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Guide and features
Science, Technology, Engineering and Mathematics
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Featured UK Key Stage 4 & 5; US Grade 11 & 12
Excel Investigation: Target Decimal
Stage: 3 and 4
What is the benefit of doing "trial and improvement" with a spreadsheet, when a calculator is often faster and more convenient?
Well firstly, I'm all in favour of calculators, and I certainly prefer quick answers to long methods.
But sometimes I need to see the things I've already tried, before I have another go, and that's where a spreadsheet helps.
So here's the puzzle:
Find a fraction a/b that is as near as possible to 0.46291
That's simple enough: 46291/100000 does it exactly.
And since 46291 and 100000 don't share any factors that's also the simplest version of the fraction.
Now try to find new a and b values, where a and b must each be less than 100.
Here's my start at this on a spreadsheet. I've put my guesses in columns A and B, and let the spreadsheet do the division.
Now it's your turn. Click
to get the Target Decimal Excel file.
(Standard click-select will open the file, but to download it to your own machine: right-click on the link, and choose Save Target As . . . )
Change my choices if you like. Add three more attempts. What was your strategy?
How would you explain your strategy so that someone else could use it on a new target decimal value?
Compare your approach with the strategies of other people working on the task.
Change the rules
How about a and b values both under 40?
What about, instead of division, multiplying a and b to get as near as possible to 789?
For the original a/b challenge, devise a scoring system that favours the player who:
takes least goes
gets closest to the target
and uses the smallest values for a and b.
How could you decide whether your system was fair?
Compare yours with someone else's system. How do you decide which system is fairer?
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.
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