standard_description: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.
problem_activity: Problem 1
In a marching band there are 24 trombones and 15 snare drums.
Heather says, “The ratio of trombones to snare drums is 24:15.” Audrey says, “No, the ratio of trombones to snare drums is 8:5.” Who is right and why?
Problem 2
You are making a mixed bag of walnuts and cashews. The ratio of the number of walnuts to the number of cashews you want to use is 5:6. You have 54 cashews to include in the mix. How many walnuts should you add? Justify your answer by showing that the new ratio you created of the number of walnuts to cashews is equivalent to 5:6.
Problem 3
Which of the ratios in the list below are equivalent to the ratio 12:8? Explain or show how you know each ratio is equivalent.
a.   8:12
b.   3:2
c.   2:3
d.   24:16
e.   6:4
f.   6:2
g.   15:10
h.   20:16


aligns: no