Applications of solving problems using patterns

In this lesson, we will learn:

• How to solve word problems for number patterns, function tables, and function formulas.

• Being able to identify and use patterns allows for better problem solving
• You can use patterns as a shortcut to find the answers for other questions where the same pattern exists; the same method can help you find solutions for multiple problems
• Using patterns can help you save time
• Ex. If there are 2 red marbles for every 3 green marbles, how many green marbles would there be if there were 264 red marbles?
• It would take a long time to draw all the marbles
• By using a pattern (using a rule) you can find the number of green marbles in just one step
• The rule is $y = \frac{3}{2}x$, so plugging in the number of red marbles $y =\frac{3}{2}$ (264) gives $y$ =396. There are 396 green marbles when there are 264 red marbles.


• When dealing with pattern word problems, rename the input and output as relevant variables (i.e. choose your variable as the first letter of the variable type)
• ex. years ($y$), hours ($h$), water ($W$), cost ($C$)


• Look for these common words in the pattern word problems
• “every” means to multiply
• Time units (such as hours, minutes, years) are usually inputs
• “there is __ this time” surrounds the first output (ex. $12 after the first hour)


• Recall that the formula for number patterns is given as $y = mx + b$
• Or, it can be thought of as:
  $(output variable) = (multiplier/divisor) x (input variable) \pm (addend/subtrahend)$


• Ex. “There are 3 frogs for every turtle at the pet store”
• The input is “turtles” ($t$) and the output is “frogs” ($f$)
• “every” means multiply with the multiplier “3” to the input ($t$)
• The formula is given as: $f = 3t$


• Ex. “It costs $0.20 for every piece of gum”
• The input is “pieces of gum” ($g$) and the output is “cost” ($C$)
• “every” means multiply with the multiplier “0.20” to the input ($g$)
• The formula is given as $C$ = 0.20g