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Trial
and Improvement can be carried out with a spreadsheet
Use
systematic trial and improvement methods and ICT tools to find solutions,
or approximate solutions, to non-linear equations (Goldilocks maths).
Goldilocks
and Spreadsheets
We're
doing Goldilocks maths today: too hot, too cold, just right; that's
how Goldilocks sorted out the three bears' porridge. That's one
of the strategies which can be used in solving number and algebraic
problems in maths.
- The
product of two numbers is 20 and their sum is 10. What are the
two numbers?
Or for a different audience x + y =10 and xy = 20. The National
Curriculum describes the solving of such numerical problems as trial
and improvement.
7
+ 3 = 10, 7 x 3 = 21 too big
8
+ 2 = 10, 8 x 2 = 16 too small
7.5
+ 2.5 = 10, 7.5 x 2.5 = 18.75 too small
7.3
+ 2.7 = 10, 7.3 x 2.7 = 19.71 too small, but pretty close.. not
close enough ? !
This
spreadsheet simulation shows how a spreadsheet can be
set up to tackle this type of problem.
- The
area of Joan Smith's lawn is 50 square metres. The length of the
lawn is one metre longer than the width. Work out the length and
width of the lawn.
l(w
+ 1) = 50
Try
using the "Who Wants to be a Millionaire?"
approach to solving x² = 23 or even x²
- x = 7 using a spreadsheet? Pupils are allowed fifteen attempts
and the closer they are to the target number the more money they
win. The formula required to calculate the amount of money won could
be devised by the pupils themselves or be part of a template set
up by the teacher.
Excel
spreadsheets: solving
x² = 23 solving x²
- x = 7
Solving
Quadratic Equations using a spreadsheet: advanced Goldilocks maths
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