Can You Level the Towers?

Recently, I've been trying to notice a agency to organize many of the amazing resources I've flora online hence I tin role them to a greater extent than easily inwards the future.  Don Steward's blog is an absolute treasure trove of activities as well as interesting problems for whatever mathematics classroom.  A few weeks ago, I went through every unmarried 1 of his weblog posts as well as took greenback of all of the activities that aligned alongside my Algebra 1 standards.  There were Influenza A virus subtype H5N1 LOT of them!  

One of the activities that caught my oculus was called "Equal Sharing."  Students are given a gear upward of towers as well as asked to brand all of the towers possess got the same height.  You must maintain the same issue of towers.  The only affair you lot tin alter is the organization of the blocks.  

I took Don's activeness canvass that featured 10 problems, stuck it inwards a publisher file, enlarged it to fit on 11" x 17" paper, as well as added a championship alongside a cute font.  I printed the puzzle on unopen to 11" x 17" cardstock (affiliate link) that is amazing for creating activities that tin easily locomote worked on past times multiple students at the same time.  It also makes pretty awesome posters!     

Then, I stuck each activeness into 1 of my novel 11" x 17" dry out erase pockets (affiliate link) to brand the activeness reusable.

I allowed students to locomote on this activeness inwards groups of ii or 3.  A few of my students chose to locomote alone.  The bulk of students were inwards pairs.

I didn't give them many details earlier I permit them loose.  I instructed them that their challenge was to rearrange the blocks hence that each tower was the same height.  They had to terminate alongside the same issue of towers that they started with.

Even though I told students earlier nosotros started that they had to terminate upward alongside the same issue of towers that they started with, I silent flora myself answering that enquiry over as well as over as well as over.

It was interesting to sentinel students examine to convince their partners that they had a superior strategy equally I circulated.

Influenza A virus subtype H5N1 few minutes into the activity, I saw students changing upward their strategy.  At the outset of the problems, the students were mark out boxes as well as moving them 1 at a time.  This worked, but students shortly flora it tedious.  Instead, the students started counting all of the boxes inwards all of the towers.

I stopped past times a grouping merely afterwards they reached the determination that in that place were 28 blocks inwards the towers.  With a perplexed hold back on my face, I asked them why that data was useful.  The grouping informed me that because they knew how many towers they needed to terminate upward alongside that they could accept the issue of blocks as well as merely split past times the issue of towers.

I exercise possess got to acknowledge that non all of my groups made this realization.  Some were enough happy to maintain using the same method that worked over as well as over as well as over.

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When my students got to enquiry 6, they began to choke confused.  Really confused.

My students who were rearranging the blocks 1 at a fourth dimension flora themselves left alongside 4 extra blocks as well as 8 towers.  How does that work?

Some groups decided to cutting the 4 blocks inwards one-half as well as distribute 1 one-half block to each tower.  The groups that were adding upward the blocks as well as dividing past times the towers seemed to possess got less problem alongside this problem.  Many groups, however, got frustrated as well as gave upward when the employment didn't locomote out evenly.

After the groups had fourth dimension to effort MOST of the problems, I began a course of written report discussion.  I asked the groups to portion their strategies.  One educatee inwards each course of written report would select upward the fact that they had flora a shortcut.  They hence proceeded to push clitoris how they had added upward all the blocks as well as divided past times the issue of towers.

After they finished explaining, I asked them what mathematical concept matched upward alongside what they had merely done.  It was hence exciting to encounter their eyes lite upward equally they realized they had merely flora the mean!

I promise that my students walked away from this lesson alongside a meliorate agreement of what the hateful is instead of merely knowing the steps to choke far at the mean.

Thanks Don Steward for this awesome activity!

I possess got uploaded my eleven x 17 sized file of Don's activeness here.

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