns Hopkins University. She has taught mathematics and science in both public and private schools, and has served as Program Faculty Chair of the Middle Grades Teacher Education Program at the University of Kentucky. Dr. Moore’s writing can be found in national journals such as Mathematics Teaching in the Middle School, Science Scope, and Middle School Journal.

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Putting Manipulatives to Work, Part 1: Developing Number Sense in K–5 with Cuisenaire Rods, Rekenreks & Place Value Chips

Putting Manipulatives to Work is a three-part series of webinars designed to take advantage of manipulatives that are likely to be available in schools and in classrooms. Each session discusses several manipulatives which can be used to support a common topic: number sense (Part 1), geometric measurement (Part 2), and algebraic expressions/equations (Part 3).

The series came about from the questions of educators in the field regarding unused manipulatives they have accumulated in their classrooms. They could have been left behind by another teacher or part of a new program, but the common theme is that these materials are available and should be used. Teachers often aren’t sure how to use them. This series highlights a mix of manipulatives–some old friends like Cuisenaire Rods, around for more than 80 years, and others newer to our classroom like Rekenreks. This webinar answers the question, how can we best use these manipulatives to enhance instruction?