Cross patterns

Cross patterns

Pencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Further Resources
This task is about rules for growing number patterns.
A cross shape was drawn in different sizes. The first two are shown. The cross with a side length of 1 has an area of 5 cm2 and the cross with a side length of  2 has an area of  20 cm2.
Here is a table for the area of crosses which have different side lengths. 

Side length of the cross (in cm)

1

2

3

4

5

10

Area of the cross (in cm2)

5

20

45

80

125

500

Question 2Change answer

a) Explain in your own words a rule for getting the area of a cross.

Question 1Change answer

b)  Complete this rule below relating the area (a) of the cross to the length of the sides (n).
a = cm2
Task administration: 
This task can be completed with pencil and paper or online.
Level:
5
Curriculum info: 
Maths, Number and Algebra, Patterns and relationships
Keywords: 
spatial patterns, functional rules, quadratic equation
Description of task: 
A spatial pattern involving the area of a shape is represented by a table and a diagram. Students describe the rule in words and as an algebraic expression.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
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)

Square the length of the side and multiply by 5
or Add on 15, 25, 35, 45 etc,
or Other correct rules.

difficult

b)

5n2 or algebraically equivalent answers.

very difficult