7.3 #13

a) 2/3 x 3/4 = 1/2
This reads as two thirds of three quarters. So the referent whole for the 2/3 is the 3/4 and the referent whole for the 3/4 is a whole one. The answer 1/2 refers to the whole one. For example: If Joe ate 2/3 of 3/4 of a pizza that was leftover from lunch, he ate 1/2 of the whole pizza. Two thirds refers to the leftover portion of the pizza, while 3/4 and 1/2 refer to the original whole pizza.

b) (1/2)/(3/4) = 2/3
This could be read as how many 3/4 in 1/2. It is the inverse of the multiplication problem. So the referent wholes are the same as in the multiplicaiton problem. Joe ate half of the whole pizza. If only 3/4 was leftover from lunch, then Joe ate 2/3 of the leftover pizza.

Test Review Ch.6, 7, & 8

You should be able to:

1. Provide a pictorial representation of fractions, whether using a discrete whole or a continuous whole.
2. Write a decimal number as a fraction in the form: i.e 2.25 = 225/100 = 9/4, or 2.2525252525... = 223/99
3. Demonstrate understanding of decimal numbers by finding numbers that would be between consecutive decimal numbers. i.e. what decimal numbers are between 0.2 and 0.3
4. Find a fraction between fractions with unlike denominators without converting to decimal numbers or using common denominators. This means understanding how “neighbor numbers” work.
5. Illustrate multiplication and division of fractions
6. Explain additive and multiplicative comparison and be able to write word problems that illustrate this knowledge
7. Illustrate multiplicative relationships (similar to the chocolate bar activity in ch.8) and use that knowledge to solve problems

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: (a) 0.079 = 79/1000 (b) 2.13 = 213/100

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: (a) 0.7979797979… = 79/99

COMPLEX REPEATING DECIMALS: Subtract the non-repeating digits from the combination of non-repeating digits and one set of the repeating decimals. Put this number in the numerator. In the denominator, the number of nines equals the number of repeating decimal digits and the number of zeros equals the number of non-repeating decimal digits. Example: (a) 0.12379797979… = (12379 - 123) / 99000 = 12256/99000 (which can then be simplified) (b) 123.797979797... = (12379-123)/99 = 12256/99

CH 3, 4, & 5 Test Review

You should be able to:

1. Write word problems that use (a) comparison subtraction, (b) take-away model of subtraction, and (c) missing addend.
2. Analyze students' methods for adding, subtracting, multiplying, or dividing. (Analyze means be able to explain the child's procedure or solution method, whether their procedure is reasonable, and if they got the answer correct or not. )
3. Make a sketch that models the multiplication of two numbers (repeated addition, array, area, Fundamental Counting Principle), whether using whole numbers or fractions.
4. Write division word problems that use equal share or repeated subtraction models.
5. Estimate and explain your thinking when dividing very large numbers to determine an approximate percent.
6. Use scientific notation to solve problems with really big numbers or really small numbers and be able to convert those numbers into other units that provide a better understanding of what those numbers represent.