Fraction Equivalents

We continued our exploration of fractions this week with three objectives:

1) Physically match up fraction equivalents such as 1/5 = 2/10 = 3/15 = 4/20 = 5/25 = 6/30 (see page one of both  attached pdfs named Fraction Equivalents K-1 and 2-5).

2) Create fraction equivalents by multiplying both the numerator and denominator by the same number by playing the dice game (K-1 would only need to double the numbers whereas 2-5 would roll another die for the multiplier; this is on pages 6-10 of each Fraction equivalent pdf).

3) Eat fractions by cutting up food into equal parts and announcing the unit fraction that they are eating. 

During class, the children were able to manipulate hundreds of unit fractions from 1/1, 1/2 to 1/32 and match up several equivalents using simple multiplication. The attached pdf called Fractions, Unit Pages 1/1 to 1/32.pdf has 23 pages of pages that the children can cut up to play this game. It may take several weeks to do this so no worries about doing it before next week.

If they try to find two fractions that make up 1/5, and they use 2/8, they will find that it will be too big for the1/5. When you count by 5 or multiply 5 by a number will you ever get 8? NO. So you should look for unit fractions that only have multiples of 5 in the denominator. For 1/3, only use 2/6, 3/9, 4/12, 5/15, 6/18, 7/21, 8/24, 9/27, or 10/30.

The fraction dice game is a lot of fun to play with another person or by yourself. First roll the dice to get two different numbers. If you roll a double, roll again. Write down the fraction as a proper fraction with the smaller number on top (see page 6 of the pdfs for directions). Then, the K-1 can simply double each of the numerator and denominator and write down the resulting fraction; then double again. Some will want to keep going. Remember, they do not need multiplication. They only need to add the number to itself. When the numbers get too difficult, roll two dice again for a new proper fraction.

The 2-5 kids can roll a single die to get a more challenging multiplier (disregard 1). Again, if you have to multiply 24 by 6, you can simply add 24, six times. I taught the children strategies to multiply by 4 and 5. To multiply by 4 they simply double the number twice (for example, 35 x 4; just double 35 to 70 and then double 70 to 140). Multiplying by eight would require doubling three times, by 16, double four times and so on. Since 5 is just half of 10, when multiplying by 5, just cut the number in half if it is even and then multiply it by 10 (tack on a zero); if the number is odd, first multiply by 10, then cut it in half. So for 48 x 5, just cut 48 in half to 24, then tack on a 0 to get 240. The 2-5 should work these equivalent fractions horizontally on the page until the numbers get too difficult, then roll another proper fraction.

As for eating fractions, I know we parents do not want our children to play with their food, lest the food should get cold. But using Mathlete strategies for cutting up the wholes into equal parts and naming the fractions are priceless moments. Try doing this with easy food like cheese and difficult food like soup. It is all about strategy. Of course, they will only do this with your permission, but .....