Fraction Capture: Hexahedral and Dodecahedral Dice

We continued our exploration of fractions by having the students learn a dice game where they have to capture a square or other polygon by coloring in more than half of it.

If the square is split into halves then they need to color in both halves to capture that square.  

If the square is split into thirds then they need to color in only two thirds to capture that square. 

If the square is split into fourths then they need to color in only three fourths to capture that square. 

If the square is split into fifths then they need to color in only three fifths to capture that square.

The game for K-1 grade only required 6-sided or hexahedral dice. This game is faster than the advanced game and is just as fun so I gave that game to all students K-5th grade.

The game for 2-5th grades requires 12-sided or dodecahedral dice. Most people do not have these dice so I included two nets for dodecahedral dice in the packet attached. If they do not want to create their own dice, just roll regular dice twice.

The fractions are generated by each dice. For example, if they roll a 3 and a 2, it an be used for both 2/3 and 3/2. It might be strategic to use the smaller proper fraction at the end of the game when many of the squares are taken, but usually, you want the larger improper fraction. The children learned that when the numerator is larger than the denominator, the fraction is larger than a whole. One restriction on the game is that you can not use a whole number roll such as any double (roll again) or 6/2, 4/2, 6/3, 6/1, 5/1, 4/1, 3/1, 2/1, etc. You would have to use the smaller proper fraction.

Many of them were curious as to what was the best roll and the worst roll. With 6-sided dice, the best roll is 5/2, and 3/2 and the worst roll is 1/6 or 1/5. The key to success in this game is using the smaller denominations first like 6ths or 5ths. If you roll 3/2, double the numerator and denominator to find the equivalent fraction 6/4 or triple it to find 9/6. Remember do not use any more of the square than you need to capture it. For example, if you are trying to capture a square split into 6ths, you only need to color 4 of them. Any more and it would be a waste.

The advanced game is much more challenging and takes longer. Not Monopoly longer but give yourself 20 minutes or more. The trick here is to use 1/12ths before 1/2s. The best roll with 12-sided dice is 11/2 or 11/3. 11/2 is equivalent to 66/12 so when you capture all three 12ths polygons with only 21/12ths (7 for each), you have 45/12 left. You can then use 15/4 or 30/8. 

For the younger children, this game is all about understanding that 5/2 is significantly larger than 2/5. That the smaller denomination has a larger number on the bottom. The other key objective is that to win a square with more than one half, you have to be strategic about what is slightly greater than 1/2. 

For the older children, this is all about the above objectives as well as mastering equivalent fractions. Many of the 4-5th graders also started to subtract fractions as well.

Please play this game and have the children bring in their game boards to class next week.

The pdfs have the rules, 4 game boards each and dice nets.