Circles and Oblongs

Problem

Fran and David were playing with a circle and an oblong on the 4 x 4 board in the picture.

Now Fran has the oblong and David has the circle. Fran knows that the oblong can only move sideways (left or right) while David knows that the circle can only move up or down. Both shapes move one square at a time. 

Where are the shapes after three moves?

Try other starting places, can the oblong and the circle land on the same square after 3 moves?

What is this problem about?

This is a simple exercise in giving and following instructions relating to direction.

Teaching sequence

1. Introduce the problem as a game for 2 players. Each player has a shape but the other player moves it. This means that you must give clear instructions for its movement.
2. As a class list the words that are useful for giving instructions.
3. Give the students the game to play in pairs. Once more check that the students understand that they have to give instructions for the other player to move their shape.
4. As the students work ask questions that focus their thinking on the moves they are making.
   What other instructions could you have given to get to this position?
   Where did you start from? Where else have you started from? (if the students can't remember encourage them to plan ways to record this ? for example, a pencil mark in the square).
5. Ask one pair to give instructions to all the other pairs in the class about where to move the shapes so that they land on one another.
   Are there any other solutions?
6. Discuss how they checked out other possibilities.

Extension to the problem

Make up movement rules for a new game.

Solution

After 3 moves (if they continue to move in the same direction) the oblong lands in the top right-hand square and the circle lands in the top left-hand square.

If the oblong starts out in any of the four corner squares of the board, then the circle can be positioned to join it on their third moves.