Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 546

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 548

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 546

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 548

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 644

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 644

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 644

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 931

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 931

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 644

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 644

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 644

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 644

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 644

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 644

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 644

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 644

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Warning: Cannot modify header information - headers already sent by (output started at /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php:613) in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 1489

Warning: Cannot modify header information - headers already sent by (output started at /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php:613) in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 1489

Warning: Cannot modify header information - headers already sent by (output started at /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php:613) in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 1489

Warning: Cannot modify header information - headers already sent by (output started at /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php:613) in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 1489
(:title Ball Mixing Activity: 4 Balls in 2 Boxes - 8th 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% below to see the whole action ***%% [tableend] ---- (:html:) (:htmlend:) >>&<< To use offline, download and unzip [[http://mathcasts.org/mtwiki/uploads/Activity/4balls2boxes_v3.zip|4balls2boxes_v3.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 have 4 balls - %red%2 Reds%% and %pra%2 Greens%%. We drop them randomly into 2 boxes. %c11 exa%Are the colors %c11 bgr%mixed%% %c11 exa%or %c11 yel%separate%%? >>&<< ---- >>&<< These '''two events''' are mutually exclusive and complete. >>&<< (a) Both boxes will have will have %red%1R%% & %pra%1G%%.    We call this event: %c11 bgr%MIXED%% colors. Attach:Activity/mix4box_mixed.png >>&<< (b) One box %pra%2G%%, other box %red%2R%%.    We call this event: %c11 yel%SEPARATE%% colors. Attach:Activity/mix4box_separate.png ---- (:showhide init=show div=div1 lshow="+" lhide="-":) %c11 exa%Guided Activity%% (:div1 id=div1 :) >>&<< %c11 ans%Do the experiment 200-1000 times.%% * What is the percent of %bgr%mixed%%? * What is the percent of %yel%separate%%? >>&<< %sol%Now for some dreaded theory ...%% Number the balls: Attach:Activity/4balls_number.jpg *How many different ways can the balls drop into the boxes? *How many times does %bgr%mixed%% occur? *Does your theory match your experiment? >>&<< (:div1end :) ---- (:div class="s9" style="margin-left:10px":) %sol%"Mutually exclusive" meaning both events cannot happen at same time and "complete" meaning no other event can occur.%% (:divend:) (:div222end:) [tableend] >>-<< * 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%3rd grade probability%% * [[DiceDifference|Throw two dice and check their difference]] %sol s9%6th 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:) [[#comment2]](:nl:)>>messagehead<< !!!!!LFS — [-27 September 2008, 15:12-] >>messageitem<< Thank-you. >><< [[#comment1]](:nl:)>>messagehead<< !!!!!Dani — [-10 September 2008, 08:47-] >>messageitem<< This is really very useful program. I will share it with others. --Dani >><< >><< [table width=100% border=0] [row] [][[activity/| Attach:main/tri_purple_up_a.gif ]] [[activity/| Up one level]] [r](:html:) (:htmlend:) [tableend]