Blocks for logarithms, multiplication, factors, and primes: The Logprimus

thingiverse

"The Logprimus" This set of blocks will help students learn how to think about the logarithmic relationships between integers and connect these facts to operations like multiplication, factorization, and the sequence of primes. Linearly stacking blocks (on their side) and comparing their total length against a log scale (or other stacks) will reinforce concepts of prime factors and integer uniqueness. Some lesson ideas are included in the instructions. v2 note: The blocks stack better now. They're also a good exercise in resolution and dynamic range... or lack of it. These are best for instruction rather than actual calculation. Note: This thing uses the OpenSCAD font library write/Write.scad from this http://www.thingiverse.com/thing:16193 Instructions Several lessons can be built around these blocks and little more than a ruler (even without log paper, or make your own). The simplest exercise is to print one set of blocks (use the Customizer to change the default number) per group and provide students with some time to explore common multiplication problems. Once the groups have figured out the "puzzle" (i.e., the length of a stack is related [logarithmically] to the product of the block-integers) you can introduce a number of exercises based on division or fractions (denominators substract blocks, numerators add blocks) or greatest common divisors, etc. Primes are a bit more difficult to work into an activity but here's one that can work with a few small groups (and more prime blocks than members). The goal is to reinforce the notion of integer uniqueness when restricting to a product of [single] primes: (1) Ask groups to select only the prime integers from their block sets [reinforces prime facts], (2) ask each student to take one prime. From here there are several variations that may work better, or worse, depending on your class size and age. The stack will be unique when any subset of students combine their blocks, so, you might pit one group against another to discover the other's "secret" by obfuscating the factors by drawing the stack's outline on the board. (N.B., this becomes error prone for large stacks). You might also apply this idea to cliques of students and use their stack outlines as "integer fingerprints" within the context of a clue game. There are many, many variants. I hope others will contribute their lesson ideas- I'm sure it'll be fun!