Tag: linear

  • Fahrenheit to Celsius – Graphically!

    Fahrenheit to Celsius – Graphically!

    Part of Wordless Wednesday…

    The beautiful and talented Heather at Freebies4Mom.com sent me a post on An Easy Way to Convert Celsius to Fahrenheit.

    It inspired me to draw the graphs of Celsius in terms of Fahrenheit and Fahrenheit in terms of Celsius.

    The conversion from Celsius to Fahrenheit and back again can be strange. One way to understand it is on a graph. And you can use this to teach some linear algebra too!

    Notice these two intersect at (-40, -40). Which means that -40°F is -40°C!

    Use it to convert temperatures.

    The x values on the red line are Celsius – so find the °C you have and then look at the y-value to convert to °F.

    It’s just the opposite on the purple line.

    Okay, fine. This isn’t the greatest way to convert – but it’s exciting to see it graphically. And it might be easier to convert this way for someone who’s more visual.

    Use it to teach math!

    These two lines are inverses of each other. So the coordinates of one are switched to make the other.

    Also, they mirror image across that 45° line. I marked the line with dashes and wrote $latex y=x$ on it.

    And if you’re into this, their functional composition (both ways) is… x! (not factorial)

    Compare and Contrast…

    Take a look at the way J.D.Roth did it and then look at the graphs I have. Let your students find the way they like the best. And encourage them to create new ways!

    Oh, yeah – and share what happens in the comments!

  • Finding Patterns in a Lokta Paper Blank Book

    Finding Patterns in a Lokta Paper Blank Book

    Written as part of the Count 10, Read 10 series.

    For my 40th birthday, I bought myself this beautiful Lokta paper book from a fabulous little store in the Houston Heights called Write Now!

    It has circles on it – one of my “things.” I love circles. But then I saw how the colors were laid out.

    “Holy cow! This is a teaching opportunity!” I thought.

    And it got even better at the Texas Home School Coalition’s convention this last week. I shared it with former math teacher and now-homeschooler Sharon Brantley and she saw even more goodies in it!

    You can use it to teach math!

    Anything that has more than one aspect/characteristic/color (pretty much everything) can be checked for patterns. Patterns are an essential, perhaps even the most important, building block for mathematical thinking and development.

    Here’s what you can see in this book cover:

    Connect the green dots and you get a square. (Also the yellow dots.)
    The pink dots form a line and then the one dot off to the side can make a perpendicular line to the other line. (Purple dots, too.)

    These blue dots make a funny little shape.

    But wait! There’s more!

    What Sharon pointed out to me was that you can draw an L from any dot to another dot of the same color!

    Optional: This “L” thing links directly to the slope, by the way. Between any two points of the same color, the slope is either 1/2 or -2. Cool, huh?

    Where do you see patterns in your world? Share it (and a link to the picture) in the comments!

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