Tag: integers

Number Lines

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.

Multiplying Integers

We have made a big deal of the times table and of other tables.Now we extend the times table to negative numbers and thus to all 4 quadrants of the real number space. We hope to build student intuition about this space and to gain a spatial sense of graphing as well as of multiplication. So we as usual focus on patternmaking and take students through extending the table first left by rows and then down by columns before we have them build the table as a whole. We moved the axes to the outside so that we do not interfere with the table. There are many things you can do with such a table and we urge you to explore it.

Sierpinski Fractals

Fractals are a new 21st century mathematics. They are patterns that repeat themselves at various scales. This one is based on the odd numbers in Pascal’s triangle. We learn to create it easily by using Conditional Formatting which enables us to color cells or text based on a quantitative relationship. To turn Pascal’s triangle into a Sierpinski fractal all we have to do is color cells that are odd numbers. Here again is an amazing pattern involving odds and evens. There are a wide number of other Sierpinski fractal patterns.

More Number Lines

We use rules to build new numberlines. For example we can start in the middle and go both forward or backward using adding and subtracting rules. You can even generate and experiment with negative numbers by subtracting below 0. As you build numberlines on spreadsheets you are building them in your mind. And by thinking of numberlines in terms of rules you are getting ready for algebra.