Section 28.4 Closing Ideas
In this section, we introduced the idea of integer chips, and used them to describe all integer addition and subtraction problems, using both positive and negative integers. But we're not limited to just these things. We can take the idea of these chips and use them with the idea of base-10 blocks by replacing the cubes with chips.
We can also imagine breaking each of the chips into wedges and using them for addition and subtraction of fractions. And since decimals are just fractions, we can also imagine using them with decimals. Not that we would actually do that, but this is is conceptually possible.
We also saw in the last couple worksheets that we can connect these chips to talking about the opposite of numbers and solving equations.
This flexibility is one of the marks of a beautiful idea in mathematics. The ability to take one idea and connect it to so many other ideas means that we now have an expanded vocabulary with which to talk about our mathematical ideas. It also means that when it comes down to solving problems, we have yet another tool in our toolbox. And broadening that toolbox is the ultimate goal of college mathematics.