Mathematics cannot be learned passively: it must be actively constructed by the person learning it. This takes time and patience with yourself! We want you to read this book actively, thinking through each step.

Here are some examples of types of questions we might ask. Play around with them, get them wrong, try the hints out. Don’t be afraid to fail: getting an answer wrong never hurts you.

Some problems will ask you to enter numbers. $3\times 2 = \answer {6}$

$3 \times 2$ is the number of objects in $3$ groups of $2$ objects

Look at this picture:

$3\times 2=6$

For this course, you should always have a paper and pencil near at hand to make notes, doodle pictures, and practice your explanations. We strongly recommend that you really grapple with each example before getting a hint, or moving on. The difference between what you learn by struggling with a problem on your own versus perusing someone else’s solution is astonishing.

With that said, even if you get an answer right you should always try any hints out afterwards. They might explain the concept from a new point of view, or challenge you to think in a different way.

We support a few different answer types. Here are some example problems from the different answer types we support:

As you complete activities the green “completion bar” moves at the top of the page. This lets you know how close you are to being done with an activity.

You advance through pages either by completing them and clicking the “next activity” button, or by navigating on the little scroll bar at the top of the page.