One of the best math investments for us were the Cuisenaire Rods. You simply can’t fail with them.
They are basically small wooden (or plastic) rods ranging from 1 cm3 to 10x1cm, of various colors. Here’s how the colors go (I am using the Gattegno notation):
M. absolutely loves them (even now, at 9!). And we just decided to “revive” them by starting Caleb Gattegno’s Textbooks.
I managed to take only a few photos and videos over the years although we have used them pretty much everywhere in math.
In this post, you’ll also find multiple links to external websites that have documented the use of Cuisenaire Rods far more than we have. I linked to our favorite App, some free lessons and books to get you started.
When it comes to math, this is the number one resource I recommend all parents to buy for their kids. Children can learn every single math concept in a fun, logical way.
M. helped me make a video presenting the Cuisenaire Rods and some of the resources we use with them, including my newest printable which you can find in our Resource Library.
Concrete-Pictorial-Abstract with Cuisenaire Rods
It’s how Singapore Math (or Math in Focus) works too, with the 3 stages of learning math concepts: concrete, pictorial and abstract.
Concrete means hands-on. Use manipulatives to SHOW how the concept works, let kids explore and figure things on their own. This is the stage where Cuisenaire Rods play an important role.
Pictorial means passing the concrete into 2d. You’re basically drawing what you saw with the concrete step. Here you use bar models to illustrate problems or draw 10 frames for mathematical operations.
Abstract is the math on paper, using abstract symbols for numbers and operations.
Cuisenaire Rods Free Play
I highly recommend you don’t “rush” to the abstract part. Let kids explore hands-on as much as they need.
I wish I could turn back time and tell my inexperienced self the same thing. There is no need for a 4-year-old to “write” his answers. I wish I’d let him play with the rods even more.
Free play with Cuisenaire is very important in order for kids to become familiarized with the rods. Equally useful is creating fun stories around them.
At first, you don’t need to assign numbers to the rods. Keep calling them by color until your children can quickly identify them. Then as you add in more structured play, start introducing the number names corresponding to each rod.
As you start using them for “real math”, don’t forget to keep creating fun stories.
Counting and numbers
Cuisenaire Rods can be used from the very first time you start introducing the concept of counting or numbers to your kids.
Here’s M. at 4, using abstract and concrete skills to find out the numbers. We could have added a pictorial too for a full experience.
He is “reading” the number cards, adding the corresponding number of buttons underneath and then finding the correct cuisenaire rods to represent the number.
He is learning the counting order by arranging the Cuisenaire Rods according to their sizes.
A story we liked to tell was that the little one wants to climb a ladder all the way to 10. We need to build that ladder quick so 1 doesn’t fall. 1 cannot jump over two spaces either, let’s help him by adding numbers.
This soon turned to 1 wants to go to 20 and beyond. Poor 1, he must be quite a climber!
You can continue this by making a ladder for 2 or 3 (learning skip counting in the process).
How many ones go into 5? What about 10? A fun way to see this is to create a story. If I remember ours correctly, we made “teeth” for every number. How many teeth (ones) does the yellow rod (5) have?
When M. started counting well, up to 100 and beyond, he arranged his blocks in bigger patterns by using our Base 10 Blocks (it’s a great addition to Cuisenaire Rods to make bigger numbers). It’s mesmerizing looking at the patterns numbers form again and again and again. It was very interesting for me to watch as well because we never got to “play” with numbers like this in school.
Of course his idea was to go on and on and on… too bad we were out of blocks and rods!
Adding and Subtracting
From counting it’s a small step to addition and subtraction because by playing and counting with them they already grasped the concept of adding one more (to count) or 2-3 more to skip count.
I introduced him to both abstract and concrete stages at the same time but it’s totally normal to do the writing for them at this stage. Just ask them the final result.
I found it very important to spend as much time as M. needed with Cuisenaire Rods until he mastered the addition and subtraction up to 10 because this would be the foundation for any further operations.
One story for addition that we LOVED was the “Party” story. I think we heard it from Educationunboxed, but I might be mistaken.
It goes like this: 10 is throwing a party where all numbers (from 1 to 10) can go, but 10 has a rule that they can only attend 10’s party in PAIRS that make 10. Poor 8, he wants to go to the party but he needs to find a pair to make a 10. Which number can he take with him to 10’s party?
Of course all the numbers threw parties with the same condition to attend. 5 allows only pairs that make 5 and so on.
I remembered M. was very into creating these little silly stories and math was going smoothly with them. He couldn’t wait to do some more addition.
Multiplication and division
When introducing multiplication, you just need to remember that instead of “times” you use “of”. So 4×5 is read as 4 of 5. You ask the kids to show you 4 fives and then count them (skip counting comes in handy here) or they can just group them: two fives and two fives.
