Students are tasked to build a times table in just two steps. They have to learn to use absolute as well as relative addressing to do, and the Lab takes them through using them. We encourage students to work with just a row or a column rather than with the table as a whole because doing so makes it easier to see what is wrong or what does not follow the pattern. We believe students should learn to struggle to solve problems and that persistence, patience, and grit are important for all of us to have. We therefore do not want to tell students how to do something but rather to let them explore and try and keep at it until they get it. Spreadsheets with their openness and feedback provide a great opportunity for doing this in Labs like this. It is one of our favorites.
Tag: multiplication table
Odd Times
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.
Square Numbers
The square numbers form an interesting pattern on the times (multiplication) table. They run along a diagonal from 1 to the top right of the table separating the table into two halves. This is the first step in looking at patterns in the multiplication table. Students build a new square number table by using a rule and then graph that the square numbers. The square numbers form a parabola on a graph.
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?
Products as Areas
Using the times table, students can see that products are always rectangles, and that they represent the area of that rectangle. They should explore the times table by playing with these rectangles whose sides are the factor of the products.