### Student Page 3.6.3 Measuring with Pretzles and Cheerios

Use pretzel sticks and cheerios to measure an 8.5-inch by 11-inch sheet of paper. The student page provides an interesting way to measure something if conventional tools are not available. As a bonus, you get to eat the pretzels and the cheerios when you're done measuring! ^{ 40 }

#### 1.

Measure each side of an 8.5-inch by 11-inch sheet of paper using as many pretzel sticks as you can without exceeding the side length of the paper. Fill in the rest of the length using Cheerios. Record your values in Table 3.6.3.1.

Side of paper | Side length (inches) | Number of pretzels, \(p\) |
Number of cheerios, \(c\) |
---|---|---|---|

Long side | 11 | ||

Short side | 8.5 |

#### 2.

For each side of the paper, write an equation to show the length in terms of the number of pretzels and the number of cheerios you needed to measure the side length.

#### 3.

Graph the equations from Student Page Exercise 3.6.3.2 on the same grid. Let \(c\) be the independent variable.

#### 4.

Do the graphs intersect? If so, what is the point of intersection?

#### 5.

What do the coordinates of the intersection point represent in the context?

#### 6.

Measure the length of a pretzel stick and the diameter of a Cheerio. Compare your measurements to your solutions in Student Page Exercise 3.6.3.4. Comment on your work based on these comparisons.