Chapter 4
Fractions
Cut a pizza for three people and nobody gets a whole one. The same thing happens with half an hour, part of a mile, or a recipe that calls for less than one cup. Whole numbers can count how many pizzas are on the table, but they cannot say how much of one is on your plate. Fractions are the language for the amounts in between. Once you can name those amounts, a question opens up: what can you actually do with them?
What You'll Explore
5 lessons.
- Understanding Fractions
What do the two numbers in a fraction actually tell you? You will look at how a whole gets split into equal parts, where a fraction sits on the number line, and why the same fraction can describe a shape, an amount, and a share.
- Equivalent Fractions and Simplifying
Can two fractions look completely different and still name exactly the same amount? Here you will explore how one quantity can be written in many fractional forms, and what it means to choose the simplest of them.
- Adding and Subtracting Fractions
You eat part of one pizza and part of another. If the two kinds of pieces are different sizes, can you still combine them directly? This lesson investigates what has to be true before fractions can be added or subtracted, and why the size of the pieces matters.
- Multiplying and Dividing Fractions
Half of two thirds sounds simple until you try to picture it, and asking how many quarter cups fit inside a cup and a half is stranger still. Multiplication and division both take on new meanings once fractions are involved, and this lesson works out what those meanings are.
- Mixed Numbers
Some amounts are more than one whole but not quite two, like two and a half pizzas or three and a quarter miles. There are two ways to write an amount like that, and the question is how they are related and when each one is more useful.