Paper Clip Games

10 min

Narrative

The purpose of this Warm-up is to elicit ideas about locations of the paper clips relative to the fractions on the number line. This will be useful when students design a game about fractions on a number line in a later activity. While students may notice and wonder many things about this image, the structure of the number line, how the paper clips are clustered or spread out, and how their locations connect to the labeled benchmark fractions are the important discussion points.

MLR2 Collect and Display. Circulate to listen for and collect the language that students use as they notice and wonder about the diagram. On a visual display, record words and phrases, such as “benchmark fractions,” “equivalent fractions,” “greater than,” and “less than.” Invite students to borrow language from the display as needed, and update it throughout the lesson.
Advances: Conversing, Reading

Launch

  • Groups of 2
  • Display the image.
  • “What do you notice? What do you wonder?”
  • 1 minute: quiet think time
Teacher Instructions
  • “Discuss your thinking with your partner.”
  • 1 minute: partner discussion
  • Share and record responses.

Student Task

What do you notice? What do you wonder?

Image of paper clips on a number line strip. 
Image of paper clips on a number line strip. Scale, 0 to 2, by halves. 10 paper clips, 5 blue, 5 black. One blue clip is close to each tick mark. Between 0 and one half, 1 black clip. Between one half and 1, 2 black clips. Between 1 and three halves, 2 black clips. Between three halves and 2, 0 black clips.

Sample Response

Students may notice:

  • Ten paper clips, 5 blue and 5 black, are on or around a long strip.
  • The strip looks like a number line that goes from 0 to 2.
  •  0, 12\frac{1}{2}, 1, 32\frac{3}{2}, and 2 are labeled on the strip.
  • Some labels have a whole number and a fraction on them.
  • Blue paper clips are more spread out.
  • Black paper clips are closer to 1.

Students may wonder:

  • Why are the paper clips on a strip with fractions like this?
  • What do the paper clips represent?
  • Were the paper clips scattered randomly, or placed in specific locations?
  • Is this a picture of a game with paper clips?
Activity Synthesis (Teacher Notes)
  • “Priya and Kiran were playing a paper clip tossing game that uses fractions and a number line. The image shows the result of one game.”
  • “Priya’s paper clips are blue. What could be a rule for this game if this picture represents a win for Priya?” (The winner is the player with the most paper clips on numbers greater than 1. The player with the most paper clips on the 0, 12,1,32,\frac{1}{2}, 1, \frac{3}{2}, and 2 wins.)
  • “What if it was a win for Kiran, whose paper clips are black?”(The winner is the player with the most paper clips on numbers between 0 and 1. You have to get the fewest paper clips on the 0, 12,1,32,\frac{1}{2}, 1, \frac{3}{2}, and 2 to win.)
  • As needed, point out the 0 and 02\frac{0}{2} labels on the number line and clarify that 0 can be represented as a fraction with 0 as the numerator, but that 0 can never be the denominator.
Standards
Building Toward
  • 4.NF.A·Extend understanding of fraction equivalence and ordering.
  • 4.NF.A·Extend understanding of fraction equivalence and ordering.

10 min

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15 min