Math lessons that adapt to your child

1. 2 pieces, one for each of you. That sounds fair.
2. But look. This sandwich has 2 pieces too, one big and one small.
3. So is counting the pieces enough? No.

1. A cut is fair only when every piece is the same size.

1. Look. I'll cut the sandwich right down the middle.
2. Now check. Are both pieces the same size? Yes, they match.
3. That's 2 fair pieces, one for you and one for your friend.

1. What if 4 friends share the sandwich?
2. Then we cut 4 pieces, and every piece is the same size.
3. Each friend gets 1 of the 4 equal pieces.

1. How can you check a cut? Just look at the pieces.
2. If every piece matches, the cut is fair.
3. If even one piece is bigger, it is not fair.

1. Here's the part people mix up.
2. Don't just COUNT the pieces and call it fair.
3. 4 pieces are not fair if one is bigger. Every piece has to be the same size.
4. Okay. Your turn.

Then it's their turn: This sandwich is cut into 3 pieces. Are the pieces fair?

1. You could just drag it across and hope it lands right.
2. But where exactly does it land? Hoping can't tell you.
3. You need the new spot of every single corner.

1. In a slide, every point moves the same distance in the same direction.

1. Take corner A. It starts at (1, 1).
2. Move it 4 to the right, and x goes from 1 up to 5.
3. Move it 2 up, and y goes from 1 up to 3.
4. So A lands on (5, 3). We call that new point A prime.

1. The other two corners do the same thing.
2. B at (3, 1) goes to (7, 3). C at (1, 3) goes to (5, 5).
3. Every corner went 4 right and 2 up.
4. Nothing stretched and nothing turned, so it is the same triangle, just moved.

1. Is there a rule that works for every point? Yes.
2. Right adds to x, and left takes away from x.
3. Up adds to y, and down takes away from y.
4. So for 4 right and 2 up, every point (x, y) becomes (x + 4, y + 2).

1. Here's the part people mix up.
2. Don't add the right move to y. Right and left change x, the FIRST number.
3. Up and down change y, the second one.
4. So 4 right and 2 up takes (1, 1) to (5, 3). Not to (3, 5).
5. Okay. Your turn.

Then it's their turn: Point A is at (2, 1). The triangle slides 5 right and 3 up. What is the x-coordinate of A′?