How Long is 10! Seconds?

A fun exploration for upper elementary or middle school students, from Numberphile:


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PUFM 1.3 Addition

Photo by Luis Argerich via flickr. In this Homeschooling Math with Profound Understanding (PUFM) Series, we are studying Elementary Mathematics for Teachers and applying its lessons to home education.

The basic idea of addition is that we are combining similar things. Once again, we meet the counting models from lesson 1.1: sets, measurement, and the numberline. As homeschooling parents, we need to keep our eyes open for a chance to use all of these models — to point them out in the “real world” or to weave them into oral story problems — so our children gain a well-rounded understanding of math.

Addition arises in the set model when we combine two sets, and in the measurement model when we combine objects and measure their total length, weight, etc.

One can also model addition as “steps on the number line”. In this number line model the two summands play different roles: the first specifies our starting point and the second specifies how many steps to take.

— Thomas H. Parker & Scott J. Baldridge
Elementary Mathematics for Teachers

Continue reading PUFM 1.3 Addition

Math Teachers at Play #50 via Mathematics for Teaching

[Photo by By Willi Heidelbach via flickr.]

Fifty is the smallest number that is the sum of two non-zero square numbers in two distinct ways: 50 = 12 + 72 and 50 = 52 + 52. … I’m a teacher I have to ask: “So what’s the next bigger number to 50 that is the sum of two non-zero square numbers in two distinct ways?” …

There is always something to investigate in math. One of the major objectives of school math is to get students into this thinking habit without us telling them to do so but I’m digressing from my topic now.

Let’s get to the great posts submitted for this edition.

Go read the carnival post at Mathematics for Teaching.

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Tell Me a (Math) Story

feature photo above by Keoni Cabral via flickr (CC BY 2.0)

My favorite playful math lessons rely on adult/child conversation — a proven method for increasing a child’s reasoning skills. What better way could there be to do math than snuggled up on a couch with your little one, or side by side at the sink while your middle-school student helps you wash the dishes, or passing the time on a car ride into town?

As soon as your little ones can count past five, start giving them simple, oral story problems to solve: “If you have a cookie and I give you two more cookies, how many cookies will you have then?”

The fastest way to a young child’s mind is through the taste buds. Children can easily visualize their favorite foods, so we use mainly edible stories at first. Then we expand our range, adding stories about other familiar things: toys, pets, trains.

Continue reading Tell Me a (Math) Story