The object of the
Darts game is to "pop" balloons located on a number line. The Darts are
"thrown" by entering a number  in
fractional form. Here is a glimpse of a game in progress. Two darts
(3/4 & 5/8) have been thrown so far. Notice that 3/4 is too big and
5/8 is too small.
What would be your next throw? Explain your strategy. |
Resources: Microworlds 2.03 or Pro (File: Dartsrb.mws*)
Environment: One computer classroom
Strategy: Students working in cooperative groups Standards (GEPA) Connections: |
Description
Darts is a Microworlds activity that requires the player to pop a balloon
that appears on a number line between 0 and 1 by throwing fractional darts.
Setting the Stage
Play this fraction game with the students. "I'm thinking of a fraction
between 0 and 1. Can you guess it? It must be stated in fractional
form with a whole numbers for the numerator and denominator." (Choose 3/4
as your fraction to guess.) A student may guess 1/2. You would say
that his or her number is too small. Another student may say 7/8 to which
you respond with that's too big. At this point the students may be stuck
because they need to find a fraction that is between 1/2 and 7/8. Some
students may realize that 3/4 is in between and would guess correctly.
At this point show them the challenge problem and explain how Darts works.
Doing the Activity
Hand out the student page and ask the students to explain mathematically
how they found a number between 3/4 and 5/8. Some possible anwers
would include:
- 7/10. I changed the numbers to decimals .75 and .625 and saw that .7 is in between. I would enter 7/10.
- 4/6. 4 is between 3 and 6 is between 4 and 8. So I think 4/6 or 2/3 would work. (See diversion below)
- 5.5/8 Make the two fractions have a common denominator so now we have 6/8 and 5/8.
Finding a number between 3/4 and 5/8 is challenging for students who have a fragile understanding of fractions. One strategy would be to look at 3/4 in an equivalent form, 6/8. Now the two numbers have a common denominator, but you need a number between 5/8 and 6/8. With fractional notation this is a difficult problem to "intuit" since we need to find a number between 5/8 & 6/8. Realizing that if we now write 5/8 as 10/16 and 6/8 as 12/16 then the number in between is 11/16. However, there is nothing wrong with an answer like 5.5 / 8. It's just that we are unaccostumed to mixing fractions and decimals. In fact, this problem is much easier if you convert to decimals. What's a number beween .75 and .625?. (Any number larger than .63 and smaller than .74 lives between 3/4 and 5/8)
Finish the lesson by playing Darts (Dartsrb.mws) on a one computer station. The class can be split into 2 teams and each team can take turns throwing an arrow.
Extensions & Additional Activities
Play a round of 5.
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References
Websites
Diversion
