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.
First I flip the triangle across the mirror line. Then I slide the flipped triangle three squares down.
Now the question: if I had slid it down first and flipped it second, would it finish in the same square?
Show the final position after both moves have been applied. Point to the mirror line (the vertical line down the middle) and name it, so pupils can see which line the triangle was reflected across. Take two or three hands-up predictions on the swap-the-order question, but do not settle it yet — the lesson is built to answer it.
Give five seconds of quiet think-time before any hands go up.
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:
Compare the two finish squares. Then look at Journey 3 (two slides) and ask whether swapping those two slides changes the finish or not.
Reminder before starting: flip across a line sends the shape to the other side; a quarter-turn clockwise goes the same way as clock hands.
Journey 1 (slide 4 right, then flip across y-axis): watch the full journey. Ask what stayed the same about the triangle itself, size and shape never change.
Worked order check (the missing LO2 demo). Same start, same two moves, both orders. Point to the start square each time so nobody restarts from the wrong place.
Slip to watch: pupils who apply Order B's slide from the Order A intermediate, or who flip then slide left to "undo". Always restart Order B from the original start.
Journey 2 (flip across x-axis, then quarter-turn clockwise): slow down, flip-then-turn is easy to muddle. Trace the turn slowly, same way as clock hands. No need to swap order here unless a pupil asks.
Journey 3 (slide 2 right, then slide 3 up): hold out for a pupil to notice that swapping the two slides lands in the same square. Contrast with Journey 1: two slides can swap; a slide and a flip usually cannot. Also point out the two slides finish like one slide of 2 right and 3 up from the same start.
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.
Today we work through three two-step sequences together on the board:
After each step we'll read out where each corner has moved to. For the last sequence, watch where the shape finishes.
Talk this through together — pupils take turns at the board and the class agrees or corrects out loud.
For each sequence, apply the first move, freeze, read off the vertices, then apply the second. The third sequence (3 right then 3 left) returns the shape to its start — let a pupil notice that the two moves undo each other before you confirm it. Watch for pupils who apply the second move from the original position rather than from where the first move left the shape. With three sequences in the slot, keep the first two brisk so the third (the undo pair) is not rushed; if time is tight, drop the middle sequence to two.
In your maths copy, plot a small triangle on a grid. Label its three corners (vertices) A, B and C. Then apply flip across the y-axis, then slide 3 down. Record the co-ordinates after each step in a small table, like this:
Fill in the actual co-ordinates for your triangle in each row.
Walk the room glancing at whether pupils are writing the after-flip co-ordinates into the middle row before doing the slide — that middle row is the whole point. No marking; this is whole-class copybook practice.
Today we match the shape to the dashed target outline using two moves. The rounds build up:
This is the practice round — pupils take turns at the board, check each answer, and the class confirms before moving on. Move briskly through the first three rounds (about 1.5 minutes each) so the final round, which is the lesson's key idea, has real time. Keep the board work brisk rather than over-explaining.
On the final round more than one answer is right — the target is a position on the grid, so any pair of moves that lands the shape on it is correct, not just one fixed move-list. Let two different pupils show two different pairs that both land on it, and revoice that they are equivalent moves.
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