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Basics of solving patterns in T-tables

Topic Notes

In this lesson, we will learn:

  • How to determine and write one-step and two-step relationships in T-tables as equations with variables
  • How to solve equations: isolating variables in two-step relationships (opposite operation to both sides)

Notes:

  • Recall that T-tables keep track of patterns and allow calculation of subsequent terms
Introduction to Solving Patterns in T-tables and Equations
    • What is a fast way to find the 100th term? Adding by 2 each time is not efficient.
  • T-table columns have a relationship between them. By writing this relationship as an equation, you can put in any number and find information about that term quickly.
    • Ask: how do you go from the left column to the right column?
      • Find one-step relationships through trial and error (if numbers are getting bigger it is + or ×; if numbers are getting smaller it is - or ÷)
    • Assign variables to each column and use these variables in your equation
Introduction to Solving Patterns in T-tables and Equations

  • For more complicated patterns (two-step relationships) the equation will have two operations: the first step will be [× or ÷] and then the second step will be [+ or -]
    • Similar to one-step relationships, they can be found through trial and error

  • Isolating variables in two-step equations by “doing the opposite to both sides” in the backwards order of operations (solve by doing + or - first and then × or ÷ after)
Introduction to Solving Patterns in T-tables and Equations