# Patterns: Applications of solving problems using patterns

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##### Intros

###### Lessons

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##### Examples

###### Lessons

**Patterns - Word Problem 1**

Siobhan picks 3 flowers every year on her birthday to add to her book of dried flowers. Her collection has 12 flowers this year.**Patterns - Word Problem 2**

Regular polygons follow a pattern for the variables: number of sides (s) and sum of total internal angles (A).**Patterns - Word Problem 3**

Kelsey found a leak in a pipe in her basement and put a measuring jar under it to catch the water. She noticed that every hour, the water level increased by 2mL in the jar.- There is 34mL of water in the jar after the 1st hour. Fill out the function table and write the rule (formula).

- How much water will there be in the jar after 1 week?
- Kelsey wants to know when she will have to dump out the jar (before it overfills). The measuring jar has a maximum capacity of 500mL. When will she have to dump out the water?

- There is 34mL of water in the jar after the 1st hour. Fill out the function table and write the rule (formula).
**Patterns - Word Problem 4**

At an airport, the pay parking costs a flat rate plus an additional cost for every hour you are parked there.**Patterns - Word Problem 5**

Nora's laptop is broken. She wants to compare the rates that are charged by two different computer repair stores. Store A charges a $50 service fee up front plus $30 per hour. Store B charges a $100 service fee up front plus $15 per hour.

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###### Topic Notes

In this lesson, we will learn:

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

__Notes:__- Being able to
**identify**and**use**allows for better__patterns__**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,
the__rename__**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

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