Skip over navigation
Guide and features
Guide and features
Science, Technology, Engineering and Mathematics
Featured Early Years Foundation Stage; US Kindergarten
Featured UK Key Stage 1&2; US Grades 1-5
Featured UK Key Stage 3-5; US Grades 6-12
Featured UK Key Stage 1, US Grade 1 & 2
Featured UK Key Stage 2; US Grade 3-5
Featured UK Key Stages 3 & 4; US Grade 6-10
Featured UK Key Stage 4 & 5; US Grade 11 & 12
Excel Investigation: Planks
Stage: 3 and 4
I have an unlimited supply of planks, of lengths 7 and 9 units. Putting planks end to end, what total lengths can be achieved?
For example, I can make a length of 30 by using three planks of length 7 units and one of length 9 units, but what about a total length of 40?
The Excel file
shows all the possible combinations: I usually right-click on the link, choose "Save Target As", and select where I want the file to be saved.
In one direction (down) are the multiples of 7, including 0, and in the other direction (across) are the multiples of 9. The numbers in the table are the totals achieved with each combination.
If you need help making a table of two independent variables check the
from October 02
Getting to the investigation:
So, is there a value after which all totals must be possible? And if so, was that value predictable?
Notice that the spreadsheet doesn't solve the problem, it just does the calculation - instantly!
If you think there is a value after which all totals must be possible, you will need to reason beyond the numbers that happen to be showing in the spreadsheet.
In fact, no spreadsheet, however many results it shows, can be a replacement for the reasoning process.
Don't move on too quickly. Play lots with the 7 and 9 situation, but when you're ready try to generalise :
Can you predict what can and cannot be done for any pair of plank lengths?
The Excel file
is similar in structure to Planks79 but the plank lengths are now variable.
Look back at October 02 to find out about
They're very easy and let you keep your attention on the numbers instead of the keyboard.
Try to generalise the investigation to cover any combination of plank lengths. Is there always a certain value, after which all totals must be possible? Can you say what that certain value will be?
Suppose the planks were 6 and 9. Remember Excel can do the calculation for you (provided you can say what you want done), but it cannot explain why anything happens (or doesn't happen).
I have also used Conditional Formatting to pick out the particular values I'm looking for at any time. Conditional Formatting is used to make values of interest conspicuous, without the effort of a cell-by-cell inspection. It is explained more fully in the techniques section.
Meet the team
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
Register for our mailing list
Copyright © 1997 - 2014. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the
Millennium Mathematics Project