Should We Put Zero Before a Decimal Point?
(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.
Arithmetic
Place Value: Decimals
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.
Place Value: Whole Numbers
We’ll be looking at various aspects of place value, starting here with the basic concepts. As soon as you learn to write numbers beyond 10, you have to start understanding this concept; so we have to begin at a concrete level and move gradually to something more abstract.
“Order of Operations” Puzzles
We have often received questions about things called “Order of Operations problems”, or some similar name. Generally, what that means is simply that they are puzzles to give lots of practice evaluating expressions using the order of operations. I have collected a few quite different puzzles in this broad category.
The 24 Game and Kin
We are looking at various mathematical puzzles and games, with a focus on discussing rules and strategies, and then letting you play. Last time we discussed Four Fours, in which we are given a fixed set of “inputs” to a calculation (usually 4, 4, 4, 4), and want to find expressions that yield as many …
Four Fours and Friends
This has been a good time for doing puzzles to stay busy (as a family, or a class, or as distanced friends, for instance). The next few posts will present various mathematical puzzles and games you might enjoy. Although often when a problem I quote was originally left unsolved, I have filled in the gap …
Hilbert’s Cookie Jar: Little Kids, Big Ideas
(A new question of the week) I enjoy getting questions from young children, as we did here. It forces us to try to express big ideas in simple words (or at least help their parents or teachers do so). A frequent subject of those questions is infinity – they seem fascinated by this concept, perhaps …
Summing Divisors
In searching for answers about counting divisors over the last couple weeks, I found a few that are about the similar question of finding the sum of a number’s divisors. In fact, a couple questions and answers confuse the two problems. Let’s finish off the topic by looking at these. (Keep in mind that “divisor” …
The Locker Problem
A classic problem we’ve seen hundreds of times involves students opening and closing lockers. I have often told people that, believe it or not, they could find the answer by searching the Ask Dr. Math site for the word “locker”. But I prefer to give them a reference to one of the answers in which …
Counting Divisors – with Conditions
(A new question of the week) Last time we looked at a classic problem for which there is a nice formula, namely counting all divisors of a given number. This time, we will examine a question from last August where we have to count the number of divisors of a specific type, making it more …