Teaching Number Concepts – Cuisenaire Rods
After publishing the previous Teaching Number Concepts post, I had a wonderful conversation with one of the readers, Terri. She recommended using Cuisenaire rods. In fact, her suggestions were so helpful, that I’d like to share them on the blog.
Terri’s photo illustrate two examples, the one on the left – for the number 8 and the one on the right – for the number 10. These examples were done by Terri’s 5-year old. As you can see, they show all the combinations of sums of two whole positive numbers that can make the original numbers.
C-rods are both similar and dissimilar to the two number concepts games I described previously. I particularly like that a child can see all the combinations at once as well as have visual proof of them adding up to exactly the same amount (being equal in length). This concrete proof of an abstract idea is extremely important for young children. It is also something, that in my opinion, should be encouraged in them – not blindly accepting our math statements, but actively challenging them.
I have not tried C-rods yet with my child, but will post an update as soon as I do. Thank you, Terri!
Have you used Cuisenaire rods? What other math manipulatives do you use to teach basic number concepts to your children?
Posted in Make
I love the idea of C-rods, and have used them a little bit starting when my daughter was 5.
I introduced C-rods to my kid with information I got from a series of old films that are on YouTube. The idea is to develop number sense at first without using numbers! First you build a staircase, from smallest to biggest and watch them grow. Then you sort of chant the colors in order (there’s to be no number association at first). So, “White, red, light green, etc.” Then chant backward. At some point, when you have a firm visual and tactile grasp on the order of the rods, and can say them without looking at the rods, you can play a game — take three or four rods in your hands (we only ever did the first four) and put your hands behind your back. One person says the color they want to see brought to the front, and you figure it out just by using touch. It worked EVERY time! I’m not kidding.
We also love the game ‘build what I have’ which came in the directions with the set we bought. I think the game is from Marilyn Burns — It’s sort of like battleship without the grid. You hide your workspace from your partner. One person builds a design one rod at a time and the other has to recreate it — the only way they can communicate is through spoken words, no gestures. The leader gives the directions, but the follower can ask for clarification. Given that there’s a lot of research showing that children think and communicate mathematically throught their bodies, specifically through gestures, I’m wondering whether limiting communication to only the verbal realm would be counter productive with young children. Perhaps it could be modified where you can talk and build at the same time as your partner, and just enjoy being able to make copies of each other’s work — the math language would still be there, but you could also move your pieces around to demonstrate placement and orientation .
I also think it would be fun to use them in symmetry activities, with a line of reflection and/or symmetry.
I would *really* love to learn more about the rods and look forward to reading more about it here.
My original interest in Cuisenaire rods stemmed from the need to explain/illustrate the concept of fractions in a more flexible way than circles cut into whole, halves, thirds, and fourths.
We purchased the Mathematics Made Meaningful instructional set which includes a double set of the rods, a book for the parent/teacher to read, and a set of cards to work through in order with the child/children.
We have just started with the fraction unit on the cards and it has been better than I even expected. The C-rods are brilliant for showing how a given number can (sometimes) be broken into multiple fractions. Like showing how the number 8 can be broken into halves, fourths, and eighths. It gives the child the opportunity to discover this for themselves. It also solidifies the concept of fractions being equal. Just wonderful!
Since we are only part way through the card series, I thought that I would include a rundown of what the instructional cards cover. You proceed through them from beginning to end as your child goes through the exercises provided and as they are ready to progress to the next concept. No pressures involved as they gently introduce new concepts and build upon previous successes.
Series A: First Games; Staircases (organizing the rods in order to form staircases and seeing how ascending and descending staircases can be assembled together to make a square); Train Games (putting different rods together end-to-end to discover number/length relationships); Sequences; Matching; Triplets (beginning equations using two rods to make a third EQUAL rod); Symmetry; Using Number Names.
Series B: Equations; Variables; Inequalities; Patterns; Numerals.
Series C: Subsets; Sets; Equal & Equivalent Sets; Union & Intersection.
Series D: Measuring (precursor to fractions — breaking a number into equal-sized units); Unit Fractions; Non-Unit Fractions; Comparing Rods (writing fractions and equivalent fractions).
Series E: Patterns of Numbers; Complements; Parentheses; Prime & Composite Numbers; Numbers to One-Hundred.
Series F: Reading Large Numbers; Trains Longer Than Orange; Choosing Problems; Finding Products; Factors & Multiples.
Series G: Equivalent Expressions; Hints for Addition; Hints for Subtraction; Hints for Multiplication; Hints for Division.
Series H: Fractions and Reciprocals; Equivalent Fractions; Adding Fractions; Multiplying Fractions; Dividing Fractions.
Series I: Towers and Place Value; Powers; Coefficients & Exponents; Non-Decimal Bases; Carrying and Place Value.
Series J: Negative Numbers; Multiplying Signed Numbers.
Series K: Metric Length; Metric Area; Metric Volume, Capacity, and Mass.
This Mathematics Made Meaningful program says that it is for Pre-K through 3rd grade. Our 5 year old has been using it periodically for the past five months and we are almost complete with Series D. Some concepts take longer than others to instill.
Hope this provides some additional ideas as to how C-rods may be used. Please ask if you have any specific questions that I have not covered here.