I love your problem for the beginning of the year. The students would be totally engaged! And, I agree you have selected some great resources from Illumiinations.

I love story problems that make students think and can be solved using a variety of strategies. Students work together to solve the problems thus building relationships with one another right away. Then having students share these solution strategies with the class gets them talking also. Make sure you have those manipulatives out there too. :-)

I might recommend some great story problems we have used with our teacher leaders to get them thinking. They in turn have taken them back to their students where the students have been totally engaged.  Here are some of my favorites to get them working together and thinking critically:

http://sdcounts.tie.wikispaces.net/file/view/BrendasBlocksTasks.pdf

http://sdcounts.tie.wikispaces.net/file/view/SheepShearingProblem1.pdf

http://sdcounts.tie.wikispaces.net/file/view/SpendingMoneyAtTheGame.pdf

My favorites from Illuminations include:

Elementary - Fraction Game - http://illuminations.nctm.org/ActivityDetail.aspx?id=18

Middle School - Barbie Bungee Lesson - http://illuminations.nctm.org/LessonDetail.aspx?ID=L646 - students have to figure out the line of best fit for dropping Barbie with a bungee and not letting her head hit the floor - talk about engaging!! And think about all that they learn - includes a great Line of Best Fit interactive and a spreadsheet to create the graphs.

High School - Compound Interest Simulator - http://illuminations.nctm.org/ActivityDetail.aspx?ID=172 - my all time favorite because of the real world aspect of money, credit, savings and the stock market. Kids always want to spend money, buy cars, etc. This gives them a real world eye opener which would be a great beginning of the year activity to talk about since most worked during the summer.