Mágoulo’s School
Mágoulo’s School for the Spiritually Gifted is a youth group gaming and learning community. We use e-s... View more
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Slope, Equivalent Fractions/Ratios, and Parallel Lines
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Slope, Equivalent Fractions/Ratios, and Parallel Lines
Let’s work on slope again. We’ll use snap cube’s to create rise/run fraction “Ls”. Then we’ll use them to draw slope lines on paper. Then we’ll try adding to the Ls:
- What happens if we double the rise, but not the run?
- What happens if we double the run, but not the rise?
- What happens if we double both?
Watch this on Parrallel lines: https://www.youtube.com/watch?v=oJaMUVv4VXE
Parallel lines always have the same slope, but this can be shown by any equivalent fraction/ratio. This is what allows designers to use different measurements and yet maintain the same slope of a trail (or a roof).
- Pick 4 fractions. Create slope Ls. Draw the lines. How do they compare? If none were parallel, create a fraction that makes at least one parallel line.
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For @etcetera and @BlackoutKnight : Slope is useful when thinking about growth. For example, the grade or slope in a hill is the “growth of steepness”. If you apply this, you can think of all growth relating to slope in some way. Think about your bank account: If you plotted the time in weeks at the bottom of a line graph, and the amount of money deposited as points a certain amount up from the bottom and then you connected those points — you’d have a line (or lines) that can be described with slope.
This is really useful when trying to understand or predict growth. So in the example of the bank account, the graph of deposits would show a line that would tell you if your earnings are growing by the same rate week-to-week (linear), or different rates (non-linear). If you have lots of fixed expenses (the same every month), non-linear could be a real problem (think about why).
When it comes to graphing growth using slope, there’s an important concept you’ll need: Slope and Y-Intercept: https://www.youtube.com/watch?v=lz8zVJxRFX8
You know what slope is. To get Y-intercept, think of a 2-D plane. It’s got X and Y, but no Z. Turn it into a 1×1 grid and measure X and Y with lines in the horizontal and vertical middle. If you plot any sloped line on the grid, it will eventually “intercept” the Y axis. That’s the Y-intercept.
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