Repeating bead patterns

Repeating bead patterns

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Further Resources
This task is about describing and predicting repeating patterns.

Practical task

Your teacher will give you some beads of different colours and some threading string.

a)   Put 5 beads on the string. Make sure you use 3 different colours.

  • Make a pattern by adding another 5 beads in exactly the same order as the first 5.
  • Carry on making this pattern by adding another 5 beads in the same order.
  • Ask your teacher to check your pattern before filling in the table below.
  • Write the colour of each bead in your pattern on the table below, starting with the first bead.

Number of bead

Colour

1

  

2

  

3

  

4

  

5

  

6

  

7

  

8

  

9

  

10

  

11

  

12

  

13

  

14

  
 
 
 
b) i)

ii)

 What colour will the 20th bead in your pattern be? _______________________

How did you work out your answer?

 

 

 
c) i)

ii)

 What colour will the 71st bead in your pattern be? _______________________

How did you work out your answer?

 

 
Task administration: 

This task is completed with pencil and paper, and other equipment.

Equipment: Coloured beads; threaders or string - each student needs to have at least three different-coloured beads.

When students have completed their bead pattern they will need to have it checked. At this point teachers can assess part a) of the task. Those students who have errors in their patterns will need to fix these before going on to do part b).

Level:
3
Curriculum info: 
Maths, Number and Algebra, Patterns and relationships
Keywords: 
repeating patterns, functional rules
Description of task: 
Students use coloured beads to make repeating pattern. They then identify the colour of specific beads in the pattern and explain how to work this out.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Patterns and relationships, sets 4-5
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 

a)

  

The pattern repeats consistently.

b)

i)
ii)

Identifies correct colour.
Any 1 of:
 
•   It will be the same as the 5th, 10th, 15th… bead.
•   It is a repeating pattern of 5.

c)

i)
ii)

Identifies correct colour.
Any 1 of:
 
•   It will be the same as the 1st, 6th, 11th, 21st, 31st… bead.
•   It is a repeating pattern of 5.

NOTE: In b) and c) do NOT accept counting on (in 1s).

 

For more information about working with functional rules, see the Algebraic Patterns Concept Map