### Sam's 4th-6th Grade Math

This week in addition to the usual work in the texts we spent quite a bit of time investigating this situation:

A boy has 45 watermelons in the desert. He needs to get them across to the Oasis fair, 15 miles away. He can only carry 15 watermelons at a time, and he eats one watermelon every mile he walks, including walking back to where he started from. He can also leave watermelons at any mile he has walked, but no fractions of a mile. How many watermelons can he possibly take to the fair? How did you arrive at your conclusion?

A boy has 45 watermelons in the desert. He needs to get them across to the Oasis fair, 15 miles away. He can only carry 15 watermelons at a time, and he eats one watermelon every mile he walks, including walking back to where he started from. He can also leave watermelons at any mile he has walked, but no fractions of a mile. How many watermelons can he possibly take to the fair? How did you arrive at your conclusion?

The class spent a good amount of time, in groups of 2 or 3, working out how to even begin to approach this problem. Much of the class initially believed it to be impossible. By the end of the first day, everyone agreed that it was possible to get at least 2 melons to the market; the task for day two was how to determine the maximum number. Investigating this problem required much more than straightforward arithmetic; it's more of a logic puzzle and while working through it our class ended up discussing ideas like resupply/refuel depots for Antarctic exploration, note-taking/tracking techniques (how do you keep track of where all the melons are, and how many are left) and the important strategies of using manipulatives, working backwards, and looking at simpler cases.

Evie, Jacob and Ben used a number line and manipulatives (beads) to help them think about the problem. |

Ishan and Juliana also used beads to represent the melons. |

### Algebra and Pre-Algebra

The seventh and eighth graders had a lot going on this week--two days with field trips and an extended OWL class that cut into our math time. Almost all the students completed an assessment this week and are either working on reviewing concepts using Khan Academy or are moving on to the next major unit of study: solving single-variable linear equations for the Pre-algebra group; linear equations in two-variables for the Beginning Algebra group; a detour into linear programming for the Completing Algebra Group.