The
object of the Fraction
Darts challenge is to "pop" balloons located on a number line
between 0 and 1. The darts are "thrown" by entering a number in
fractional form. Here is a glimpse of a game in progress. Two
darts (5/8 and 3/4) 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. |
Resource:
Microworlds Applet
Environment: Strategy: Students work in cooperative groups Standards
Connections: Understand Number and Operations |
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 Fraction
Darts
works.
Doing the Activity
Hand out the student page and ask the students working in groups 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 the fraction
darts microworld*
on a one
computer station.
The class can be split into 2 teams and each team can take turns
throwing
an arrow.
*If the
activity does not work, you may need to download the
Microworld EX web player.
Extensions & Additional
Activities
Play a round of 5.
|
|
Throws-Team 1 |
|
|
|
||
|
|
||
|
|
||
|
|
||
|
|
||
| TOTAL= |
|
An Interesting Diversion
An interesting (though not necessarily
pedagogically sound) way to find
a number between 3/4 and 5/8 is to add the two numerators (3+5=8) and
the
two denominators (4+8=12) and form the fraction 8/12 (or 2/3) which
happens
to fall between the two original fractions. 2/3’s middle stature can be
easily confirmed by looking at the three fractions with the common
denominator
24. (18/24; 16/24; 15/24.). Was that just a coincidence or does that
always
work? It turns out that it always works. Here’s a proof.
Copyright © 1999-2004 Stevens Institute of Technology Center for Innovation in Engineering and Science Education, All Rights Reserved.