I would suggest, for the first one, to tell your students to concentrate on the denominator, and ask which number is half of the denominator. (i.e. for a, 1/2 of 48 would be 24). Then ask if the numerator is the same as that number, smaller, or larger.
2) Explain that since none of these numbers are negative, zero will be the smallest. And because the rest are fractions where the number in the numerator is smaller than the number of the denominator, we know that they are less than one, so 1 is the largest number. From there it is a matter of figuring out which order the fractions go in and we have: 5/8, 3/10, and 3/11. of these, 5/8 is the biggest because it is bigger than 1/2 while the others are smaller than 1/2. (that is 5/8 > 4/8, 3/10<5/10, 3/11<5.5/11). then look at the two remaining 3/1 0 & 3/11. the numerators are the same but the denoms are diff. 11 is bigger so the 3 is divided over a larger number of portions which means there will be smaller portions.
its helpful with 7th graders to use a food analogy to teach fractions, i.e. I have 3 apples that I want to split between 10 people, and 3 between 11 people, which is bigger/smaller.
3) show them how to change the fractions so the denominators are the same: what is 5 * 11? 55. so common denom is 55. but you need to do the same to the top so 3*11 = 33/55 & 35/55. therefore 3/5 < 7/11, etc.
hope this helps!
· 1 decade ago