Image of the Week

Noticing Relationships in Cuisenaire Rods

Take a close look at the Cuisenaire rods in the image of the week. What do you notice?

Some things you might see are:

• The rods together make a rectangle.
• The rectangle is made of five columns of rods.
• The black rod on the left is the longest and it goes from the top to the bottom of the rectangle.

These initial observations can be used to start to fuel whole number comparisons and equivalencies, such as:

• Light Green = 3 White
• Red = 2 White
• Black = Dark Green + White = 2 Light Green + White = 3 Red + White = 3 White + Purple
• 2 Light Green = 3 Red
• If we understand the White block as a unit, then we can see the Red = 2, Light Green = 3, Purple = 4, Dark Green = 6, and the Black = 7
• The rectangle then is 7 x 5 units and has an area of 35 square units.

Students might also think about part and whole relationships, with observations like:

• White = ½ Red
• Red = 2/3 Light Green
• White = 1/3 Light Green
• Red = ½ Purple
• Light Green = ½ Dark Green
• Light Green = 1 ½ Red
• White = ¼ Purple

These are just the beginning of the observations students might make about the relationships between the rods shown in this image, whether whole number or fractional. Notice that one of the keys is that fractions only exist in relationship to a whole. For instance, the White cube is ½ in relationship to the Red as a whole, but it is 1/3 in relationship to the Light Green as a whole. Press students to be precise about both the part and the whole and explore how a single rod can be thought of as many different numbers is the whole changes.

Packed inside this one image are dozens of relationships that students can notice, explain, prove, and draw. Consider providing students with the pdf version of this activity so they can annotate the relationships they see. These artifacts can then be shared and compared in a class discussion, or a digital or physical gallery walk.

You can use this – or any of our Cuisenaire rod images – to open up conversations about representing relationships abstractly (where “The Red and White are the same as the Light Green” can become Red + White = Light Green, or even R + W = LG), composing and decomposing numbers, or part and whole relationships.

As an extension, consider inviting students to create their own Cuisenaire rod rectangle to explore the different relationships they contain. Students can take photos and swap with other groups to find and describe new relationships.

To multiplicity, cheers!

Jen Munson and the multiplicity lab group