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.
     This can be used with any collaborative activity.  We use Super Star Math each week. It's a great program for developing critical-thinking in math. 
     The poster helps students to:
1) develop the habit of being prepared for their small group meeting with pens only and their Super Star paper, 
2) be actively involved and focused only on this task, and 
3) begin their contribution 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.
 We're all in this together!
Growing Grade By Grade
Share :

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, both 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!

Growing Grade By Grade
Share :

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!
Growing Grade By Grade
Share :

The Hundreds Chart With A Twist: A Powerful Math Tool


     Most primary and many elementary teachers use a hundreds chart as a powerful tool in their math classes. It can help students master 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 hundreds chart are powerful tools in developing number sense.

     I've used hundreds charts for years in 5th grade.  My kids especially like the activities where I ask a question or present a problem, they put a chip on the answer, and it makes a self-checking picture at the end - much more fun than a skill worksheet.

     Several years ago, it dawned on me that the traditional hundreds chart, starting with the one (1) in the upper left-hand corner, might seem backward to some children.  It certainly did to me!  

     Starting 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 often physically move down for subtraction and up for addition.  Most importantly, our language should match our math.  We say, “Add up the numbers”, “low numbers”, “one step forward, two steps back” and “count down”!   One day, I sat down and developed this chart to help my students connect what they hear with what they see and do.

     This chart 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” hundreds chart is just what many of my students needed to develop number sense and see how our number system works with our algorithms!    

How to use the “Different Hundreds Chart”:

     Begin by providing a cube or game piece for students to move when finding numbers.  As students become more confident, they may move a finger to find sums or differences.

     Start with easier tasks, such as adding/subtracting tens. Here are some sample directions.

1.     Add/Subtract 10:  Call out a beginning number for everyone to mark.  Help students see that if they add 10, they will move directly up one line, a full ten spaces.  If they subtract 10, they move directly down one line.  Challenge students to add/subtract 20 or 30 and see where they land.  Try these:
         ➤Start at 50.  Add 10.  Add 20.  Subtract 10.  Add 20.  Where should we be? 90.
         ➤Start at 60.  Subtract 20.  Add 30.  Subtract 10.  Subtract 10.  Where should we be?  50

     Next, explore the patterns of adding/subtracting elevens and nines.

2.    Add/Subtract 11: Once students are confident with tens, help them discover that adding 11 moves directly up and to the right one space.  Subtracting 11 moves directly down and to the left one.  Try these:
       ➤Start at 40.  Add 11. (Students will have to move to 51.)  Add 22.  Add 11.  Subtract 22.  Add 33.  Where should we  be?  95.
       ➤Start at 35.  Add 22.  Subtract 33.  Add 11.  Add 11.  Where should we be?  46.

3.     Add/Subtract 9: Continue with 9s.  Adding  9 moves directly up one line and to the left one space.  Subtracting 9 moves directly down one line and to the right one space.   Try these:
         ➤Start at 25.  Add 9.  Add 18.  Subtract 9.  Add 27. (Students will have to move to 70.)  Subtract 9.  Where should we be?  63
         ➤Start at 46.  Subtract 9.  Subtract 9.  Add 27.  Add 9.  Where should we be?  64

4.     Now, you can challenge students to follow a series of mixed additions or subtractions and see if everyone lands on the correct number.  Try these:
          ➤Start at 45.  Add 10.  Subtract 11.  Add 20.  Add 9.  Subtract 11.  Where should we be?  62
          ➤Start at 12.  Add 30.  Add 11.  Subtract 9.  Add 11.  Where should we be?  56

     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! 
Growing Grade By Grade
Share :

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!
Growing Grade By Grade
Share :

Scoot Games:How To 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.
Growing Grade By Grade
Share :
[name=Pat McFadyen] [img=https://1.bp.blogspot.com/-WsQ2WGbGKhw/WpNrBnYYvfI/AAAAAAAATcs/Gbqf3hYwwjwX2smDpvLCmtgfWB3ur47mACLcBGAs/s1600/Pat.jpg] [description=My purpose is to support YOU and your students with practical solutions and curriculum materials that teach, play, practice, and assess.] (facebook=https://www.facebook.com/GrowingIn5thGrade/)

Follow @georgialoustudios