# Splitting 25 EDUC 415

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#### Storyboard Text

• ﻿Splitting 25  Find a set of numbers that sum to 25 and calculate their product to find the highest possible product
• Great idea, but let's avoid 1 because that won't help us to get any a larger number through multiplication.
• ﻿Let's  try and break 25 into as many parts as possible to  get the most multiplication.
• ﻿   25﻿  10                            15 5             5             5              10    2      3      2     3      2       3     5           5                                                   2     3       2    3
• ﻿So this gives us 25 * 35 which equals 7776. But another group got over 9000. How???
• ﻿OH!!!! What if we try using decimals? We were restricting ourselves to just whole numbers.
• ﻿   25﻿  10                            15 5             5             5              10    2      3      2     3      2       3     5           5                                                   2     3       2    3
• ﻿Yes! 2.510 ﻿equals 9536.74. Now that we can use decimals can we get an even larger product? How can we search for this? Can we make a function?
• What if we were to split  the 5's into 2.5 and 2.5, rather than 2 and 3, then maybe we will get a larger product.﻿
• ﻿This panel is showing how we were getting our hands dirty with the problem by just trying something. We  were also exploring ideas and  building on each others .
• As the groups got going with solving the problem, the permeable  nature of  adjacent  groups started to spread ideas.
• Now after getting a feel for how the problem worked we thought about finding a better technique to give us the largest product. Creating a function and searching for the maximum was one way but finding the function would be tricky.
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