3 Steps to Great Math Collaboration

     My students are still learning to collaborate in most areas.  It's exciting to see their growth, especially in math!  Thanks to help from an awesome teaching friend, I whittled down what I want students to be able to do during a collaboration activity and came up with this poster that we review before most sessions.
     We use Super Star Math each week. It's a great program for developing critical-thinking in math. 
     The poster helps students 1) develop the habit of being prepared for their small group meeting with pens only and their Super Star paper, 2) to be actively involved and focused only on this task, and 3) to contribute beginning with their strategies, not their answers to the problems.  I remind them that to start with the answer shuts down the conversation.
     Please let me know in the comments what you use to help develop good mathematical conversations in your classroom.
Pat McFadyen
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Measurement Conversions With A Memory Trick

     By 5th grade, students have been making measurement conversions for a while.  I still like to review the history of both measurement systems, standard and metric, the three measurement attributes we use (standard: length, capacity, weight and metric: length, volume, and mass), and the basic facts.  I supply students with this information in their math notebooks.
     When making conversions, I like to show a number of examples and let kids tell me what's happening when we convert from one unit to another.  For example, I might put this on the SmartBoard:
12 feet = 4 yards
60 inches = 5 feet
8 quarts = 2 gallons
4,000 pounds = 2 tons
     I ask students three questions:
1.  What can you tell me about the change in units: did we convert from large to small or small to large?  In this example, we converted smaller units to larger units. 
2.  Then, I ask what happened to the numbers.  They reply that the numbers got smaller.  Through discussion, I want students to see that when you take a lot of little things and put them in larger groups, you'll end up with fewer groups.  For example, taking 12 feet (a smaller unit) and grouping them into yards (a larger unit), I'll end up with fewer yards than feet.
3.   The last question, then, is: What operation did I use to do that?  The answer is divide.  When we divide, we'll end up with a quotient that's smaller than our dividend.
     Of course, it's just the opposite when we convert from larger to smaller.
6 yards = 18 feet
4 feet = 48 inches
6 gallons = 24 quarts
3 tons = 6,000 pounds
1.  We converted from larger to smaller.
2.  The numbers got bigger.
3.  We multiplied to make that happen.
     Still, it can take some time for students to process this concept so that it's automatic for them.  In the meantime, we still have to make conversions.  Several years ago, I learned this memory trick and it's really been helpful.  A picture is worth a thousand words: 
     We focus on the beginning letters of the phrases: 
Snakes Love Ditches = When we convert from small units to large units, we divide, and  
Large Snakes Multiply = When we convert from large units to small units, we multiply.
     To pull it all together, the display looks like this:
     I don't remember when we decided to name the snakes "Monty", but there it is!
     A student's work looks like this:
Write the problem and label the units as small or large.

Say the correct "ditty": Snakes love ditches" and record the operation you'll use.
State the basic fact: There are 3 feet in one yard.  Record it.

Use the number you've been given; in this case, 12 feet.  Almost done!

     This is a long blog post, but when it comes to the conversions, it honestly can be done in 15 seconds.  Give it a try and let me know how it works for you.
Complete the math.  You've made a successful conversion!

Pat McFadyen
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Hands-On Volume, On a Budget, On the Fly

     My 5th grade students have pretty-well grasped the concept of volume, but I wanted them to get some more practice measuring, recording, and labeling different items.  Last week was typically hectic and I forgot (imagine that) to ask them to bring in empty boxes from home.
      With my mind racing like a hamster in a cage - does yours ever do that? - I started scavenging items from around the room and a few from the discarded boxes pile in the hall.  Here's what I collected:
  • a tissue box
  • a paper box lid
  • some rectangular prisms from my geometrical shapes box
  • the geometrical shapes box
  • some boxes with things still in them
     I put them in 11 spots (stations), used sticky notes to number the stations, and dropped a tape measure at each one.  I used my craft sticks with names on them to quickly create student pairs.  Students paired up and went to a station.
      Instructions were to measure all three dimensions in inches, record the dimensions, find the volume, then record and correctly label the volume in cubic inches.  We'll do metric next time.

  It worked pretty well.  The pro results: Students were quickly engaged in meaningful, hands-on math.  They followed directions, for the most part.  The noise level was pretty good.  The con results: Due to my on-the-fly preparation, some of the stations had the same kind of box.  Believe me, the kids let me know.  Oops.
     As usual, I had a few early-finishers who asked, as usual, "What do we do when we're done?"  After I replied, as usual, "Well, you never ask me the question 'What do we do when we're done'", I suggested they find another rectangular prism to measure. A filing cabinet sufficed nicely.
     Do you have a favorite volume activity?  I'd love to hear your comments!
Pat McFadyen
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The Hundred Board: A Little Different Way

     Most primary and elementary teachers use a hundred board as a tool in math.  It can help teach so many concepts: counting, skip counting, one-to-one correspondence, patterns, basic facts,...the list goes on. In addition, the visual and kinesthetic components of a Hundred Board are powerful tools in developing number sense.
      I've used them for years.  My kids especially like the activities where I ask a question, they put a chip on the answer, and it makes a self-checking picture at the end - much more fun than a worksheet.
     Several years ago, it dawned on me that the traditional hundred board that starts with the 1 in the upper left-hand corner might seem backward to some children.
Starting with 1 in the upper left corner and moving down to add, or moving up to subtract is contrary to our language and our algorithms. Of course, algorithms are not our primary focus in math.  However, we do tend to move down for subtraction and up for addition.  Even our language says, “Add up the numbers”, “low numbers”, “one step forward, two steps back” and “count down”!   I developed this board to help students connect what they hear with what they see.
      This board starts with 1 in the lower left corner.  It allows students to move up the board as they count higher or add.  They subtract and move down the board, more in line with algorithmic directions.  
     This “upside down” hundred board is just what students need to develop number sense and see how our number system works with our algorithms!  

