Place the following fractions in order from least to greatest - 1/2, 1/4, 5/6, 1 1/6, 1 11/12
Someone might immediately say -"1 11/12 is the biggest because 11 of 12 pieces is nearly a whole so that might as well be two and two would be the largest.
This type of thinking works for those who know fractions well and/or can visualize them. For others, it may sound good and they have the answer, but since they can't actually visualize it, they won't be able to apply it in the future. What these students need are a plan of action. They need what is called an algorithm.
An algorithm is a step by step procedure (normally for calculations). The algorithm should be 5 steps or less.
For yesterday's problem, the algorithm may look like this:
- Ask, "Are the denominators the same?". No.
- Ask, "Is the largest denominator divisible by the other denominators?". Yes.
- Use the largest denominator as the common denominator.
- Convert each fraction using an equivalent with the common denominator.
- Order the fractions from least to greatest using the numerator.
Your turn: exchange your homework with the partner you had yesterday. Read your partner's explanation. Does it make sense? Could you work with this explanation? Could it be improved? How so? Is it TMI? Turn, talk with your partner, and answer these questions.