Number Lines introduce students to functional thinking and the use of formulas in spreadsheets. For younger students we call these formulas “rules” and ask students to build a variety of number lines using rules. For example they can build a whole number line by creating a rule that adds 1 to the number in the previous cell (=J9+1) and then copy that rule across the numberline cells. They build numberlines with only odd numbers, even numbers, and starting with different numbers. We encourage them to explore a variety of rules to make different numberlines.
Tag: symmetry
Similar Triangles
Scatterplot graphs enable us to build shapes using spreadsheets and to practice transformational geometry. They are surprisingly flexible tools. And since they depend upon a table of value and that table can have both fixed numbers and rules, we can not only build shapes but change them and watch the graph immediately reflect those changes. In this lab we use that capability to get students to explore scaling, reflection, and transposition of a triangle. This is only the beginning and we hope students will take this further exploring symmetries for example.
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.
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.
Commutativity
The symmetry of the multiplication table around the square numbers diagonal we call commutativity or the commutative property. It means that in a 12 by 12 multiplication table we need only learn 72 or so facts and not 144. It also means that the square numbers are not the only important diagonal patterns in the table. As with so many of the things we do on spreadsheets, we not only encourage students to explore, we encourage them to be look for the beauty in math.