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Wednesday, May 17, 2017

Math In Practice: Fifth Grade

Welcome back to my second post about the Math in Practice series from Heinemann.  You can read my first post about this series, Math in Practice: Proficiency and Beliefs, by clicking on the link at the bottom of this post.  You can also go to the website for this series and download a sample for each grade (a link is included at the bottom of this post).  Fifth grade's sample just happens to be the volume module, which is exactly where I was headed in math.  The fifth grade has fifteen modules in total that cover all the CCSS for mathematics.  Each module includes the following:
  • The content standards associated with the module, as well as the progressions for the module
  • Visual representations, discussion starters, and writing prompts to get students thinking more deeply about the mathematics
  • Literature connections
  • Ideas for differentiation
  • Center ideas for practice
  • "I can" statements and more
Today I am going to dig into the math in the fifth grade volume and talk about what I really liked.

I started with the Introduction to Volume: Counting Cubes lesson (pg. 249).  The students each cut a piece of centimeter grid paper into a 12 x 12 square.  Then each student cut a corner of their square out, folded the paper, and taped it into a box.  Some cut out a 2x2 square from each corner, others a 3x3 or 4x4. I made sure that each table had several different sizes being cut.

We used the boxes to begin our investigation into volume.  Students compared their boxes and figured out how many centimeter cubes it would take to fill the bottom of the box.  We talked about the area of the box and how to label the units and then we talked about the number of layers needed to fill the box, which led to the formulas of base times height (volume = b x h) and length times width times height (volume = l x w x h).

Then we started putting the various sized boxes together so that my students could begin to see the additive nature of volume.  We had a lot of fun putting 2, 3, and even 4 boxes together before calculating their total volume.

The next day I used the worksheet included in the online resources and brought in a bunch of boxes.

My students measured and calculated volume over and over, giving them a lot of practice.

These were all great activities and my students really got a grasp on volume, but a few days later we were working with measurement conversions and this is where I really fell in love with this resource.  I went through my files and pulled out the questions I had used previously.  I thought they were great questions.  I'm actually pretty good at writing math tasks. But when I opened up module 11 and found tasks that required more of my students than the ones I had previously used, I got really excited.  Here's a few examples:

Mr. Short had 5 pieces of wood to create the border for his garden.  
Each piece of wood was 80 centimeters long. 
His garden was 5 meters long and 3.5 meters wide.  
Did he have enough wood to make a border for his garden? Explain.

There was so much to this problem! My students were converting back and forth between meters and centimeters, discussing perimeter, trying to figure out how many more pieces of wood he needed to buy and how much he would have left.  It was a really great problem that not only gave my students practice in converting measurements (which was my goal), but it reenforced their knowledge of perimeter, created a lot of good mathematical conversations, and had students completing a lot of different computations.

Next, I used a question that required the students to combine 3 times: 43 seconds, 2.5 minutes, and 37 seconds.  I was surprised at how many students made the mistake of adding like there were 100 minutes in an hour.  When they started seeing two different answers emerging, everyone went back to recalculate.  Then they started talking to each other to see what they were doing differently.  When someone discovered that the problem was not considering the number of seconds in a minute, we had a great discussion and students were able to correct their mistakes.

I saved my favorite problem for last.  It included a list of some of the heaviest land mammals.  Their weights were all given in kilograms.  Students were asked to convert some weights into grams, compare some weights, and combine weights.  The questions required adding, subtracting, and converting through multiplication.  The questions were really great and of course, animals are always an engaging topic.

I really wish this book had been in my classroom at the beginning of the year. There's so much in it that I can't wait to use next year.  My next post will be about some of the activities in grades K-4, so please come back for that.  In the meantime, here are a few links that may be helpful:

My first post about this series is Math in Practice: Proficiency and Beliefs. You can also view more information about this series at Heinemann, where you can also download a sample for your grade level.

Happy Problem Solving!

Sunday, May 14, 2017

Math in Practice: Proficiency and Beliefs

There are a few things that I always love.  Getting packages in the mail, peanut M-n-M's, and great math tasks are up there pretty high on my list of great things.  Take a look at what came in the mail.

This picture shows the fifth grade set, plus samples from all grades and publication information.
This is one of Heinemann's newest publications.  Math in Practice comes with two books: A Guide for Teachers and Teaching Fifth-Grade Math. But don't worry there's a set for every grade K-5.  I thought I would take a peek in the fifth grade set and see if it was worth a blog post.  But I have to's better than I hoped.  So instead of a blog post, I've decided to make this into a small series of posts.  Today will be Part 1, Math in Practice: Proficiency and Beliefs.  Our mathematical beliefs are so important to us as teachers, as well as to our students.  What we believe as math teachers affects the way we teach, the way we look at students, and the way students think of themselves as mathematicians.  So let's dip into the introduction of A Guide for Teachers.

What is mathematical proficiency?  This is such a loaded question and I know my answer has drastically changed over the years.  Proficiency is so much more than getting the right answers or knowing all of your math facts.  So what do we want out students to do?  Page 4 gives us a list of ten things we want our students to do.

  • Understand the big ideas  I can't even count the number of times I have taught a lesson and focused on getting my students to the right answer rather than the big idea.  
  • Create models of math ideas  Modeling mathematical ideas is not just for young mathematicians.  Our older students can use models to think deeper, show their understanding, and justify their thinking.
  • Have computational fluency  This is so much more than memorizing facts, it includes performing operations with decimals, fractions, and whole numbers in efficient ways.
  • Have a strong sense of numbers  Number sense is something we talk about a lot in the lower grades, but older students need it too.  We want them to compose and decompose quickly.  We want them to perform computations in a variety of ways, make predictions, and interpret solutions.  This all requires a strong sense of numbers.
  • Understand the math procedures they do before memorizing them  Getting to an efficient algorithm is important, but not until they have a deep understanding.  We need to allow time for students to export concepts and develop their understanding first.
  • Understand how math ideas are connected  Our students can't build on prior knowledge, if they don't see or understand the connections.  Everything in math is connected, our students need to see this.  
  • Solve a variety of math problems  Students not only need to know how to perform computations, but they need to know when to perform them.  Applying their math skills to real life situations is important.  They need to learn to use their skills and strategies in complex situation.
  • Reason mathematically  This includes analyzing, proving conjectures, and drawing conclusions.  Reasoning mathematically is so much more than getting the right answer.
  • Communicate their math ideas  The conversation is so important in today's math class.  Rich mathematical discussions can allow students to share their ideas, defend and refine their thinking, and learn from one another.  Students also need to learn to communicate their ideas through writing.
  • Have a positive disposition  I love math and I want my students to love math.  I don't remember ever having a first grader tell me they hate math.  But by the time they get to fifth grade, I'm shocked at how many kids have a negative attitude toward math. We have to change their attitudes if we want them to persevere through hard tasks, take risks, and feel confident in their own abilities.
I honestly can't tell you how excited I am about this book series.  A math book for each grade that is full of fabulous tasks and questions and holds the same beliefs I do about teaching math?  I didn't even know that was possible.  But this is it.  You can use this with whatever program your district currently uses. It's not a full math program, it's a book filled with great tasks, questions, hands-on activities and teaching resources.  I have already been using some of the fifth grade content and that's what my next post will be about, but there's a book for each grade. You can check this resource out at Heinemann.  You can also read my second post about this series here.