This unit introduces some of the key concepts of position and direction in the context of a series of activities around mazes.
- Use the language of direction to describe the route through a maze.
- Use the language of direction to guide a partner through a maze.
- Rotate their body and other objects through 1/4 and 1/2 turns.
- Follow a sequence of directions.
At Level 1 the Position element of Geometry consists of gaining experience in using everyday language to describe position and direction of movement, and interpreting others’ descriptions of position and movement. In this unit students will gain experience using the language of direction, including up, down, left, right, forwards, backwards in the context of mazes. For more activities that involve students giving and following instructions using the language of position and direction you might like to try Directing Me.
Spatial understandings are developed around four types of mathematical questions: direction (which way?), distance (how far?), location (where?), and representation (what objects?). In answering these questions, students need to develop a variety of skills that relate to direction, distance, and position in space.
Teachers should extend young students' knowledge of relative position in space through conversations, demonstrations, and stories. When students act out the story of the three billy goats and illustrate over and under, near and far, and between, they are learning about location, space, and shape. Gradually students should distinguish navigation ideas such as left and right along with the concepts of distance and measurement. As they build three-dimensional models and read maps of their own environments, students can discuss which blocks are used to represent various objects like a desk or a file cabinet. They can mark paths on the model, such as from a table to the wastebasket, with masking tape to emphasise the shape of the path. Teachers should help students relate their models to other representations by drawing a map of the same room that includes the path. In similar activities, older students should develop map skills that include making route maps and using simple coordinates to locate their school on a city map (Liben and Downs 1989).
There are many books of mazes and online interactive mazes available. Try to have different resources available in the classroom while you are working on this unit. Early finishers could be given the opportunity to work with the other mazes or draw their own.
Most students will have some experience of using mazes, whether it is walking through mazes, or solving pen and paper mazes in puzzle books. Therefore this should be a familiar context in which to work.
- Draw a simple maze on the board (or photocopy one up to A3).
- Ask students if they can see the path to take to get through it (possibly students could have individual photocopies of the maze to draw their own answer on.)
- Choose a volunteer to come up and draw the path through the maze.
- Now ask students how they could explain to someone who can’t see the maze where the line has been drawn. Encourage the use of accurate terms like up, down, left, and right. Follow the line through the maze as students describe it.
- Draw another example on the board.
- Ask students to describe the route they would take to get through the maze. Draw the route as they describe it. Individual students should only give one direction at a time (ie. Go down first). If students give unspecific instructions such as go round the corner draw the line incorrectly to force them to describe the route accurately.
In this activity one student has a picture of a maze and the other has a blank grid. There are 4 mazes (two basic and two harder), and two blank grids (one for the basic mazes and one for the harder ones) available as copymasters. You can also easily make more mazes by using a vivid to draw walls on the blank grids.
- The student with the maze has to solve the maze and then give their partner instructions for the route to follow through the maze (the instructions should include a direction and a number of squares eg. go down 2 squares). The partner with the grid should draw a line on a grid to show the route described to them. Make sure they start in the correct place.
- Once the person following the instructions has completed a line across their grid they can check the answer by comparing the mazes and looking to see if the path drawn goes through any walls.
- This could also be done as a whole class activity, with all students having a blank grid and the teacher giving instructions. Then a student could be given the opportunity to give instructions to the class, or students could break off into pairs.
Put Yourself in the Maze
For this extension to Maze Pairs tell students that they have to imagine that they are actually in the maze themselves, and that the only things they can do are to move forward or to turn left or right. This makes the activity much more challenging, as they now need to keep track of the direction they are facing as well as where in the maze they are. Counters with an arrow drawn on to indicate direction faced would be a useful aid.
The activity proceeds as in Maze Pairs above but both partners should use a counter with an arrow as they plot their route through the maze.
Compass Direction Maze
In this extension to Maze Pairs students can use compass directions to describe the route through the maze. Draw a north arrow on each sheet and ensure that students know their compass directions (if necessary draw a crossed arrow which includes south, east and west).
The activity proceeds as in Maze Pairs, but all directions should be given as compass directions rather than using up, down, left and right.
In this activity students take the direction giving skills they have used in the classroom outside and onto a larger scale.
- Draw a large but fairly simple maze on the tennis court with chalk.
- Get students to take it in turns to be blindfolded and directed through the maze by a partner who is not allowed to touch them, but has to give instructions about direction and distance.
- The challenge is to get through the maze with as few instructions as possible and without touching or crossing the lines.
- This could be a good opportunity to talk to students about the difficulties faced by blind people. Was it easy to get through the maze? Was it easy to give someone else directions through the maze?
Let students draw their own mazes on grid paper, and challenge a friend to first solve it, and then give instructions for how to get through it.
You may need to give some guidance in drawing mazes – ensure that they are solvable, but try to have plenty of false paths and dead ends.
Possibly students could take their mazes to another class and show them how they have learned to give accurate directions through the maze.