Math = Love: Quarter the Cross

## Thursday, December 29, 2016

### Quarter the Cross

If you haven't tried "Quarter the Cross" yet with your students, what are you waiting for???  Not sure what "Quarter the Cross" is?  You must stop immediately and read David Butler's blog post about it!  David has created a hundred solutions to this puzzle and made them into a beautiful graphic.  Seriously, stop reading this post and start reading his!

Want to know a fun fact?  David works at Adelaide University, the same university in Australia that my husband graduated from.  It's crazy how twitter makes the world seem SO much smaller!

This year, I am teaching a class called "Math Concepts."  It is a class for 9th graders who are not yet ready for Algebra 1.  During the first semester, we worked on basic equation solving, integers, fractions, and decimals.  Fractions were a huge struggle for the entire class, and I have to admit that I did not realize just how many misconceptions they had.  We definitely improved in our understanding of fractions, but I still feel like these students have sooooooo many gaps.

Initially, I was scared to give my students this assignment because I was afraid they wouldn't be able to figure out how to shade 1/4 of the cross.  At first, they wanted to color in one of the squares.  We had a lovely conversation about how that wouldn't work because that would mean we had colored only 1/5 of the shape.  Soon, a student suggested that we could just draw lines to divide the cross into four shapes.  Then, we could color one of these sections.  Once my students saw what 1/4 of the shape looked like, they started coming up with all kinds of their own solutions.  I shouldn't have doubted what these students were capable of!

One student was super pleased with one of the designs she came up with, so she kept showing it to other students.  So, a few of the designs are a bit more similar than I had hoped for.  I can't get too mad, though, because it's super exciting to see my students excited about math!

Here are their solutions:

I love that even the imperfect solutions give me insights into how my students visualize fractions. I think the bottom left solution in the above picture would be a good conversation starter with students!

Want this awesome sheet to use with your students?  I downloaded it from David Butler's blog post.  He also has a sheet that has one large cross for students to decorate.  I printed these out, but we ran out of time.  I think we may go back and revisit this activity after Christmas Break is over because one of my students mentioned during the last week of last semester that we should do "those cross things again."  I guess that means this activity is a true keeper!