Why we teach for conceptual understanding

http://www.youtube.com/watch?v=zs_z1M2yrLg

Word problems for Division with Fractions

Dividing by a fraction can be thought about as repeated subtraction or sharing equally. In section 7.3; here are some sample problems.

Repeated subtraction:

15a. If a tortoise is timed traveling an average of 1 2/3 miles per hour, how long would it take the tortoise to travel 6 miles?

15a. The recipe you use to make holiday cookies uses 1 2/3 cups of flour for each batch of cookies. How many batches of cookies can you make with the 6 cups of flour.

15b. How many 2 ¾ feet long strips of ribbon can be cut from a ribbon that is 7 ½ feet long?

15b. If your pea patch is only 7 ½ square yards and the melon plants you want to grow require 2 ¾ square yards each. How many melon plants can you put into your pea patch? Show your work and explain your reasoning.


Sharing Equally:

15b. You have 7 ½ bags of mulch to cover 2 ¾ square yards of garden bed. If you want to distribute the mulch evenly over the garden bed, how many bags will you need to use for each square yard?

15c. If you want to share1 7/8 pizza with 3 people, how much pizza would each person get?

Converting Decimals to Fractions

TERMINATING DECIMALS: Put the decimal’s digits in the numerator. In the denominator, the number of zeros equals the number of digits behind the decimal. Example: 0.079 = 79/1000
SIMPLE REPEATING DECIMALS: Put the decimal’s repeating digits in the numerator. In the denominator, the number of nines equals the number of repeating digits. Example: 0.7979797979… = 79/99.
COMPLEX REPEATING DECIMALS: Subtract the non-repeating digits from the digits after the decimal point that include one set of the repeating decimals. Put this number in the numerator. In the denominator, the number of nines equals the number of repeating digits and the number of zeros equals the number of non-repeating digits. Example: 0.12379797979… = (12379 - 123) / 99000 = 12256/99000 (which can then be simplified).