Beehive patterns

Beehive patterns

Pencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about continuing a spatial pattern and describing its rule.

Question 1Change answer

Jade was looking at beehives and noticed each hive was made up of regular hexagons.
They used some sticks to make a pattern of a long strip of hexagons.
Here is how the hexagons looked.
bee
bee
Jade needed 6 sticks to make 1 hexagon. How many sticks do they need to make  
     2 hexagons? 
     3 hexagons? 
     10 hexagons? 
     100 hexagons? 

Question 1Change answer

b) Complete the rule below which relates the number of matches (m) and the number of hexagons (n) Jade made.
     m = 
Task administration: 
This task is completed with pencil and paper or online with some auto-marking.
Levels:
4, 5
Curriculum info: 
Maths, Number and Algebra, Patterns and relationships
Keywords: 
spatial patterns, functional rules, linear equations
Description of task: 
Students continue a spatial pattern of hexagons, then describe its rule.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Patterns and relationships, sets 5-6
Patterns and relationships, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 

   

Y10 (10/1999)

a)

i)
ii)
iii)
iv)

11
16
51
501

both i) and ii) correct – very easy
moderate
difficult

b)

  

Any 1 of:

•   5n + 1
•   6 + 5(n – 1)
•   6n – (n – 1)
•   Any other algebraically equivalent expression.

difficult
Diagnostic and formative information: 
   Common error Likely calculation Likely reason
 a) i)
    ii)
    iii)
    iv)

12
18
60
600

2 × 6
3 × 6
10 × 6
100 × 6

 Assumes always 6 matches per hexagon.
a) iv)

Answer to a) iii) × 10
(e.g., 510)

 51 × 10 Does not deduct the 9 matches where the 10 groups of 10 hexagons join.