What is Expanded Form?

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!

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.

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.

How Much Does the Earth Curve?

We’ve looked at how to find the circumference of the earth, and how far we can see over the horizon. Another kind of question we’ve had about the curvature of the earth is, how much does it curve over a given distance? That has been asked in several different ways, which lead to some intriguing …

How Much Does the Earth Curve? Read More »

How Far Can I See?

We have been looking at questions about the roundness of the earth, starting with the general fact, and then the determination of the size of the earth. A very common question is about how that roundness affects what we can see, sometimes as a challenge (“If I can see this, then how can the earth …

How Far Can I See? Read More »

Eratosthenes Measures the Earth

Last time we looked at a couple questions about proving the earth is round, which led into questions about how Eratosthenes measured the earth (though that in itself did not prove the earth is not flat). Let’s look at two questions about that project itself.

Proving the Earth is Round … or Not

Can you use mathematics to prove that the earth is round? That’s a question we get from time to time, sometimes from people who want to prove the earth is flat, sometimes from people who want to convince their friends otherwise, and sometimes just from students. Let’s think about it.

Impossible? Try anyway!

(An archive question of the week) Here’s a little problem with some big lessons for problem solving.

Bayes and Virus Testing

News about testing for viruses has reminded me of a couple problems that I linked to some time ago, but never dealt with directly. The question is, given data such as the result of a (fallible) blood or swab test, how sure can we be of the results? The answer is sometimes surprising.