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Posts Tagged as "fourth grade"

Confused about fractions? Visualize brownies, not pizzas

Friday, September 3rd, 2010

Pizzas. They’re the best way to represent fractions, right? Everyone has seen a pizza. Everyone knows you can slice a pizza different ways. When you need to visually represent fractions, pizzas are the go-to metaphor, right?

Well, that’s what I thought until I tried using pizzas to teach equivalent fractions. Sure, it’s easy to use a pizza to represent quarters, sixths, eighths. Thirds aren’t even too bad.

But just try dividing a circle into five equal pieces. Or seven. Or ten. Even though I’m a grown-up and a professional math educator, it’s really hard for me to consistently do this.

And as for showing visually how two fifths equals four tenths? Unless I do an impossibly immaculate job of dividing those pizzas into pieces, forget about it.

DSCN0716
Are they really the same?

Fortunately, I’ve found a much better way to represent fractions visually: the Math-U-See fraction overlays. If we’re going to use a food metaphor, they’re flat and square, like brownies from a square pan.

And like brownies, they are much easier to slice evenly than pizzas. In fact, because they’re reusable transparent overlays, you don’t even have to draw (or slice) anything. You just arrange them on top of each other.

Check it:

DSCN0717

Awwww, yeah! Those fractions are DEFINITELY equivalent!

You can use the overlays to represent basic fractions with divisors from two through seven, or combine multiple overlays to build other denominators.

Not only do they make it really easy to see how equivalent fractions work, but using them is way easier than drawing pizzas and hoping the slices come out even.

The fraction overlays make the concepts extremely clear, and because they’re tactile, visual, and kinesthetic, they make fractions feel like a game instead of work. Whenever I’ve used them with my students, either in person or during online tutoring sessions with a webcam, they’ve react the same way: “This is fun!”

Now that’s how I want my students to feel about fractions!

Related Posts:
Doing fractions “In Chinese”?!
The best algebra book in the world?
Gallon man to the rescue!
Five fun ways to help your kids learn math this summer

Posts Tagged as "fourth grade"

Gallon man to the rescue!

Thursday, June 3rd, 2010

Do you need a way to remember unit conversion effortlessly and forever? Or just a way to calculate how many cups there are in a gallon?

Here’s how to figure it out. Draw a gallon man!

First, draw a really big capital G. (This is the gallon.)
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Inside the G, draw four big Qs. (These are the quarts.)
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Inside each Q, draw two Ps. (These are the pints.)
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Inside each P, draw two cs. (These are the cups.)
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For the final flourish, draw an arrow to one of the cs and write “8 ounces.” (There are eight ounces in every cup.)
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When one of my students, a fifth grader, taught me about Gallon Man, I thought, I wish I had learned about this in fifth grade! My entire life, I’ve had to look up each of the conversions and never really internalized how they all fit together.

Since I’ve been introduced to Gallon Man, I’ve gleefully shared him with a fourth grade tutoring student (online), a friend who is a professional organic farmer (in person), innocent bystanders (at a restaurant), and most recently, my Mom (over the phone…”first, draw a really big G…”)!

They’ve all found Gallon Man helpful. Responses have included: “Can I take that drawing home with me?”, “Oh…I get it!”, and “I’m going to hold onto this.”

Gallon Man is totally visual and works for many learning styles. You can SEE how many quarts are INSIDE a gallon. Gallon Man is intuitive for all grade levels (unlike dimensional analysis, you don’t have to worry about the numerators or denominators). Gallon Man is practical. You can use it in your kitchen or in the grocery store. Gallon Man is easy to remember. And Gallon Man is fun to draw!

Gallon Man has recently gotten some airtime from other math bloggers, including Sam J Shah, who pointed out that it really helped him to see someone drawing Gallon Man. Here’s Sam’s post and video.

Yay for mnemonic devices!

*Are you looking for an online math tutor who uses multisensory methods? I’d love to help! Give me a call at 617-888-0160 to discuss your situation.

*Visiting from the Math Teachers at Play Carnival (Adventure Edition)? Welcome, I’m glad to see you here! Below are a few other posts you might enjoy!

Related posts:

Tips for how to help your kid with their math homework
Doing Fractions “In Chinese”?!
An easy way to remember how logarithmic notation works
Case study: a homeschooler prepares for the SAT

Posts Tagged as "fourth grade"

When learning feels like a forced march

Friday, February 12th, 2010

I recently posted about how external rewards can destroy children’s intrinsic motivation, and noted that my participation in Pizza Hut’s read-a-book-get-a-pizza program, “Book It,” did not interfere with my extremely strong intrinsic motivation to read.

