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Defining Mathematics Education *REDUCED*

Defining Mathematics Education

The Seventy-fifth Yearbook is a celebration and reflection of the history of the NCTM yearbooks, and is a great resource on the key issues of mathematics education through the years.

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Sense of size

The activities suggested are intended to strengthen students' sense of the relative size of fractions by:

  • requiring students to consider the size of fractions in relation to a fixed and familiar reference point (or quantity), that is, one whole, one-half or zero
  • encouraging students to discuss and test their strategies
  • requiring students to explain and justify their thinking
  • providing immediate feedback to allow revision of responses.

The fractions used in all the activities can be adjusted to fit the needs of the students.


Activity 1: Which is closer to one?

Which fraction is closer to one, \(\frac{1}{4}\) or \(\frac{3}{4}\)?

How do you know?

Fold a strip of paper to show the two fractions.

Mark them on a number line.


Activity 2: Which is closer?

Which fraction is closer to zero, \(\frac{1}{4}\) or \(\frac{1}{5}\)?

How do you know?

Which fraction is closer to half?

Which fraction is closer to one?


Activity 3: Looking for patterns

Download and watch the Sorting Fractions Cards Task slide presentation to see how sorting a variety of fractions works.


Activity 4: If you added…

If you added \(\frac{3}{4}\) and \(\frac{1}{8}\) would the answer be less than one, equal to one or more than one? How do you know? Find a way to show you are correct.