Cuisenaire Rods
for Modelling Mathematical Concepts

Cuisenaire rods are excellent concrete representational materials for teaching arithmetic concepts and algebraic ideas.

Learning the rod values: a sequence for using Cuisenaire rods

Step 1: Free play and exploration

Each child has a container of rods and working alone or with others, is encouraged to design, construct, take apart, rearrange, copy, extend, make bigger, smaller, higher, wider and so on.  They should be encouraged to talk about their constructions and designs.  This develops representation and communication, the beginning of abstraction and generalisation.

During free play they make decisions, solve problems of representation,
design, understand balance, symmetry, patterns and spatial awareness.

Ask questions such as:

• What did you make?

• Tell me about what you have made.

• Does it have a name?

• Which colour rods did you use to make your  …?

• How many rods did you use?

• What shall we build next?

• Can you describe your … to your neighbour?

Children should be encouraged to tell and write stories about the things they make.  This story-telling  develops mathematical language, application and communication skills in children.

Activities should try to incorporate the six levels of knowing.  For example children may begin by discovering the interrelationships between rods
(intuitive); manipulate rods to explore number relationships (concrete); trace, draw and colour the various patterns (pictorial); find codes for the rods in the form of letters and numbers and use these codes to express ideas (abstract);
use number relationships to solve practical problems or make their own
problems (application); share their activities with others (communication).

Step 2: Classification, Ordering and One-to-One Correspondence

To provide experience in the concept of classification, the children should be asked to separate the rods according to colour. The teacher should ask
questions relating to size, similarity and dissimilarity.

Teacher: Show me a rod which is bigger/smaller than this one and is different
to your neighbour’s.

Repeat this with many examples, acknowledging each child’s answer.  You
should go to each child and place your rod next to the child’s rod to show
other children that the answer is correct.  If a child has an incorrect answer,
help him/her by comparing his rod with yours.

When children see that there are several possible correct answers they are motivated to see that mathematics questions may have multiple answers. 

For example, if you had the yellow rod in your hand and a child holds the
brown rod, ask him to compare the two rods by stating: The brown rod is
longer than the yellow rod.

Now ask the child to say it again using the words shorter, smaller etc.

Later on similar statements are made using the numerical values of the rods.

E.g. Show me a rod which is smaller than 6; Show me a rod which is longer
than three and different to your neighbour’s, etc.

Staircase Model 

Teacher:  I want you to make a staircase using one rod of each colour.

• If some children have difficulty with this, ask them to watch
  a child who is succeeding.

• If more practice is needed, ask them to mess up their first staircase,
  then see how quickly they can remake it.

• Ask them to close their eyes and name the order of colours
  of the staircase.

• Let each child say one colour in turn in the correct order,
  the first child beginning with white, the next one red, and so on.

Step 3: Representation of rods into number, learning the number
value of each rod  - effective use of Cuisenaire rods in deriving arithmetic
facts is not possible unless the teacher and children first know the colour and numerical names of the rods.

Which rod is missing?

• Divide the whole class into pairs, each pair having a staircase of rods.

• One child closes his/her eyes while the other removes a rod and
  closes the gap.

• When he/she identifies the missing rod he she returns it to the
  correct place.

• After several successful turns, two rods may be removed.

• Children should be encouraged to describe the process and
  the strategy they use to identify the missing rod.

Rod values

• Teacher: (Showing a red rod) Take a red rod and place it in front of
  you. How many white rods do you need to make them as long as the
  red one?

Children: Two

Teacher:   If we call the white rod ‘one’, what should we call the red one?

Children: Two, or two ones.

• Repeat this for all the rods, making sure that each rod has been
  identified by colour and number.

• Ask individual children to identify the number of the rod you have
  in your hand.  They may refer to their staircase.

• Ask the children to cover their staircases and take from their tray,
  the rod which corresponds to the number you call, holding it up.

• Ask a child to come forward and repeat this activity.

• To reinforce, take a rod and ask for different names for it.
  E.g. yellow rod, five, five ones.

Step 4: Teaching Addition and MultiplicationFacts (as on theNumber Relationships video.)

necessary in order to develop the child’s visual perception and strategy skills.

Mahesh Sharma is Professor of Education  at Cambridge College,
Cambridge, Massachusetts, USA .

He is the Director of the Center for Teaching/Learning of Mathematics.
He edits Focus on Learning Problems in Mathematics, an international and interdisciplinary journal dealing with the learning and teaching of
mathematics, in particular with issues dealing with learning problems
in mathematics such as: dyscalculia, acalculia, mathematics anxiety
and specific learning disabilities in mathematics.
He also writes Math Notebook, a newsletter for teachers and parents.

His Center for Teaching and Learning of Mathematics is affiliated to
Berkshire Mathematics in the U.K. run by Patricia Brazil.
She organises Prof. Sharma’s lectures and courses, and produces videos / DVDs, which are for sale along with the U.S. publications.

Tel: 0118 947 4864 Fax: 0118 946 1574
Email: info@berkshiremathematics.com

© Mahesh Sharma/Patricia Brazil , Berkshire Mathematics 1999.