Ladder patterns

Ladder patterns

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about continuing a pattern and stating the rule for the pattern.

ladder with 30 centimetre rungs

The distance between each rung of a ladder is 30 cm, and there is an additional 30 cm at the top and bottom of the ladder, as shown in the diagram.

a)
Complete this table, giving the lengths of ladders with different numbers of rungs (Do not count the thickness of the rungs):  
 

Number of rungs

4

5

6

7

8

9

Length of ladder (cm)

150

180

        
 
b)
 
Complete the following sentence to make a rule for calculating the length of a ladder with any number of rungs.
 
To get the length of a ladder, multiply the number of __________ by __________ and
 
then add __________.
 
c)
Because it has to lean at an angle, a ladder will only reach to a height equal to 4⁄5 of its length.
Mr Carpenter has a 10-rung ladder, and wants to step onto a roof 3 metres above the ground.
Show how to work out whether his ladder will be long enough.
 
    

    

    

    

    Will his ladder be long enough? __________
Task administration: 
This task is completed with pencil and paper only.
Levels:
4, 5
Curriculum info: 
Maths, Number and Algebra, Patterns and relationships
Key Competencies: 
Thinking, Using language, symbols, and texts
Keywords: 
number patterns, functional rules, linear equations
Description of task: 
Students complete a table showing the number of rungs for different sized ladders. They complete a sentence stating the rule to calculate the number of rungs given the length, and use the rule to identify if a ladder, at a lean, will reach a given height and show their working.
Curriculum Links: 
Key competencies
This resource involves solving a multi-step problem involving number patterns and recording the strategy they used. This relates to the Key Competencies: Thinking and Using language, symbols and text.
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: 
  

Y8 (04/1997)

Y9 (04/1997)
a)
6 7 8 9
210 240 270 300
easy easy
b) ... [rungs], [30], [30]. very difficult difficult
c) No

  • 10-rung ladder = 330 cm
  • 4/5 of this = 264 cm
very difficult

very difficult
very difficult

difficult

 

Diagnostic and formative information: 
   Student response Likely calculation Likely misconception
c) Length = 3 m
Ladder will fit		 30 × 10 = 3 m Ignored the extra 30 cm on 10 rung ladder.
Ignored that the ladder reaches only 4/5 of its length.
Next steps: 
Extension:
a) Draw a scale diagram of the ladder leaning against the wall. How far out from the wall will it be?
b) What is the least number of rungs the ladder must be to reach to the roof (if it only reaches a height of 4/5 of its length)?