How many of the products in a 12 by 12 times table are odd numbers? This is a question we rarely ask in paper-based math classrooms, yet it is an important and a very interesting question. We ask students to explore it, learning to Show and Hide rows and columns in their spreadsheet at the same time. Here again is an interesting pattern in mathematics, one we do not generally expect. Odds and evens often seem to students to be an unimportant distinction, but it is not. Odd and even numbers appear again and again across all of mathematics and in many of our Labs. It is important not only as a pattern, but it tells us to pay attention to odd number products because they are rarer than even number products.
Tag: factors and multiples
Magic Rectangle
Multiplication tables have some wonderful and quite surprising patterns. This is one of them. Draw any rectangle in a multiplication table and you will find that the products of opposite corners are equal. For example a rectangle around a full 12 by 12 table will be 1144 and 1212. Try it, is it always true? Why?
Lights Out
This is one of those math puzzles that come up in contests but which turn out to be quite interesting mathematically. Imagine a long hallway with lights in the ceiling, all on and each controlled by its own chain. A long line of people (as many as there are lights) walk down the hallway. The first one pulls every chain, the second one every other chain, the 3rd pulls every 3rd chain and so on. When all the people have walked down the hallway, what lights, if any, will still be lit? What more can you learn from this puzzle about multiplication?
Factor Table
Spreadsheets always automatically perform the operations you ask them to do. But sometimes we want to see the process. We can make spreadsheets show us that in several ways. Here we show the factors and have students build a times table showing the factors by using a special formula called Concatenate which means join together. This enables us to create a table of factors that we can see with a single rule. Concatenate has a wide variety of uses and it is worth playing with both to visualize factors and to build interesting spreadsheets.
Factor Pairs
Multiplying creates products, factoring separates a product into the numbers that make it up. We thus start with the table and then look at the axes to find the factor pairs that make the product. Once again we focus on the patterns in the times table so that you can not only go from factors to their products but from products back to their factors. Factors and factoring become very important in algebra and in making headmath much easier.