[CN, ME, R, T, V]
| (a) |
Develop a generalization about what type of number results from the squaring of a rational number. |
| (b) |
Describe strategies for determining if a rational number is a perfect square. |
| (c) |
Determine the square root of a rational number that is a perfect square. |
| (d) |
Determine the rational number for which a given rational number is its square root (e.g., $4/3$ is the square root of what rational number?). |
| (e) |
Explain and apply strategies involving benchmarks for determining an estimate of the square root of a rational number that is not a perfect square. |
| (f) |
Determine, with the use of technology, an approximate value for the square root of a rational number that is not a perfect square. |
| (g) |
Explain why the value shown by technology may only be an approximation of the square root of a rational number. |
| (h) |
Describe a strategy that, if applied to writing a decimal number, would result in an irrational number (e.g., students describe a strategy in which they repeatedly write the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 but separate each group of these digits by an increasing number of repeats of the digit 7 or 0.0123456789701234567897701234567897770123...). |
| (i) |
Determine a rational number whose square root would be between two given rational numbers and explain the reasoning used (e.g., a rational number whose square root is between $1/2$ and $1/3$ would be between $1/4$ and $1/9$ because those are $1/2$ and $1/3$ squared. I need to find a number between $1/4$ and $1/9$. I can do this by making the two fractions into fractions of the same type: $9/36$ and $4/36$. One number between these is $6/36$ or $8/36$). |
