Florida B.E.S.T. MA.912.LT.2.6
The Standard
Solve problems concerning optimizing resource usage using bin-packing techniques.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students assign items of different sizes to containers with fixed capacities. They compare packing methods, minimize the number of containers, and justify why a solution cannot be improved.
What Mastery Looks Like
- Students create a valid packing that respects each bin’s capacity and uses as few bins as possible. They calculate a lower bound and use it to justify whether their solution is optimal.
Common Misconceptions
- Students may place items together when their total exceeds the bin capacity. They may assume the first valid arrangement is optimal or that a greedy method always uses the fewest bins.
How to Assess It
- Exit ticket: Pack items sized 6, 5, 4, 4, 3, and 2 into capacity-10 bins. Show an arrangement and justify the minimum number needed.
Lesson moves
Ways to Teach It
Give groups item cards and capacity-labeled envelopes, then have them find and defend a packing that uses the fewest envelopes.
Ask students to compare first-fit and best-fit results, then write which method worked better for the given item list and why.
Run a packing challenge where pairs earn points for valid arrangements and bonus points for proving no solution uses fewer bins.
Plan delivery truck loads from package weights and truck limits, then compare wasted capacity across two possible loading plans.
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