      You can get this Little Different Hundred Board as a freebie right here.  Please download, try it out, and let me know what you think.  I'd love to hear your feedback! 
Pat McFadyen
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Writing About Our Math

    When we teach students to write about the math that we do, we are automatically raising their level of critical thinking. We are also strengthening their non-fiction writing skills.  I want to make this a central focus of my math lessons this year and, believe me, I'll be building this airplane while I'm flying it!

     Our first lessons during this past week began with a fairly simple word problem.  I tried to lower potential stress levels by reminding students that we were training ourselves to write in math and that grades were not an issue right now.

      I started with an anchor chart that explains the basic steps in the process.  It is a really simple list of steps in the process.  Each step could be fleshed out, but I'm starting small.  The big deal that I'm stressing is to justify, justify, justify!  Prove it!  Convince me!

 I solved the problem myself, following the steps on our anchor chart.  The problem was:

 "Jennifer earned $5.25 per hour last week.  She got a raise and will receive $5.85 next week.  She works 40 hours each week.  How much more will Jennifer earn next week than she did last week?"

My response went like this:

1.  The question asks for the difference in two amounts, so I know I will subtract at some point.
2.  I need to find the amount Jennifer earned last week.  I know I can add $5.25 for 40 times or, to be more efficient, I can multiply.  
3.  I multiplied $5.25 times 40 hours and got $210 for her salary last week.
4.  I need to find the amount Jennifer will earn next week with her raise.  I will multiply again.
5.  I multiplied $5.85 times 40 hours and got $234.
6.  Now, I'll subtract the two amounts: $234 - $210 = $24.
7.  Jennifer will earn $24 more next week with her raise than she earned last week.

     Students worked in pairs to solve a new problem.  After they agreed on how to solve the problem, they wrote their steps on paper, making sure they justified each step.

     They went to a Chromebook and created a document with their steps.

     Their last step was to set up their Chromebooks on their desks and we did a "gallery walk" around the room, reading each others documents.  I told them they would see some documents that had a better explanation than their own and some that didn't sound as good as their own.  Either way, we're learning.
     I'll be honest - I could use some help with this.  How do you teach writing in math?  I'd love to hear your comments!
Pat McFadyen
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Type First. Format Last...a Freebie

     Do your kiddies get excited and distracted by all of the formatting options available when they’re word processing?  Fonts, sizes, colors, bold, italics, underlined…it’s just so darned fun!
     It’s a great technology lesson to teach various formatting options and discuss when and where it’s appropriate to use them. Students could take turns teaching the class how to use different ones.
     It’s also helpful to point out how much time can be wasted by playing around trying to decide which font is best instead of going straight to the assignment content. After calling out several students - several times - I decided I needed a quick and easy way to remind them without fussing.  The “Type first. Format Last.” rule is now part of our classroom.
     My expectation is now posted prominently on the wall and we review it each time we create a document or presentation!  You can get it free here Type First Format Last Freebie
Pat McFadyen
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Scoot: Make Your Own and A Freebie!

     I've trained my students to play Scoot and we love it!
     If you're new to the game, here it is in a nutshell: You need a set of cards with one problem or task on each one. The cards should be numbered (1,2,3,...) and you need one for each child.
     Decide how you want students to move from desk to desk, that is, the traffic pattern. Place a card on each child's desk, according to your traffic pattern.
     Each student prepares a sheet of paper numbered like the cards (1,2,3,...).
     When all is ready, have students push under their chairs and stand behind them.
     You say, "Go", and students solve the problem or do the task that is one their own desk.  They write the answer on their paper at the correct number.
     When you feel they've had enough time, say, "Scoot!" and students move to the next desk.  Again, give them just enough time to solve the problem, then say, "Scoot!"
     Continue until each student is back at his/her own desk.  The game is over.
     Scoot can be used as a fun, movement-filled review activity or as an assessment.  Consider putting up cardboard privacy screens to keep eyes from wandering. After all, the students are standing and can see better.  Once it's over, you can share and score their answers.
    Other Scoot games are just for movement and can be used as a Brain Break or an indoor PE activity.  Here's my latest one and it's free for you here Brain Break Scoot! Freebie
     I recently wanted to play Scoot to practice simplifying exponents on our calculators.  It was a last minute idea - many of mine are! - and I didn't have time to prepare the cards.  Flying by the seat of my pants, I told students to take out their slates and markers.  They were to write a factor form 1 to 10  in the middle of their slate and give it an exponent from 1 to 6.  I quickly walked around and number the slates.

     It worked!  Students left their calculators on their desks and cleared them each time I said, "Scoot!"  I'll be making a Scoot game for exponent soon!
     Do you play Scoot?  Are you interested in trying it out?  Let me know how you use it in your classroom and about your successes.
Pat McFadyen
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