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(:title Dice Difference Problem: 6th grade probability :) [table border=1 cellpadding=5 width=100%] [row] [c] [table border=0] [row] [ valign=middle]%c12 exa%*** Click on  []Attach:Activity/cat1try.jpg  Attach:Activity/down_cat.gif [ valign=middle]%c12 exa% to see the whole action ***%% [tableend] ---- (:html:) (:htmlend:) >>&<< To use offline, download and unzip [[http://mathcasts.org/mtwiki/uploads/Activity/DiceDifference.zip|%exa%DiceDifference.zip%%]]. >>&<>&<< >>&<< Scratch file designed by [[mailto:emath@emathforall.com?subject=scratch|Linda Fahlberg-Stojanovska]]. [ valign=middle] (:div222 style="margin-left:3px":) %c12 mor b%Activity Notes%% >>&<< ---- We throw 2 dice - %ref%1 Blue%% and %pra%1 Green%%. %c11 exa%What is the difference in values?%% >>&<< ---- >>&<< >>&<<%exa%The difference can be 0, 1, 2, 3, 4, '''or''' 5%% >>-<< %pra c11%I say to my friend: (:div1222 style="margin-left:10px":) %reg c11%I win if the difference is a 0, 1 or 2. %up c11%You win if it is a 3, 4 or 5.%% %ref c11%Each of us has 3 chances to win.%% %exa c11%Let's play!%% (:div1222end:) >>&<< ---- (:showhide init=hide div=div1 lshow="+" lhide="-":) %c11 exa%Guided Activity%% (:div1 id=div1 :) >>&<< %c11 bgr%Do the experiment 200-1000 times.%% * Is my game fair? * Which difference happens most often? * Which difference happens least often? >>&<< %sol%Now for some dreaded theory ...%% *Make a table with the %pra c11%value of the green die%% across the %pra c11%top row%% and the %ref c11%value of the blue die%% going down the %ref c11%first column%% and the difference between the values at their "intersection" (:showhide init=hide div=div12 lshow="+" lhide="-":) Show me! (:div12 id=div12 :) ->   Attach:die_game.jpg (:div12end:) *Theoretically, how many possible combinations of dice can be thrown? *Theoretically, how many of these combinations will have a difference of 1? ** How many ways can a difference of 5 happen? ** What percentage of times should 0 happen? *Does this agree with your experimental results? *What is the percentage of times that a 0, 1 or 2 occurs? How about a 3, 4 or 5? >>&<< (:div1end :) ---- (:div class="s9" style="margin-left:10px":) %sol%The 6 events - a difference of 0, 1, 2, 3, 4 or 5 are mutually exclusive and complete. "Mutually exclusive" means no 2 events can happen at same time and "complete" means no other events can occur.%% (:divend:) [tableend] (:div222end:) >>-<< * To change Scratch file, download and install freeware Scratch. See [[http://scratch.mit.edu|Scratch-MIT]] for more information. >>&<< ---- >>&<< %rel b%Related Topics%% * [[2Balls|2 Balls - Vertical Box]] %sol s9%6th grade probability%% * [[4Balls2Boxes|4 Balls - 2 Reds and 2 Greens Drop into 2 Boxes]] %sol s9%8th grade probability%% * [[6Balls3Boxes|6 Balls - 3 Reds and 3 Greens Drop into 3 Boxes]] %sol s9%8-10th grade probability%% >>&<< ---- >>&<< (:showhide3 init=hide div=box4 lshow='Add Comment' lhide='Close':) >>id=box4<< (:commentbox:) >><< [table width=100% border=0] [row] [][[activity/| Attach:main/tri_purple_up_a.gif ]] [[activity/| Up one level]] [r](:html:) (:htmlend:) [tableend]