Voxitatis (this Web site) has announced the development of an “app” for its Answer Maryland system at maryland-k12.org. The demo is available, free of charge and free of advertising, here.
But don’t stop here. This is a collaborative effort, because we don’t pretend to have all the answers for how to use technology in real classrooms. Our apps on “Answer Maryland” involve open-source access to the app itself. If you want to modify it to fit some other need, please start with our baseline app and take it from there. Teachers everywhere, time to get into technology and use it as a collaborator, not simply as a reader.
The US Common Core curriculum for mathematics in fourth grade has, among other concepts students might be tested on, the following:
Number & Operations—Fractions [limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100]
Extend understanding of fraction equivalence and ordering.
Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
One of my hallmark theories is that kids learn best by self-directed exploration of concepts, even from the earliest of ages. This online manipulative is more than just a set of practice problems or drills. It lets kids manipulate the four fractions and then compare the amount shaded in the fraction bars themselves.
On a test, they might be asked something like this:
Put the following fractions in order from least to greatest:
1/2, 2/3, 3/4, 4/10
This tool will actually let them explore, make mistakes without the consequences of a high-stakes test, and—simply put—learn at their own pace.
Let them explore what happens to the shaded area as they increase the denominator. Let them find out if 1/3 and 4/12 actually line up, representing equivalent fractions. Just let them play with it, without any testing or quizzes. After a while, you will find they have learned more than they would have learned if you had been quizzing and drilling them in a high-speed manner all along.
As always, Answer Maryland is free for everyone. If you sign up for an account on the service, you will be able to start a conversation about this manipulative demo or about any other topic your heart desires. If your teachers, parents, classmates, or friends have accounts as well, your conversation will be available for them, to help as might be needed.
- The Common Core in fourth grade strictly limits the denominators that may be used in testing. It’s much easier, with an online tool, to just let kids manipulate the denominators to whatever number they want, so that’s how this tool works. It seemed ridiculous to limit their exploration to fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100.
- Version 2 of the demo will allow students to see an extended number sentence, something like 1/2 = 4/8 < 2/3 < 3/4. It will also color-code the number sentence with the colors of the fraction bars and show equivalent fractions for each with a common denominator, a common numerator, and decimal equivalents.