Challenge

Task 56 ... Years 2 - 8

Summary

Blocks are placed on the board so that the difference between the blocks on either end of any line is not 1.
  • Can you find one solution?
  • Can you find more than one solution?
  • What happens if...?
 

Materials

  • Blocks numbered from 1 to 8
  • Playing board

Content

  • difference between two numbers
  • spatial perception
  • reasoning skills
Challenge

Iceberg

A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.
   

There are many answers to this problem, so it shouldn't take too long before one is found. However, if the students seem to be working without a strategy, you could suggest 'Break the problem into smaller parts' and combining that with 'Try every possible case'. One way to do this is to suggest something like:

Have you thought of placing the smallest number in the left box and then working out the possibilities?
Doing so immediately limits what can be placed in the top and bottom of the left column of three and could lead to a solution such as:

    5   3    
1   7   8   6
    4   2    

So, what happens if we try each of the numbers in turn in the left box? Can a solution be found in each case?

    6   8    
2   4   3   5
    7   1    
 
    1   4    
3   7   8   6
    5   2    

    7   5    
4   1   3   2
    6   8    
 
    3   1    
5   7   8   6
    2   4    

    4   7    
6   1   2   3
    8   5    
 
    4   6    
7   1   8   2
    3   5    

    3   1    
8   6   5   7
    2   4    

Could there be more solutions in each case? Studying the solutions so far indicates there can be. For example, consider the solutions for 2 and 4 above. Reflecting the solution for 4 gives:

    5   7    
2   3   1   4
    8   6    

which is not the same as the previous solution for 2. So, now the problem has been broken into smaller parts by choosing the left box number, and in each case the questions can be asked:

  • How many solutions are there?
  • How do we know when we have found them all?
But a mathematician is never finished with a problem:
  • What happens if we change the set of numbers?
  • What happens if we change the difference that is not allowed?
  • What happens if we change the design of the playing board?

Whole Class Investigation

Tasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works.
   

To convert this task to a whole class lesson you will need copies of the playing board in the photograph, which are easy to make with a drawing package, or the drawing tools within a word processor. Instead of the blocks you can make a set of numbers to match the squares on your board using the table tools of the word processor. Students can quickly cut up the sheet you give them into the numbers they need. Alternatively, folding and tearing scrap paper will produce number tiles more quickly.

The focus for the lesson would be on strategies for finding more than one solution; in fact, the search for all solutions.

At this stage, Challenge does not have a matching lesson on Maths300.

Is it in Maths With Attitude?

Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner.
   

The Challenge task is an integral part of:

  • MWA Number & Computation Years 3 & 4
This task is also included in the Task Centre Kit for Aboriginal Students.

Green Line
Follow this link to Task Centre Home page.