Place Value Structures, Class #2

We're continuing our exploration of Base 5, along with several other mathematical concepts. We covered a lot today...
While waiting for students to arrive, we enjoyed the book Easy Math Puzzles by David Adler. This is a fun book that I've used with several classes. Each puzzle is short but takes a significant amount of thought.

We opened the regular session with Moja Means One; Swahili Counting Book by Muriel Feelings. I chose this book after reading this idea connecting it to base 5:

"People have been counting on their hands for centuries. In some languages, the word "hand" means "five." If you ask a farmer how many goats he had and the farmer answered, "hand," how many goats would that be? (Five.) Suppose you have not yet thought to use two hands but just use one hand for counting. You can use toothpicks for this, and put down one I, then another 11, and another III, and one more IIII, until you have five IIIII. Now, how do you represent six if you can't count on your other hand? (Maybe you could just use the same hand over again, or cross the picks.). Lead children to discover the following:
6 is 5 and one more
7 is 5 and 2 more
8 is 5 and 3 more
9 is 5 and 4 more
10 is two 5s"

We discussed ways that larger numbers could be represented if hand = five. How could we represent 25? 50? I asked them to consider how this idea related to the exploration we did last week with our place value mats and cubes.

We continued with a very brief review of the Base 5/place value mat/cube counting. I asked them to give me a "thumbs-up" as long as I counted correctly and a "thumbs-down" if I made a mistake. They were all quick to catch my errors!

We used lessons from Bridges (Math Learning Center) looking at collections of Base 5 pieces. How many strips and units does it take to make a given number? Then we traded our strips for more and more pieces until we used only units.

We defined "minimal collection" and built more examples of base 5 collections. We recorded our work and looked for patterns.

 After learning to build minimal collections, we played "Up to the Mat and Back," racing to build and dismantle (add/subtract) Base 5 collections.

Along with all the Base 5 work we looked at odd/even numbers and played a subtraction/probability game, concluding with an enjoyable reading of Math Curse by Jon Scieszka (which does have some base work in it!)

Busy day! Thanks for all your hard work!