We’re looking at the concept of vectors at an introductory level. Last week we looked at how they are defined in this context (as quantities with magnitude and direction), and how they are added (which is really part of the definition). Our collection of answers from Ask Dr. Math this time focuses on the ideas …
(A new question of the week) A question we got at the end of March asked about a standard kind of algebra word problem that can be solved in a couple very different ways. It illustrates several choices that can be made (both about the meaning of the problem and how to solve it), as …
Because we have had a number of questions about vectors recently, I thought it might be time to look at various facets of that topic. Here, we will start with some ideas about what vectors, and their most basic operations, are. Next week, we’ll get into the far more interesting topic of multiplying vectors. What …
A new question of the week We haven’t done much with vectors here, though there have been many problems of that sort lately. Let’s look at a recent question that touches on the basics, yet is by no means a simple problem. The problem This came from Stefan in March: Determine the angle between vectors …
I’ll finish this series on place value and writing numbers, with a question that’s not quite as simple as you might think: why we use commas and decimal points as we do. Americans may be surprised at some of the answers – and some of the questions. Commas are just a convenience We’ll start with …
Last time we looked at how to convert a number between decimal and word form. Now we’ll move into some tricky cases such as where to use “and” or a hyphen, to eliminate ambiguity. Do I need a “one”? We’ll start with this, from 2001: Written Form of Decimals What is the CORRECT way to …
We’ve been looking at the place value concept, and writing number in expanded form(s); but how about the word form of decimals? This can be confusing at several points. We’ll start with reading a number and writing its word form, and then do the reverse. Reading decimals: the basics We’ll start with this, from 1997: …
A concept regularly taught along with place value is “expanded form”, a way to write a number that displays each place separately. As we’ll see, there is considerable variation in terminology here, so parents may have to check what form a teacher wants, rather than look it up and expect a single answer! Whole numbers …
(An archive question of the week) Last time we ended with questions about writing (or ignoring) zeros at the end of a decimal. I didn’t have room for one more question, so I’ll put it here. Zeros at the start This question comes from 2000: Zero Before the Decimal Point? A fellow instructional designer and …
Last time we looked at the concept of place value as children first learn it, with whole numbers. Here, we’ll expand that to look at decimals. What do we mean by decimal? First, we need to deal with what the word means, because it is used ambiguously. Here is a question from 2004: Defining Decimal …