Model Drawing at the Middle Grades Conference in Louisville, KY

Elapsed Time

I just spent a wonderful week in Salt Lake City, Phoenix, and Albuquerque.  The #1 question was, "How do I help my students with elapsed time?"  Here are some suggestions.  I look forward to your comments on other ways to teach this difficult concept in a way that makes sense to students.

First, student should understand how to use number bonds to add time or to break minutes into hours and minutes.  This is stressing the concept that the hour is a unit.

From there, they can move to model drawing.  

The biggest challenge for students is deciding how to divide up the unit. It helps the kids to label the beginning and ending times.  Reading one piece at a time and plugging it into the model really helps!

 Remember, not all the models will look the same.  Some may divide it into 15 minute chunks and some will see the whole hour.  As long as its labeled and they can explain it, I take it!

This is a two-step, part-whole problem.  Reading one piece at a time is the key to success!

This problem is a little harder.  First, you'll need to discuss the answer statement with your students.  I decided to leave a place for "will" or "will not" in mine.  You'll notice my unit bar didn't end proportional.  Oops!  That's why we do math in pencil.

How do you teach elapsed time?  I'd love to hear your suggestions.

SDE's Singapore Math Website

I'm so excited about SDE's new Singapore Math website.  This is a great way to introduce Singapore Math to others, including your parents.  There are some great videos (with more to come!) and resources.  Please take some time to explore!

http://sde.com/singapore-math/

Starting Number Bonds

I got a great question today in MN.  Kitty asked how to start number bonds.  Number bonds (also called fact families) can be started in pre-k.  In kindergarten, you want to focus on number bonds to 10.  Mastering those in critical to later success.

Start at the concrete level, using a variety of manipulatives and oral language.  In kinder, I like to start with the number 4, and keep going up as they master each number.  Use hula hoops to tell human number bond stories. Have students work in groups of 4, each contributing one shoe.  You can also use zoo pal plates and number bracelets to work on number bonds at the concrete level.

Here's a great you tube video showing how some teachers in North Carolina are using number bonds.  

Adding a sidetab--Common Core Standards

I'm pretty impressed with myself.  If you're looking for information on the Common Core State Standards, you can pull them out from the side tab -------------------->

I learned how to do it from another website.  http://www.masteryconnect.com/learn-more/core-app.html 

We're all exploring the CCSS...and how they will change our thinking.  I'm just doing some work on this now and will share more with you as I go on my journey.  Here's my big "ah-ha."  This isn't a new set of standards or objectives.  This is about deeper thinking and problem solving.

How Would Your Class (or you) Solve This?

I presented this to a 5th grade class last week.  It's on their class blog.  I can't wait to see how they'll solve it.  The teacher and I had to work on it awhile before we got matching answers.  The kids loved that it was real life and love working on a blog.  I'll let you know how it goes!  


I'm trying to keep track of how far I walk every day but I forgot to wear my pedometer on my trip last week.  I could use your help to figure this one out.  At the Denver Airport, I landed at gate B11 and walked to gate B43.  Then they changed the gate to B29.  I counted and I take 39 steps to get from one gate to another.  But there's more information you need to figure in.

All the odd gates are on one side and the even gates are the other side.  

Between gate B29 and B31 is a shopping plaza that measures 52 steps.  

Between gate B35 and B37 is a food court that measures 173 steps.

Is there any other information you need to know?

Concrete-->Pictorial-->Abstract

I had a teacher ask me how to teach 2 digit x 2 digit subtraction with manipulatives.  I thought this would be a great time to share this and talk about the importance of the CPA model of instruction.  Jerome Bruner's research has shown us that when we teach using manipulatives first (concrete), then moving to a pictorial represention (pictorial), and finally to the traditional algorithm (abstract), our students learn to a greater degree of mastery and have greater retention...yay!  Here's an example.

Using base 10 blocks, I've set up 12 x 21.  (It's important students see that numbers outside the lines not get added back in to the final product.)  Now I can start setting up the array.

I'm not sure why this picture rotated but I think you can still see it.  Students can see 10 x 10 =100 here and 1 x 10 = 100.  My students understood they needed to make a complete rectangle.  They really like to push it together!  (By the way, while place value disks are my favorite, this works much better with base 10 blocks.)

To build the pictorial, we go to the array model.
                                           https://docs.google.com/drawings/pub?id=1ciUj-11Q74c7oOlQcCw9pjLNQ3RpDA7jI7g8mJhxUS0&w=480&h=360


It wouldn't let me insert a table.  Having major computer issues today (for a change!)
Draw a connection between each of these partial products and the pictures above.

Now students can take it to partial product or traditional algoritm.

                           21
                  x12
                      2  It's all about language here.  2 x 1 = 2
                    40  2 x 20 = 40
                    10  10 x 1 = 10 (Can you find it in the pic and the array?)
                  200  10 x20 = 200  
                          252
Partial products are great to use if your kids "put down the wrong number and carry the wrong number." It means they aren't using place value and this will help them.

Looking for a practice game?  Me too!  Have students each deal out 4 cards and arrange them to make a 2 digit x 2 digit problem.  Record the product.  Play 5 rounds.  Total them.  Person with the highest sum wins.  Do you have a double digit multiplication game?

QR Codes and Scavenger Hunt

One of my workshops this week calls for incorporating technology into math.  I love technology.  Not that I'm all that good at it, but I'm not afraid of it, so I'm game.  I just learned about QR codes--you know, those funny boxes that have turned up on ads all over the place?  When you aim a QR reader on your smartphone at them, they take you to a website.  Thanks to Lori Elliot http://www.lorislatestlinks.com/ I learned how to make a QR code. 

First, go to URL shortener: http://goo.gl/

Type in or paste the website address

Choose shorten

Click on details next to the new shortened address.  You'll see the QR code!  (I had to scroll up.)

Copy and paste it to your document.

Then I discovered this website http://classtools.net/QR/  

You type in 5 questions with answers.  It turns it into a QR scavenger hunt.  I can picture using it for 3D shapes, or having the answers be room numbers.  What uses can you think of?  

Football and Math

I'm sitting on a Saturday afternoon, watching college football, and thinking about all the ways it can be used in the math classroom.  Our youngest children can identify jersey numbers.  They can look at the players and compare taller and shorter, larger and smaller, heavier and lighter.  Our first and second graders can find the difference between scores.  We can take our questioning deeper by looking at the UCLA (Go Bruins!) vs. Oregon St. Beavers game. 

                    UCLA      27

                    Oregon   19

     How could Oregon have scored 19 points?  Is there more than one correct answer?  (And could you solve it with model drawing?)  Here's a great place to practice your questioning!  

     For the upper grades, we have trouble finding real life examples of big numbers, but how about Reser Stadium that holds 45,674 seats?  Working on division?  The Beavers managed only 88 yards in 29 carries.  What about integers?  That ball moves up and down the field a lot!  
     What other math is found in such a high interest sport?  Time, percentages, fractions (the game is played in quarters and halves!)  Ask your students to write some questions.