We’ve looked at what prime numbers are, and how the concept extends (or doesn’t) to 0, 1, and negative integers. The next question many students have is, how can I make a list of prime numbers (or write a computer program to do so)? We’ll learn about the Sieve of Eratosthenes, and list all the …
We’ve looked at the basic idea of primes, then at where 0 and 1 fit in. But what about negative integers? Can they be prime? If so, how does that affect the definition? And can you factorize a negative number if you don’t have negative primes?
Last week we looked at the definitions of prime and composite numbers, and saw that 1 is neither. The same is true of 0. What, then, are they? That raises some deep questions that we’ll look at here.
I’ll begin a short series of posts on prime numbers with several questions on the basics: What are prime (and composite) numbers, and why do they matter?
(A new question of the week) Some problems can be done either by algebra or by basic arithmetic methods and some creativity; and although algebra generally makes work easier by making it routine, sometimes special-purpose thinking (once you have thought it!) can be quicker. Here we have a problem where a creative method didn’t quite …
For the last two weeks, we have examined new and old ways to think about proportions. This time, we’ll look at an old method called the Rule of Three (both “single” and “double”), and how you might have learned to solve these problems 200 years ago without algebra. Be prepared for a deep dive!
Last week we looked at a set of special rules for working with proportions, which have been largely replaced by the more general “tool” of algebra (the “Swiss army knife” of problem solving, which can do the job of many specialized tools), though the latter can still be useful. We still find that many students …
Last time we looked at explanations for the product of negative numbers in terms of various concrete models or examples. But it really requires a mathematical proof, as we’ll explain and demonstrate here, first with a couple different proofs, then with the bigger picture, giving the context of such proofs.
One of the more common questions we’ve been asked is, How can the product of two negative numbers be positive? Between this post and the next, I’ll put together many of the answers we have given, starting here with examples from the “real world” (gradually getting more abstract), and next time we’ll look at proofs. …
Negative x Negative = Positive? Concrete Illustrations Read More »
Last time we looked into terminology related to negative numbers; one subtopic was too big to fit, so I’ve broken it out into a separate post. How are the concepts of “negative” and “minus” (subtraction) related? How much do we need to distinguish them? We’ll look at two questions, the first from a child focused …