However, what actually did come close to killing my intrinsic motivation to read was the crushing required reading lists I had during my first three semesters of college. This experience turned reading from something I loved doing to something to just be endured.

For example, in my first semester of college, I took a required course on the Epic in Western Literature. My amazing teacher taught with great passion, drawing on her experience both as a poet and a scholar fluent in multiple languages.

She was the only professor I had in my undergraduate career who incorporated the arts into an academic class. In addition to our analytical essays, everyone also completed an art project of their own design inspired by what we’d read. My art project, a cello piece based on text from the Aeneid, actually ended up growing into a much larger piece after the class was over.

Despite my teacher’s exceptional amazingness, this class almost caused me to lose my love of reading. I experienced the course as a forced march through the great works of Western literature. In one semester we plowed right through the Iliad, the Odyssey, the Aeneid, Paradise Lost, and Dante’s Inferno. I read it all, but I rarely enjoyed it, and I almost lost my love of reading.

At the end of the year, I actually told one of my friends that I “didn’t like books” anymore. This is coming from a kid who inhaled literature out of sheer pleasure my entire life until I got to college.

What happened? When I had been inhaling books before, they were all books I chose freely. And I moved at my own pace. But I definitely couldn’t choose what I was reading in this course. The course itself was required. And moreover, I felt there was no time to understand anything or connect to anything.

In retrospect, it reminds me of the trips I made to the National Gallery of Art when I was in fourth grade. My teacher tried to cram as much as possible into each trip—upon entering a new room, she’d instruct us to stand by our favorite painting before purposefully marching on into the next room. At the end of the trip, she would proudly exclaim, “We saw so much art!”

I’m sure her intention was to cultivate a love of the arts in her students, but even though I loved art before and after those trips, I don’t remember anything about the art I saw on those fourth grade trips.

I feel like a work of art can be like meeting a person. There’s so much to be revealed. But what is the point of speed-dating artworks? What do you really learn from speedwalking through galleries or speed-reading through epics?

I believe the point is not exposure, but connection. If we read something but don’t connect to it and don’t remember it, does it even matter? The one bit of the Aeneid that I do remember is the piece of text I used in my art project. I spent so much time setting it to music that now it’s part of who I am.

Once, while visiting a small art museum in DC, I stumbled across a Miró painting I never dreamed I’d see in person, and I was so happy that I actually laughed out loud. The museum guard glared at me—I guess for breaking the silence of the deserted gallery. In my heart, I thought Miró would have been glad I was excited to see him.

I think the whole point is that a piece of art will pierce your heart and help you feel less alone, and move you to laughter and tears.

I wish we were encouraged to digest things more, and had enough time with what we’re learning to get to know it and let it affect us.

Related Posts:
Praise and Intrinsic Motivation–an answer?
On Stickers
“Simple, but not easy.”

Posts Tagged as "fourth grade"

Case Study: Confused by Math Instruction in a Foreign Language

Wednesday, December 9th, 2009

One of my favorite success stories is a student who came to me as a fourth grader. She was extremely confused about math because her first three years of elementary school were at a French language school. Not only was math taught in French, which was not her first language, but the math instructors were also really bad. Also, she would get emotional about math—sometimes she’d get so upset that she would freeze up.

We started with a lot of math drill, reviewing arithmetic concepts that were unclear from years of math instruction in French. Then we moved on to mixing that with a review of what she was working on in class. We worked very slowly, and at the end of every page or every problem I would give her a high five and a special sticker. (Now, after all I’ve learned about rewards and motivation, I might not give her a sticker every single time.)

Another helpful strategy was paying attention to her emotions of frustration and anxiety, and modeling how to handle them. When she got frustrated or anxious, I would stay calm, just like I hoped she’d learn to stay calm in the face of a challenge.

One day she got really upset about some things in her life that were stressing her out, and I could tell she needed a break. (I was trying to build on what I’d learned from working with another student who broke down during tutoring once.) So we packed up our work and spent the rest of the session leisurely exploring the beautiful library where we met for tutoring.

Very gradually, things improved to the point where she even told me that she “loved” certain kinds of problems. This made me so proud of her! It was amazing to see her going from feeling scared and confused about math to actually being comfortable and delighted with it. Overall, I think what worked for her was just personalized and caring attention with a stress-free vibe.

Related Posts:

Case Study: Regaining Love of Math
Case Study: Learning Geometry with a Spatial Disability