Generate two numerical patterns using two given rules, plotting the points, and identify relationships between corresponding terms.
Melissa and Joe are reading their books during independent reading. Because Joe’s book has more pictures in it, he can read more pages in the same amount of time. When Melissa is done with 2 pages of reading, Joe is done with 4 pages.
|Number of Pages Melissa Reads||Number of Pages Joe Reads|
Xavier is making two different patterns. Pattern P has a starting number of 0 and he adds 12 each time. Pattern Q also has a starting number of 0, but he adds 3 each time.
Lars wrote rules for two patterns.
|Pattern for x-values||Pattern for y-values|
|Starting number =1||Starting number =1|
|Rule: Add 2||Rule: Multiply by 2|
Lars then wrote ordered pairs ($$x$$, $$y$$) using the patterns above. Which ordered pair could Lars have written?
From EngageNY.org of the New York State Education Department. New York State Testing Program Grade 6 Common Core Mathematics Test Released Questions with Annotations August 2014. Internet. Available from https://www.engageny.org/resource/new-york-state-common-core-sample-questions; accessed May 23, 2018, 12:20 p.m..
Cora and Cecilia each use chalk to make their own number patterns on the sidewalk. They make each of their patterns 10 boxes long and line their patterns up so they are next to each other.
a. Complete each girl's sidewalk pattern.
b. How many times greater is Cecilia’s number in the fifth box than Cora’s number in the fifth box? What about the numbers in the eighth box? The tenth box?
c. What pattern do you notice in your answers for part (b)? Why do you think that pattern exists?
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