We've known numbers forever. We learn to count when we're about two and we never stop. It's kind of like they're our school friend we grew up with, sharing graham crackers and juice boxes. But this unit is kind of like what happens when that friend goes to camp over the summer and comes back sort of different, with a whole new vocabulary. We know they're the same, basically, but they don't really look like it.
Numbers can take all kinds of forms, and we have to be ready for any of them. Since we're used to talking mostly about positive integers, we have to adjust our thinking a little. Numbers can be negative. They don't have to be whole. They can be a composite of a couple of pieces, even. And if they are any of those things, the operations we can do with them have to change, too.
It's just like how you had to learn to play all the new games your friend brought back from camp, even if they were better suited to a campfire setting.
We're going to talk a lot about fractions. We know that they represent parts of a whole thing. But the real challenge is doing multiplication or subtraction when a fraction is involved. That's going to take learning some new rules. The same goes for numbers with decimals or numbers that are negative.
There is a lot to cover, and it may feel a little overwhelming. The important thing is to try and think about where the rules are coming from. It makes them easier to remember and makes this whole thing feel arbitrary.
But really, this is all a good thing. After all, math is about solving problems in the real world. And the real world is rarely so kind as to provide us with all whole, positive numbers. A lot of the time, there's decimals hanging around. And negative numbers can play an important role. By learning all these new rules, we make ourselves better equipped to answer all kinds of problems. And that's the goal, right?
It's kind of a bummer when a friend changes. But once you realize that they're still the same person with fun new features and capabilities added on, it makes it all better. Let's start expanding our number horizons.
By the end of this unit, you should know and be able to