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Half a drum is filled. A third of a drum more is added. The pieces do not match, so you cannot count them yet.

Halves and thirds do not cut at the same marks.

This is Part I, Chapter 8, Working with Fractions.

What you will learn

Naming a fraction past one whole, and renaming pieces so they match.
Adding, taking away, and mixed numbers with a whole part.
A fraction of a number. A fraction of a fraction. And the flip, which swaps top and bottom.
How many pieces of one size fit inside another.
Cancelling before you multiply, so the numbers stay small.
Sharing a fraction equally among some children.
Which way dividing moves an amount: bigger or smaller.
Taking a fraction of what is left, not of the whole.

Two short checkpoints sit inside this track. Retry them as often as you like.

These ideas come from Class 6.

Naming a fraction, and its place on the number line.
One amount, many names — and which piece is more.
Adding pieces of one size.
Counting up in steps, and numbers that share a factor. A factor divides a number exactly.
Times and share, from Track Zero.

Try each move on a strip or a tray first. The rule comes after, once the move has worked a few times.