Summary
Educators and parents often ask us, ‘where do we start’ with using Cuisenaire® rods. This fabulous blog by our friends at https://cuisenaire.co.uk leads you through the initial activities.
Cuisenaire® rods are a versatile manipulative which encourage children to learn mathematical principles through the process of play.
Educators and parents often ask us, ‘where do we start’ with using Cuisenaire® rods. This fabulous blog by our friends at
Much of this blog post will refer to activities or games encouraged by Cuisenaire and Gattegno themselves and are taken from Maths Textbook 1.
The Maths Textbook series were written as a curriculum by Gattegno to be used with the Cuisenaire® Rods, and also the cardboard materials designed by Georges Cuisenaire ( https://cuisenaire.co.uk/product-category/cuisenaire/cardboard-materials/
https://cuisenaire.co.uk/product-category/cuisenaire/pupils-textbooks/)
This blog post mainly contains excerpts from the first chapters of Maths Textbook 1 written by Dr Gattegno and then links to further resources which can all be found on the Cuisenaire website.
In Maths Textbook 1 the rods are described by their colour rather than the number that colour represents.
As students become more familiar with the rods and have spent time doing activities referring only to the rods by their colour name, they are then, in Part 4 of textbook 1 ( page 32 ,‘Number Work , Measure, Study of Number up to 10’) encouraged to do activities which allow them to discover how many whites will be needed to make equivalent lengths of the other coloured rods.
The rods are initially referred to as white, red, light green, purple, yellow, dark green, black, brown (or TAN), blue and orange. When written about by their colour letter it is as follows w, r, g, p, y, d, b, t, B and o
Please bear in mind that although the activities shared in this blog are aimed at younger children, and are taken directly from Maths Textbook 1, adults or older students who either have dyscalculia or a difficult relationship with mathematics can also go through these activities and find some sense of simplicity, comfort, ease and reassurance these coloured sticks allow.
Gattegno, in Maths Text book 1, encourages the beginners to play with the rods initially by tipping them out of the box and onto the table or floor.
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There are several activities we can ask the learners to do with the pile of rods before them.
One is to play with them and make all sorts of shapes and patterns at will, and to talk about those images and why the students used those colours and what images they tried to create with them.
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Another activity is to group all of the rods into the same colours or ask them to group them into the same length.
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Another great starting activity is to put the rods back into the box where they fit. This helps with sorting, recognizing lengths and how they fit into the correct sized compartment for their size. It can be quite absorbing and also involves a lot of trial and error for the smaller sized rods, less so with the bigger rods.
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In Maths Textbook 1, Gattegno asks that the students make trains with the rods.
‘Make a train the same length as the tan rod or a blue rod with any of the other smaller rods’
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In his next task he brings in the use of the word equivalence:
‘Can you make trains using more than two rods the equivalent length of any of these rods:
Orange, black, dark green, blue, tan.’
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He then goes on to describe the trains that are equivalent to one rod a pattern. He asks that patterns to be made for the other rods, and that when the student has made all of the possible patterns for one rod, says that that is a complete pattern of that rod.
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Another activity Gattegno suggests is for the student to make their own trains and then get another student to guess which rod is equivalent to the trains.
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Smaller, bigger, longer, shorter, same and different activities:
The students are asked to put the red rod and orange rod end to end and then see if that train is bigger or smaller than a blue rod, a tan, a black, an orange and a white, an orange and a light green.
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Try doing this again with two other rods and find the missing one.
MAKING A STAIRCASE!
Most people cannot help themselves making a staircase with the rods when they first start playing with them. However, smaller children don’t always do this immediately, so we can encourage them to take one rod of each colour and make a staircase and then ask these questions –
Which rod is the biggest? Which rod is the smallest? Which rod comes before the biggest? Which one comes after the smallest?
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Move up the staircase saying the colours of the rods and then move down the staircase saying doing the same thing.
Then do it again but with eyes shut starting first with the white rod going towards the orange rod and then again in the opposite direction.
See which rod you need to make all the rods of the staircase the same length, or level with the orange rod?
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Take them away and try to visualize which different rod is needed this time.
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Activities relating to Addition, Difference and Equivalence and Literal work in Maths Textbook 1.
Compare a black rod and an orange rod.
Which rod will you put end to end with the black rod to make a train of equivalent length to the orange rod?
The length of the rod that fits is called the difference between the length of the black and the length of the orange.
Find the rod whose length is the difference between the blue and the pink, the dark green and the red, the light green and the dark green, the red and the white.
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At this point in the activities Gattegno introduces writing about what is happening mathematically. He introduces the symbols for addition, subtraction and equivalent to in such a comprehensive way. Here is an example:
“When we wish to write that two rods are end to end we put the sign +, and read it plus.
w + r tells us the white rod and the red rod are end to end.
Let us write – between two letters when we wish to show that we have two lengths, and we are measuring the difference between them. We shall read this sign minus.
o – w tells us we want the rod whose length is the difference between the lengths of the orange and the white rods. You can find that B is equivalent to o – w.
What is equivalent to y – r ?
Let us put = whenever we would say equivalent to.
For what we have just done you could write:
g = y – r “
Within the book there are many more exercises he asks the students to perform.
The introduction of more complex mathematics is made so simple by the way in which Gattegno introduces these activities.
His language can be dated but any modern-day math teacher can transpose his words into more contemporary language for modern day students. What he does do is appeal to the deep intrinsic intelligence that all children possess and presents it in a way in which they can access that through the investigative tasks he presents before them.
The most important pedagogy underpinning Cuisenaire® Rods and the Cuisenaire Gattegno approach to mathematics is that the students make the discoveries for themselves, and the rods give them a concrete visual and tangible way in which to see mathematics. Colour, size, space, manipulation; these different forms of instigating learning and understanding are all within a set of Cuisenaire rods.
The teacher must let the children use them, hold them, do the activities themselves without showing it to them. That is key with all of Gattegno’s educational principles and pedagogy.
Discovery through play, or what feels like play, makes it a joy to learn.
Caroline Ainsworth has had incredible results with her primary school students using the approach and the activities outlined in the Gattegno Mathematics Text book series.
Everything you need to know lies within these pages, and we as a company recommend that teachers and parents go through these books yourselves before starting to work with your students or children so that you can see for yourself how comprehensive and brilliant the Cuisenaire® Rods alongside the text books are as a basis for mathematical grounding for children who just cannot learn in the current educational system or with the crazy demands that the national curriculum imposes on the innate learning ability each individual possesses.
Links to Caroline Ainsworth’s work can be found on the Cuisenaire website here: https://cuisenaire.co.uk/cuisenaire-rods-in-the-classroom/
For a more mathematically sophisticated article about using the Cuisenaire rods please click on this link here:https://cuisenaire.co.uk/wp-content/uploads/2023/11/LESSONS-WITH-CUISENAIRE-RODS.pdf
This link will also be of interest as it is no longer available as a book, but again a great resource packed full of ideas: https://cuisenaire.co.uk/wp-content/uploads/2023/07/bookofideasjpegBinder2.pdf
This link takes you to an article written by John V Trivett for teachers:https://cuisenaire.co.uk/wp-content/uploads/2023/10/coloured_sticks.pdf
The pedagogy behind the creation and the subsequent math text book series is that the students, through being led to discover for themselves a solid understanding of basic mathematical concepts will then be able to manage more complexity through the understanding and foundation in mathematics they have gained from using Cuisenaire® Rods in this way.
