Fold a strip of paper into fourths and shade in of the paper strip. Now fold each of your fourths into 3 equal pieces.
(a)
How many parts are in the strip of paper now?
(b)
Are these parts equal to each other? Why?
(c)
What fraction of the original paper strip is each individual new part after you finish all of your folding? How do you know?
(d)
How many of the parts are shaded? How do you know?
(e)
What new fraction of your paper strip is now shown by the shading?
(f)
Draw ONE careful picture showing both the original strip and the new folds in the strip. Your drawing should illustrate the method and reasoning behind your creation of a fraction equivalent to of your original strip of paper.
Let’s try this again, but without the paper strip. Instead, imagine working with a new paper strip. Make sketches to illustrate your thoughts, but don’t draw all of the little pieces.
(a)
Explain to your group how you would fold your imaginary strip to show the fraction .
(b)
Explain to your group how you would make a fraction equivalent to using the same paper strip. That is, what steps would you take?
(c)
What new fraction of your imaginary paper strip is now shown by the shading?
(d)
How many different fractions could you make that are equivalent to the original fraction ?
When you learned how to “make equivalent fractions” in school, you learned a rule that was something like “multiply top and bottom by the same number”, as shown in this formula:

Explain how this rule encapsulates the ideas of the process that you have done in the previous problems. We haven’t talked about multiplication, yet, so how can you use your picture to explain why this multiplication makes sense?

Use folding to compare the fractions and .
(a)
Explain to your group how you would fold two different imaginary strips to show these fractions. (What must we keep in mind about these imaginary strips?)
(b)
Once you have a sketch (because we aren’t going to make that many folds), how could you re-fold the two strips to make it easy to compare the two fractions?
(c)
How many parts would be in each imaginary strip of paper now? Why?
(d)
How many of the parts are shaded in each strip?
(e)
Which fraction is larger? How can you be sure?
Suppose you were trying to convert the fraction into a percent. You probably learned to do this by solving the following problem:

Explain how you might use a strip of (imaginary!) paper to solve this problem.

2026-07-17 02:45:37