I have been working with eHow.com to get some common math questions answered. One of the questions was, “How are the areas of a rectangle and triangle with the same base and height related?”
Curiously, all rectangles can be cut into triangles. And all triangles can be doubled to make a rectangle. Watch this video – and then get out the construction paper, scissors and glue.
Grab a kid and have some fun watching them discover!
You can’t get a more dense set of math words crammed into a small space than “scalar factors of scalar ratios” – shoot me.
@Milehimama, a friend of mine on Twitter and fearless leader of the Houston Blogging Chicks asked me yesterday what was up with this strange math thing. And why her son was being asked to do a table with them instead of doing it the way it seemed most natural to him.
I could go on and on – not just about the boring-ness of the table, but also the coolness of scalar factors. I’ll spare you (and her) the insane rant/passionate pep rally. I’ve limited my answer to 6 minutes in the video below.
A number system is a highly advanced concept. And yet we throw it at first grade math students expecting them to immediately grasp it.
Our number system is based on place value, like any number system (like clocks, years, etc.). Which means everything wraps around. Once you get to the “top” of the list of numerals, you have to start over, in a sense. This is crazy weird – it’s no wonder kids struggle at this point!
I promised to help a teacher this weekend who was struggling teaching place value to her first grade math class. I dug out a MathRack, a brand of rekenrek, which was part of a set MathRack.com shared with me months ago. I peeked at their book Mastering the MathRack to Build Mathematical Minds to get an idea of how to teach place value using this amazing tool.
The video above uses the MathRack 20 and some place value cards. I followed the Hidden Numbers activity on page 61 of the book. (As of writing this, I’m unable to find the book online. The site where it is supposed to be doesn’t seem to be functioning anymore.)
Glenda, the first grade math teacher, specifically wanted help teaching the comparing numbers and ordering numbers. So here goes…
Comparing numbers is easier when visualized.
Children can see the value of two digit numbers better when they see the quantity of beads. Let them practice comparing numbers for a while using both the rekenrek and the place value cards. The more they practice, the better feel they’ll get for the place values in our number system.
I’m not sure what the structure of a first grade math class is, but the more days they can “play” with their MathRack like this, the better they will get at comparing numbers. If you have limited time, do a few minutes each day for more days, rather than more time on fewer days.
Ordering numbers is also easier when children see it.
Once the children have played a while with the rekenrek, they will have some comparison skills. Ordering numbers is the next step. Teach them that the act of ordering numbers is just comparing numbers many times.
Computers order numbers by comparing them one at a time to each of the other numbers. Let students try ordering numbers this way, as well as other ways. The one-at-a-time method might be slower, but it could be what the child needs.
Keep trying and share what you learn.
How about it – can you use this for your first grade number system lessons? Do you have a MathRack or can you make one? Share your successes in the comments!
Have you run into this? You get the “wrong answer” when you use a calculator and the Law of Sines to find an obtuse angle.
The problem isn’t that the Law of Sines doesn’t work (thanks @GMichaelGuy), but that you have to be cautious when dealing with the arcsine with an obtuse angle. Here’re the details:
I’ve concocted a triangle that’s pretty simple but has an obtuse angle. That’s the key here. The law of sines always “works” when you have all acute angles. It’s only when the angle in question is an obtuse angle that we have a problem. (and, as @GMichaelGuy pointed out, it always works, it just makes us do a little more work.)
Notice I used the arcsine. Turns out, the arcsine isn’t a function. Which means when you “undo” all the bits in the law of sines, technically you’ll get an infinite number of answers.
So it all boils down to the calculator not being able to determine if you want the obtuse angle when you solve for x using the law of sines!
What do you think? Any other questions on trig? Ask them in the comments.
Yup – only three. Said by you, the parent and grownup. Say them loud, say them often. And contact me when you wonder where math is in your world – or leave a comment here!
No formulas here, only how to figure out which formula you might need to use if you’re working with present value annuities or future value annuities. (These are part of finance and often found in a Finite Math class.)
This past Monday we had a great #mathchat via Twitter. The topic was: “If you could clear one misconception about mathematics and/or teaching it, what would it be?”
I was getting a bit frustrated that a couple of people kept bringing up the misconception that girls aren’t good at math. Even to the point of creating their own hashtag #girlsaregoodatmath2.
In my life, I’ve never heard anyone say this – in any other form than somebody complaining that people say it.
So here’s my response to everyone who keeps saying to me, “I wish people would stop saying, ‘Girls aren’t good at math.’”
What do you think? What will you say from here on out?
I’ve been itching to get into some basic abstract algebra goodies. With the help of the Cuisenaire Rods, Simply Fun Sumology number tiles and the Discovery Toys Busy Bugs, I’m able to do that.
Start with wrap around addition.
This type of math is officially called “modular arithmetic.” We are only going to use the numbers 0, 1 and 2.
It begins as regular addition. And since we are only using those three numbers, all our answers have to be either 0, 1 or 2. So when we add 1+2, we wrap around.
If we were to count in our system, we’d say: “0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, …”
The addition table looks like this:
(Notice you could do this with numbers from 1- 12 and it would be clock addition!)
Now things get buggy.
Switch out all the number tiles with some pretty color Cuisenaire Rods. They don’t have to be the “right” rods. We’re only looking at the colors. Here’s the progression I did:
The end result is a very abstract chart!
You can “bug” two things together.
Like this:
(I know – a spider isn’t a bug. But run with me on this, okay?)
Notice that each of these are directly from the “spider table” above.
You can read this as, “Purple spider green equals green,” just like you would say, “Zero plus one equals one.”
