Decomposing fractions

The first instance of  is under the 4th Grade Math Mission. This exercise concentrates on breaking fractions down with common denominators, effectively concentrating on the numerator as number and denominator as size, or denomination.

Types of Problems
There are four types of problems in this exercise:


 * 1) Use the dots to compare: This problem has several sums of fractions aligned on the left. The student selects the dots to compare the sums to a given fraction.DECOM1.png
 * 2) Make the sum: This problem has a list of fraction. The student selects the fractions from the list which, when added together, become a given number.DECOM2.png
 * 3) Select those that work: This problem gives a fraction and asks the student to select all of the sums that will work to add to become that fraction.DECOM3.png
 * 4) Fill in blank: This problem asks the student to fill in a missing fraction to make a statement true. The statement involves distinct ways to sum fractions so that one gets the same result.DECOM4.png

Strategies
This exercise is easy to get accuracy badges because you can concentrate on the numerators and effectively view the denominators as units. Speed badges are medium difficulty at this time because selecting multiple dots and solutions does not always go quickly.


 * 1) If the answer to Fill in the blank is a fraction, an acceptable answer list will appear.
 * 2) All denominators are the same, therefore the problem can be viewed as work with the numerators. This can make it feel like integers, and might be faster to do.