What do I mean? Tell a group of students to compose a square from the rods: you’ll get some good squares. (3) The rod is arbitrary, but it defines the others. Liping Ma has made theĪrgument that Chinese math teachers are able to convey deep ideas around composition andįurthermore, it is interesting that these powerful terms stem from the use of the abacus and thus stem from a manipulative. Like “compose” or “decompose” is ‘ordered’: composing cubes always This modulo 3 kind of relationship means an operation Shape is adjacent to two different shapes. (2) The pattern of three shapes means each Tenths and hundredths naming “reflects over 1″ while the shapes do not. Coincidentally aligning with the digit grouping normsĪnd the repetitive naming structure (in short-count English anyway). There are other interesting properties here: Shows: the digital medium affords us this space! This means weĬan repeat infinitely… given we have the space. Merely cycling through shapes that always exist in 3 dimensions. We do not run out of dimensions, because we are There is a looping pattern of the three shapesĬorresponding to the powers of ten. Square! (value 100,000) Stack ten squares together and you’d get a massive Only that, but this row is a rod! Compile ten rods together and you’d get a Ten “thousand-cubes” and finds that they have ten-thousand unit cubes. Shows elementary students can build 10,000 quite easily… and in doing so we However, the North Carolina lesson plan, e.g., A 4D hypercube 10,000 is difficult to imagine. In this framework, we now notice we have run out of spatialĭimensions. The rod is a 1D line segment, the square is 2D, theġ000-cube is 3D. The initial small cube is “0″ĭimensions, a point.
To consider each moving up the dimensions. What would it look like to allow these and other non-numeralīased explorations of quantity in the digital realm?Ĭonsider, one way to interpret these shapes is Of reasoning about quantity– allowing success and learning even if numeral These kinds of lessons can give students an alternative method Sample lesson plans and descriptions: (1) Marilyn Burns (2) North Carolina Public Schools (page 5) (3) Hand2Mind. Square, Cube, corresponds with the counts of units inside: 1, 10, 100, 1000.
Ten units join to make a rod, ten rods join to make a “flat” or a square,Īnd ten squares make a large cube. Used manipulatives in elementary classrooms. Seen as cycling to a cube every eight, so we might think it “Powers We see illustrated below, reminiscent of the classic Powers of Ten video: Larger numbers graphically? In the digital medium, we might “zoom out” as