N3D9TNp17

Answer to Problem 17:

1)  .9

Possible Explanation:  .9³ asks that you multiply  .9 x.9 x .9  Every time that you multiply by a decimal umber the answer gets smaller e.g. .9 x .9 is .81 which is smaller than the original .9.

2)   

Possible Explanation:  5 ÷ ½ is the larger number because as you divide by a fraction the number gets larger.  5/ (1/2) = 10 because it doubles in size.

3)  6                   

Possible Explanation:  The square root of 36 is the answer 6 which means that 6 must be larger than the square root of 33 which is a bit over 5 but less than 6.

4)   (greater than 5; )

Students should be able to defend their selection without calculating (or using some non-mental method) what each expression’s value would be.  Each of these problems are asking students to understand and be able to describe the impact certain operations have on particular values.  For number 1, it is important for students to realize that raising a number to a power is not necessarily going to make the value larger.  Likewise, in number 2, division has a variety of impacts based on what and how the number is being divided.  Changing this problem to .5 or .5 divided by ½ would make this a more interesting discussion.   Each of these should be more than just the answer generated, but also how the result is generated and why the numbers act in this manner.  In problems 3 and 4, understanding radical notation and the impact of these operators is an extension of the ideas listed above.