Here is a triangle on a grid. The straight up-and-down line through the middle is our mirror line. When we flip the triangle, it swaps to the other side of that line, the same way your reflection swaps sides in a mirror.

Now the question: if I had slid it down first and flipped it second, would it finish in the same square?

We use two mirror lines: the y-axis goes straight up and down, the x-axis goes flat across. The interactive shows three two-step journeys, each moving the same starting triangle twice. Watch where it sits after the first move, then where it lands after the second.

After Journey 1 we will settle the order question with one clear check. We take the same two moves from Journey 1, slide 4 right and flip across the y-axis, and run them both ways from the same start:

• Order A: slide 4 right first, then flip across the y-axis. Mark the finish square.
• Order B: flip across the y-axis first, then slide 4 right. Mark that finish square.

Compare the two finish squares. Then look at Journey 3 (two slides) and ask whether swapping those two slides changes the finish or not.

A vertex is a corner of the shape. Our triangle has three vertices, and we'll call them A, B and C. After each move we'll say where each corner ends up.

After each step we'll read out where each corner has moved to. For the last sequence, watch where the shape finishes.

Today we match the shape to the dashed target outline using two moves. The rounds build up:

• a slide, then a flip
• a flip, then a turn
• two slides in a row
• find a different pair of moves that reaches the target on the board