Much was learned during our extensive study in patterns. We were able to come up with new ways to identify and interpret mathematical, as well as pictorial, patterns by using “In and Out” tables. As mentioned before, this unit was rather extensive, not only did we explore “In and Out” tables; we also discovered functions, domain and ranges of data sets, summation notation, consecutive numbers, factorials, arithmetic sequence and order of operations. On top of that, we investigated triangular numbers, finding formulas, the number of diagonals in a polygon, the sum of interior angles in a polygon, measure of angles in regular polygons, exponents, and squaring negative numbers. As you can see, this was a productive unit!
The “In and Out” tables were a vital piece of this unit. Not only were they an effective way to show information, we were also able to solve patterns using them and find missing terms in a sequence with them. In the example “In and Out” table below: “To find the out value, multiply the in value by itself and then subtracts three.” In
“In and Out” tables taught us to look at problems differently and to find multiple ways as to how to address a problem.
When we solved the “In and Out” tables, we came up with functions to express a rule derived from the table that could describe how to find the out value from the in value and would work for all numbers being applied to it. By solving the functions, we were able to come up with formulas. Upon coming up with formulas, we were able to also solve for missing domains and ranges in the tables. Domains are the inputs in data sets and ranges are the outputs.
Another useful way to display data sets is through summation notation. Summation notation uses the “Sigma” sign and can represent data up to a certain specified limit.
Consecutive and triangular numbers seemed to pop up a lot in this unit while investigating patterns. We noticed that with consecutive...
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