It all adds up! (A puzzle)

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In this post we look at the problem of finding a sum of consecutive numbers that has a specified value. This is one of Occupy Math’s new activity posts. Let’s look at an example. “Find a sum of consecutive whole numbers that add to 100” could be solved by 18+19+20+21+22=100. This sort of problem is good for practicing arithmetic while also building the logic muscles. Best of all, if you are a parent or teacher, this post will show you how to find exactly which of these problems have answers, which don’t, and for the ones that do have answers, what all the possible answers are.

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The Riddle of the Sphinx

sphinxThis post is about an activity that helps students practice recognizing which numbers are factors of others. It is intended for grade five and above. The activity has several different forms and we will comment on which are harder as each variant is described. In order to run this activity, the parent or teacher will play the part of the Sphinx. If you have an Egyptian head dress or other prop, that helps set the mood.

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Coloring Book Math: An Activity

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This post is about an activity — so it begins with the ages the activity is intended for.

  1. Ages 3-6: just color the pictures, have fun!
  2. Ages 7-9: color the pictures but also try to answer the first question. A parent or teacher should help, and maybe look at this article on rotational symmetry.
  3. Ages 10-12: color the pictures and use them to answer all the questions if you can. Students may need help from a parent or teacher.
  4. Ages 13+: just color the pictures. Answer the questions if you’re interested.

This week’s Occupy Math is the first post in a new category: materials and activities. In response to a reader comment, Occupy Math is working up math-related activities. This one is a coloring book intended to introduce symmetry. A colored version of one of the images from the book appears above. The first page of the book asks five questions; all the other pages are intended to be colored. This post discusses and answers the five questions for a teacher or parent that might be using the activity.

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Prime Numbers and Teaching Fractions

Primes

This week’s post is a follow-up to a post objecting to the way fractions are taught post from a while back. This is also Occupy Math’s third post about prime numbers. It should be much more down to earth than the first and, unlike the second, there are no insects or implications for ecology. This post explains why students who know about prime numbers will find it easier to do arithmetic with fractions. Being able to find the prime factors of numbers gives those numbers character: prime factors are like personality traits. Another way to say it is that numbers with a prime factor in common form a sort of a tribe with common characteristics. Also, there are some games you can play with prime numbers near the end of the post.

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Secrets of the Guild: How Occupy Math found one.

The phrase secrets of the guild was used by Bertie Wooster to describe the reason that his manservant, Jeeves, could not divulge the ingredients of his morning pick-me-up. This post is intended to give pieces that could be used for discovery learning about basket curves, a modified type of petal curve. Occupy Math has looked at petal curves before, to make flowers. This post highlights a “secret” in the form of a not-completely-obvious pattern that permits students to make complex and interesting pictures.

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Improving Fraction Teaching with a Game: FRAX!

FRAXThis post is the second on the game FRAX and spends some time explaining how the game works and where it came from. The first post was on Occupy Math’s sister blog Dan and Andrew’s Game Place. FRAX seems, based on our initial testing, to be a fun game in addition to giving the players practice with fraction arithmetic. To get the rules to FRAX (and if you’re interested in testing the game), click the link! We are giving away FRAX sets to people who will help us with the play testing. FRAX is a card game, not a computer game, though we have some thoughts in that direction.

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Why are we Requiring Teachers to do a Bad Job?

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This week’s Occupy Math is on a familiar topic, the effective teaching of math, but it was sparked by a number of recent media reports on why students in Occupy Math’s part of Canada are doing worse into the teeth of increased spending and emphasis on math. The problem has two parts. The first is the elementary teachers are not required to learn math themselves and are often afraid of it. The second is they are being handed a teaching strategy that cannot work and then getting no help trying to make it work. This is a big multi-part problem and Occupy Math hopes we can all dive in and help.

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Announcing a Calculus Book by Occupy Math

textFor the past three years Occupy Math has been working on a calculus text for the integrated first-year math and physics course he co-designed. The regular books did not have the right topics in the correct order. This post announces that the book is ready. It is the second edition (now with far fewer errors!) We used the book last year and found a need to revise and extend.  The book is not a standard calculus book and the rest of the post is about that. The big points are: we got the cost down to less than half that of the book it replaces. It covers all the topics of a standard first year calculus course for science majors. The presentation is different based on decades of experience with what does and does not work.

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Problem Factories

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One of the things a math teacher needs is a supply of good problems. Occupy Math and his collaborator Andrew McEachern have coined a new term in connection with this need: Problem Factories. A problem factory has two parts. The first is a basic understanding of a mathematical fact, the second is a general type of problem or puzzle based on that fact. Ideally the understanding of the math will specify which versions of the problem can be done and give an idea of how hard they are. From this point, the way forward lies in an example.

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Points on a test are not gold coins!

anxiousOne problem that Occupy Math has in teaching his first year courses is that many of the students have been trained, by their high school experience, to believe that a math class is a game that is scored in points with the goal of a grade. If it weren’t actually true in some of their high school classes, it would be nonsensical, and the whole notion is counter-productive to the goal of getting an education. Every year, Occupy Math has some students who are trying to do just enough work to pass the course, no more. Many of them flunk because a math course builds technique upon technique. What appears to be the correct level of effort for a D near the beginning of the term is actually preparation for an F or an F–. These grade-management tools from high school are also used as fear-management tools; instead of engaging with math, the student tries to scam a passing grade and so avoids the math. This has all sorts of bad downstream effects. In this week’s Occupy Math, we want to look at the issues of effort, fear, and effective teaching and learning.

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