Maria's Math News, Vol. 52, April 2011

CONCEPTUA FRACTIONS - Your child CAN learn fractions! Conceptua Fractions uses interactive visual models to build understanding in fractions. -Over 400 fractions activities with built-in support. -Flexible tools let you customize for your child. -Affordable pricing for homeschool families. Get started today with our Free Fractions Tools.

Hello again! This newsletter is quite filled, so I hope you will find something interesting, no matter what level of math you teach.

1. Math Mammoth placement advice
2. The value of manipulatives
3. Conceptua Fractions free tools
4. Free money worksheets
5. A problem with a chord: find the radius
6. Tidbits

1. Math Mammoth placement advice

As you may know, I provide placement tests for Math Mammoth. These tests are end-of-year or exit tests for a given grade. They will work, whether you're planning to place the child in the grade-level series (Light Blue), or to use the topical books (Blue).

Many people don't know what to do if their child doesn't totally "flunk" the test but almost passes, or if their child does well in other areas, but misses the problems in some particular topic, such as fractions or multiplication. On that page, I provide advice for these situations.

Recently I also added suggestions as to what to do if the student does well in other areas, but can't do the word problems in the test.

I also provide personal guidance to anyone who sends in the test results. Over the years, I've done quite a bit of that type of "counseling". So your child's case, however "disastrous" it might be, is probably not unique.

Plenty of people write to me how their child "bombed" the test, or is many grade levels behind, and they need to know what to do. Nearly universally I can find a solution using my Blue Series books as supplements.

So, don't hesitate to contact me about the placement, if you need help.

2. The value of manipulatives

(Note: I'm "resurrecting" an old post, with added information and a video. The topic is still very much valid.)

Manipulatives are IN, in math education. But do they TRULY facilitate learning to such an extent as people promoting them claim?

The entry at Text Savvy, Hands-on, Brains-Off, explains some of the pitfalls in manipulative use. Very enlightening!

Quoting from an article at Education Week (Studies Find That Use of Learning Toys Can Backfire):
In a similar series of experiments at the elementary-school level, the researchers found that children taught to do two-digit subtraction by the traditional written method performed just as well as children who used a commercially available set of manipulatives made up of individual blocks that could be interlocked to form units of 10.

Later on, though, the children who used the toys had trouble transferring their knowledge to paper-and-pencil representations. Mr. Uttal and his colleagues also found that the hands-on lessons took three times as long as the traditional teaching methods did.

The video below also illustrates how manipulative use can lead to problems.

Keep reading & watch the video!

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    3. Conceptua Fractions free tools

    I've heard a lot of good things about the free fraction tools at Conceptua Fractions. They are interactive online tools that use visual models to teach all fraction operations. They have a tool for identifying fractions, another for equivalent fractions, another for adding fractions with like denominators, another for adding with unlike denominators, and so on.

    These tools exceed anything I've seen in the past... truly comprehensive and excellent. They always include several different visual models, and you can switch between them in an instant... the pie, a bar, a rectangle, a number line, or a dot model. You hover over the area to see the slider, and then you can drag it to partition your model into however many parts you want (well, up to 90 or 100 or so). Then you color or uncolor the parts with a single click inside the parts.

    I want to mention that these tools are meant for the teacher, to illustrate the concepts. You would best use these tools when teaching the concepts, whether in whole-class instruction, in a homeschool, or in tutoring. They do have a few example problems, just a few of various kinds, to show what you can do with the student(s), but they don't provide quizzes or a slew of ready-made problems for the student to complete.

    Ok, enough talking. Go try them out -- they're free. For each tool, it's maybe easiest to first look at the sample problems or watch the video that shows how to use it. Then you can go experiment with the tool itself. Lessons plans are also provided.

    4. Free money worksheets

    I'm glad to announce these additions to the worksheet generators at Use them to generate customizable free worksheets for counting coins and bills.

    US money worksheets (dollars & cents)
    Canadian money worksheets (dollars & cents)
    Australian money worksheets (dollars & cents)
    British money worksheets (pounds & pence)
    South African money worksheets (rand & cents)
    European money worksheets (euros & cents)

    5. A problem with a chord: find the radius

    Today I had the opportunity to solve a real math problem involving a circle and a chord of known length in it. I had to find the radius. It wasn't a textbook problem or a puzzle on some website, but a math problem I needed to solve for my own needs.

    For a tiny while I thought I could find the answer online, but I didn't, so I'm writing it out in case someone else needs it -- they should be able to find this solution by searching the Internet.

    I wanted to make a kind of "moon-sliver shapes" in CorelDraw, to use as watermarks in my new books. I have the height and the width of the "sliver".

    Here's the problem mathematically:
    I have a chord of a circle, 17 mm in length in my example, and the other distance marked in the image is 5 mm. I need to find the radius of the circle, AND the angle measure of the arc of the circle that makes the sliver's rounded part.

    Keep reading & see the pictures

    6. Tidbits

    • One-minute cool math video
      This is a cool 'n' short math video (HT Denise) from a math blog Love 4 Math. My kids laughed... good fun! Good job!
    • Real-Life Math Lessons
      Engaging math lessons based in real-life activities that include printable lesson plans, student worksheets, and videos. Cell phone plans, design clothing, design a bedroom, LeBron James' basketball skills, NFL Quarterbacks , Rock/Paper/Scissors & probability, etc.
    • Metal brainteasers
      Monkey Pod games produces high-quality, yet affordable wooden and metal brain teasers and puzzles. I got to review their Metal Brain Teasers Gift Set II. It has four things in it.
    • Measuring obesity with BAI
      I'm not real super interested in obesity or calculations of people's weights, fat levels etc. but I ran across something half interesting that might be of interest to you. It is a new way to measure obesity or to check if a person is underweight, normal weight, or overweight -- and it doesn't even use your weight in the calculation!
    • Math genius at age 12
      Some of you might enjoy reading this article... a 12-year old boy (Jacob Barnett) is about done studying college-level studies in astrophysics and they want him to start doing research. He's also mildly autistic.
    • A homeschooler wins Intel's competition
      Just an interesting tidbit... 17-year-old Evan O'Dorney has won the first prize of $100K in The Intel Science Talent Search 2011 competition. He is and has been homeschooled. His entry to the competition had to do with math.

    Till next time,
    Maria Miller

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