Do not introduce kids to the classic lists of multiplication tables that need to be memorized. They need to understand how numbers work by using Cuisenaire whenever they need, and not “forcing” them to remember the facts.
You can see below how we used the Cuisenaire to find out the square roots of numbers. Basically learning the doubles in multiplication. M. found out all their values on his own.
I let M. use the rods any time he needs them. Even though he needs them less and less as he practices more math facts, sometimes he will ask for them just for fun.
For practicing multiplication and division, we still use games of all kinds. They help with speed and memorizing the facts.
You can download our favorite games from the Resource Library.
Games using Cuisenaire Rods
One thing I learned with math in general is that you can’t go wrong with games. Here are 2 of the games we love playing with Cuisenaire:
Gobble up! – an addition and subtraction game
We adapted this from a version over at Educationunboxed. Check them out for more Cuisenaire ideas and games!
You can access our version in our Resource Library. Print it out and start playing.
You need 2 dice and your cuisenaire. The number 1 rods will be used as markers as well.
The dice numbers can be added or subtracted and the result is then “gobbled up” by a one marker. The person to cover their side of the game board first, wins.
Castle Walls Game – multiplication with Cuisenaire
One of our favorite games is CASTLE WALLS:
- each player rolls 2 dice (you can use more) and multiplies the 2 numbers
- with a highlighter they color their rows and columns according to the numbers they rolled (the bricks of the castle wall)
- then they write down the multiplication sentence and the answer.
- you keep going until the sheet is full and you can then compute who covered more area.
You can download the game sheet and rules from our Resource Library.
M. is very good at fractions. More often than not he understands them better than I do. I “blame” it all on cuisenaire and the way they wired his brain over the years of using them.
You can see below examples of a lesson we saw on educationunboxed and applied it ourselves.
Cuisenaire Rods Resources
I created a mini workbook for you to get started with these wonderful manipulatives that can be downloaded from the Resource Library.
You can also download our favorite games, Gobble up and Castle Walls, from there as well.
For more resources, check the links below.
Shop for manipulatives
We are using a couple of more manipulatives to complement our Cuisenaire Rods set: Base 10 Blocks (they allow you to continue the learning of bigger numbers- into thousands), Number Rod Track (it was useful at first, for showing place value, partitioning, multiplication and division).
UK: Cuisenaire Shop– the original Cuisenaire shop. You can buy books and manipulatives from here.
RO: You can find the Cuisenaire Set here.
Base 10 Blocks
UK: You can buy these on Amazon here.
RO: Buy the base 10 Blocks from here.
Number Rod Track
You can buy them from Bookdepository (free shipping).
RO: buy them here.
We use Math in Focus as our main math program and Cuisenaire Rods work perfectly with it.
If you want something specifically created with Cuisenaire Rods in mind, check Miquon Math. It’s a different way of approaching math concepts and I love their workbooks. I just let M. work as he pleases through these.
You could also go to the source of it all, and buy Caleb Gattengno’s Textbooks. We just started using them and I am sorry I didn’t discover them sooner. Here’s a list of what you should buy:
- Gattegno Mathematics Textbook 1
- Gattegno Mathematics Textbook 2
- Gattegno Mathematics Textbook 4
- Gattegno Mathematics Textbook 5
- Gattegno Mathematics Textbook 6
- Gattegno Mathematics Textbook 7
Virtual Cuisenaire Rods
If you want to try out the Cuisenaire Rods before investing in a physical kit, you can check out the links below for virtual manipulatives:
- Mathigon-Polypad multiple virtual manipulatives (note that you need to change the color of each rod to match the ones you will have in a physical set)
Blogs and Websites to Follow
- Cuisenaire Rods, the way of Zen
- FREE COURSE to get you started: Play Discover Learn 247
- Education unboxed website and video lessons (the best example on how to use Cuisenaire!)
- Free video lessons that we used for inspiration and we absolutely love over at Educationunboxed.
- Check these 3 videos to convince yourself of the efficacy of Cuisenaire Rods.
- Check this playlist to see a primary teacher use the Cuisenaire Rods.
- Multiple videos with cuisenaire and other manipulatives
Cuisenaire Worksheets and Printables
- Worksheets for addition and subtraction with Cuisenaire Rods.
- Pinterest ideas
- To continue playing with Cuisenaire, I found this wonderful resource by Miranda, perfect for young children which has games and free play ideas. Make sure you download the cards as well.
- You can buy more resources from PDL‘s Teachers Pay Teachers Shop.
Dragon Box App
One of our favorite apps to learn about Cuisenaire Rods is Numbers by Dragonbox.
The journey continues with their other apps which you can see here. We own them all and I will write a review about them.
M. made a video showing you how he plays with the Dragonbox App.
How do you use Cuisenaire? What are your favorite resources for these wonderful rods? Let me know in the comments below, I’m always on the lookout for hidden gems.
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