Thursday, November 1, 2018

Cuisenaire Rods


If you have a set of Cuisenaire rods handy, this would be a GREAT time to take them out and USE them as we "play" with ideas about using Cuisenaire Rods for mathematical instruction. If you don't have any Cuisenaire rods readily available, borrow a set of rods from your intermediate grade level classrooms (sets of them were sent this past summer). In the meantime, you can click one of the links below to access an interactive website for Cuisenaire Rods (using physical rods is far better if you have them available!)



STAGES & PHASES

Most students (and teachers) have very little experience using Cuisenaire rods for mathematical instruction.
ALL STUDENTS should begin at the beginning. Even our older students (and their teachers!) need to begin by having free play with the Rods before trying to "do something" with them.  As you continue reading, look for activity ideas indicated by this icon 🔺.

GETTING STARTED with FREE PLAY

When introducing math manipulatives, an essential first step is to allow the students some free play with them. Free play should be, just that, free. Giving specific directions or over-organizing this initial activity destroys the essential character of free play. It takes a certain amount of faith to stand by watching children building towers and making animal pictures from the rods - especially when the construction seems to have no particular mathematical significance, but the time to explore will pay off in the end (I promise!).

Free play gives teachers a chance to observe their students' creativity and problem-solving skills and allows for informal conversations about what they see. As students "play", they learn to make choices in regards to which rods to use – this will be an invaluable skill when they use Cuisenaire rods later during instruction.

Using the math manipulatives during free play is time well-spent, but it doesn't have to happen just during the precious little time you have for math instruction; you might decide to offer the manipulatives that will be used later in the week/month for free play on a rainy day during indoor recess or perhaps as part of a brain break activity.



DEVELOPING AN UNDERSTANDING OF EQUIVALENCE

After taking time to explore the Cuisenaire rods in a free play setting, the first concept you will want to formally tackle is equivalence. Your students should have opportunities to sort, name, order, and use equivalence to form various patterns using the rods. A simple way to begin is to place a pile of Cuisenaire rods in front of students and ask them, "What do you notice?" Give them a bit of time to touch and explore. Do not end this exploration time too soon. Be patient. Encourage small groups to talk. Then stand back and watch the ideas about equivalence pour out:
"Two red rods are the same length as 1 purple rod."
"Three white rods are the same length as 1 green rod."
"A red rod and a green rod together are the same as 1 yellow." 
"If the white rod is 1, then the yellow rod is 5." 


FORMALIZING YOUR EXPLORATION

You've given time for free play and some time to just "notice". Now let's take a look at specific activities you can use in your classroom to develop your students' number sense and their ability to use the Cuisenaire rods to solve math problems. 
🔺Place the YELLOW ROD in front you. How many ways can you make a length that is equivalent to the yellow rod? Can you think of any other ways that are not shown on the graphic to the right?




🔺Which single rods are equivalent to doubles of another? How many combinations can you find?  Do you notice any patterns? Can we predict which rods can be made with a double?

DEVELOPING AN UNDERSTANDING OF THE WHOLE

Cuisenaire rods are excellent tools for developing flexible thinking. A major component of using the Cuisenaire rods effectively is being mindful of "the whole". The whole can change with each question and understanding what represents the whole helps to bring meaning and context to the rest of the rods. Because the whole is not always the same color rod, it forces us to think more flexibly and to constantly assess the value of each rod in terms of the whole. The whole can even be made of two or more rods that have been pushed together (crazy, I know!).

🔺 If the blue rod is one whole, which rod represents 1/3? How do you know? What is another way you can know? 


🔺 If the red rod represents 1/3, which rod represents the whole? What question did you ask yourself to begin answering this question? 


🔺 If the whole is the orange rod and red rod pushed together, which rod represents 1/2? What strategy did you use to determine the answer? What other strategy could be used?






🔺 A train that is made from two rods has an equivalent length to brown. If one of the rods is yellow, what color is the other rod? (equivalence)
How would having physical rods help you to discover that the other rod must be light green?



🔺 Make a train with 2 rods: One of the rods is half the length of the other rod. What does the train look like? What is the fractional value of each color rod in this model as compared to the whole? What other combinations of rods could be used to build a different train with the same parameters? (fractions)
How would having physical rods help you to discover that there are multiple representations? Is there a pattern to the rods that can/cannot be used to build this train? Notice how using the rods makes the complex idea that the light green (which is 1/2 the length of the dark green) represents 1/3 of the whole. 


🔺 What is 10 divided by 4? How does this model demonstrate the quotient? (division with fractional quotients)
Do you see the solution of 2½ in the model below?  The orange rod is 10 units. The purple rod is 4 units. We needed 2½ purple rods to equal the same length of one orange rod.




🔺 Is 21 a multiple of 3?  How does the model below help you to know?  (multiples)
🔺 Is 21 a multiple of 4?  How does the model below help you to know?  (multiples)
Notice that the value of 21 was made from 2 ten rods (orange) and a 1 rod (white).
How does the model below help you to see that 21 is a multiple of 3, but not 4? 


🔺 Is 3 a factor of 21? How does the model above help you to know?  (factors)
🔺 Is 4 a factor of 21? How does the model above help you to know?  (factors)
How does the model shown above help you to see that 3 IS a factor of 21, but 4 is not? 




🔺 What is the sum of 3/5 and 1/3. How do you know?  (fractions)
How does this model help you to see that the sum is 14/15? 

🔺 The area of a rectangle is 56. One side of the rectangle is 7 units. What are the lengths of the other sides? (geometry)
How does this model help you see that the lengths of the sides are 7, 7, 8, and 8?


🔺 What is 1/2 of 1/3? Use the image below (or better yet, build the model!) to find the solution. (fraction calculation) 
How does this model help you see that 1/2 of 1/3 is 1/6? 








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