Giving directions

Giving directions

Pencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about getting and giving directions using left, right, and straight ahead.

Question

a)  A blue car is driving down the road.
 
At the first corner it turns to its right.
It drives on to the next corner.
The car then turns to its left and goes straight ahead. 
blue car driving along the street
Where does the blue car get to?

 

    • the movies

    • the church

    • the marae

    • the park

    • the zoo

Question 1Change answer

b)  This map shows where a green car is.

green car driving down the street

Write down the directions for the shortest way for the green car to drive along the streets to home (use the words "right" and "left").

Task administration: 
This task can be completed with pencil and paper or online (with SOME auto-marking).
Level:
2
Curriculum info: 
Maths, Geometry and Measurement, Position and orientation
Keywords: 
direction, left, right, maps, peer assessment
Description of task: 
Students respond to and give directions about a simple path on a map involving right or left turns.
Curriculum Links: 
This resource can be used to help to identify students' understanding of direction and maps.​
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Geometric thinking, set 3
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
    Y4 (10/2010)
a) C (Marae) difficult
b) Left, right, left, left
[Accept if an extra "left" is included, indicating she needs to turn left off the road to his home]		 very difficult

NOTE: When students use words such as "straight", "forwards", or "walk" etc. generally this indicates the parts between turns. So "straight, left, straight, right, straight, left, straight, left, straight" is equivalent to "left, right, left, left".
Do NOT Accept "West, South, West, South, East, (North)", but ask the student to say it using Right and Left instead.

Teaching and learning: 

This question assesses a student's ability to visualise how a person moves along a pathway making quarter turns. They need the ability to visualise how the person is re-oriented as they make each turn. The greater the number of turns, and the more the student needs to re-orient, and hence the greater complexity of the task. Students' instructions should use "right" and "left" rather than points of the compass. The latter is easier as it does not involve re-orientation, although it does require them to know the compass points.

Diagnostic and formative information: 
  Common response Likely misconception

a)
b)

E (Zoo)
R, L, R, R 

Confuses right and left

 
b)

 
L, L, L, R 
L, D, L, D, R or D, L, D, R
L, L, R 

Describes the directions on the map 
Describes movement as left or right on the page.
Describes movement as left, right, up, or down on the page.
Describes left and right on the page, ignoring the "down".

b)

L, R, L, R 

Gets the last direction incorrect

b)

R, L, L or
L, R, L

 Ignores the initial or final turn

b)

S, W, S, E or
W, S, W, S, E 

Describes compass bearings on the page
Next steps: 

Confuses right and left
These students need to consolidate their knowledge of right and left. Some students consistently transpose these. They may need some kind of visual reminder about which is their left hand and which is their right. They could play some games which required them to make left or right turns. These students were of significantly lower mean ability than students who had the other misconceptions listed above.

Describes the directions on the map
Students need to appreciate that the person changes their orientation on the map each time that they make a turn. This means that it is inadequate to just give the instructions as if the person is always facing in the same direction as they started in (i.e., "Left" or "West"). Get them to place a counter with an arrow on it and move it along the route. The arrow needs to be turned to the new direction the person is walking each time they turn. Get the student to turn the counter "Left" at the first corner and reorient the arrow. Ask them "Which way will they need to turn at the next corner?" If the student cannot visualise this, get them to physically move the counter again, taking account of the left and right sides of the counter or arrow. If this is still difficult, write "L" and "R" on each side of the arrow.

Gets the last direction incorrect
These students may not be able to cope with reorienting the car more than 180 degrees (a half turn). Ask them to use a counter with an arrow as above to help them with this last turn.

Ignores the initial or final turn
Question the student to see if this is a simple omission, or if they have one of the last two misconceptions above.

Describes compass bearings on the page
This is an alternative way of giving instructions, but is not what was required of students in this task. Get the person to repeat the exercise using "right" and "left". Students could imagine that Sarah does not know where North is. While their initial response is correct, these students need to be able to give direction in terms of "left" and "right", and to visualise the re-orientations that occur, as had been modelled in part a).

Peer assessment
This resource presents an excellent opportunity for students to assess each others' responses. Those who have mastery can demonstrate this as they assess other students' responses. Those who can visualise and re-orient correctly for two or three turns can assess students who are still learning to visualise or who are learning to distinguish left and right. Students could give instructions while another followed them.