Singapore Math Method for Compensation Subtraction

After years of doing intervention work with subtraction across a zero, I was so excited when I learned about compensation subtraction.  It's also called constant difference.  It helped so many kids and it wasn't just a trick.  They understood why they were doing it!

When I taught larger numbers, I generally reverted to the traditional method, or used many steps.  After spending a really fun week in Cleveland, MS, Lon Hayes sent me an email describing this method of compensation subtraction with larger numbers.  Thanks so much Lon!!

Try this with your class and let me know how it goes!

Singapore Math--Extending a Problem

This was a comment on another post...I just wish I had the original problem!

Today I posted some of the part/whole problems around the classroom for student pairs to go around and make models/solve. I had one kid that needed more of a challenge, so I asked him to write more problems... Here are his two problems: Joe bought 26 chairs. They each cost $7.25. How much money did he have to pay? 

 Logan made 64 chairs. He needs 6 wood planks to make 2 chairs. How many planks does he need to make 64 chairs?

Singapore Math Addition Strategies

We tend to think our children need to learn their math facts--then go to double digit addition, first with no regrouping, then with regrouping.  Once they can add two digit numbers, it should generalize to larger numbers.  But is it that easy?  Lately, during my workshops, I've been asking teachers to see how many ways they can find to add.  I do the traditional algorithm, just to take it out of the mix.  My wonderful North Carolina teachers came up with all these different ways to add numbers together.

We started talking about manipulatives.  Using Zolton Dienes theories, we went from proportional, everyday materials to non proportional materials.  Then we went to lots of our favorite Singapore Math strategies like number bonds (building 10s) and left to right addition (based on place value.

We also talked about other methods that children should be comfortable using--hundreds charts and open number lines.  Finally, we went to partial sums, which I think is a critical, missing piece.  The traditional algorithm is the last piece.

Thanks Murphey Traditional teachers for putting in the work to make this as a teacher anchor chart!  

Anchor Charts

Take an objective look at your room.  What percent of the space is taken up with each content area?  What is taken up with store-bought materials that just becomes wallpaper?  Does math have equal representation? Your walls should reflect your teaching style.  Our walls need to be dynamic and part of our instruction   I strongly believe in anchor charts.

This is an anchor chart used in my old school district

 I wish I could remember where I got this one!!

Anchor charts don't have to be cute.  As a matter of fact, I believe they should be made with your students and should be in the children's natural language.  You may continue to edit them as you continue instruction in that area or spiral back to it, increasing the depth and complexity.  They need to be referenced during instruction so they don't just become wall paper.  Studies show that students look towards these anchor charts, even though they are removed or covered during testing, as a memory trigger.

 This came from a classroom in Holland, MI

Thanks, Jana Hazekamp for sharing these!

You can see lots more on my pinterest anchor chart page.  Pinterest.com/Ricky_Mikelman

Place Value Workstation

 I'll only make a workstation if it can be used more than one way or more at more than one level.  I wanted was working on some workstations for counting and place value for grades K-2 and something I saw on Pinterest sparked this idea.  Kindergarten students made their initials with unifix cubes and counted them, focusing on making tens.

The first and second graders built them with base 10 blocks.  It got interesting as we worked on making trades between 10s and 1s.

To get even higher values, we built names instead of initials.  Need more ideas?  Build spelling words or sight words!

Primary Workstations

I just returned from North Carolina, where we explored number sense through workstations.  There were kindergarten, first, and second grade teachers.
If I'm going to make a workstation, I want to make sure there are options built in (for me and the children) and differentiation in included in the workstation.

                                                       Shape Puzzles

 I used the school die cut machine to cut out shapes and assigned a value.to each.  The kinder and first grade teachers worked with numbers within 10.  

 The second grade standard was working on adding by 10s to 120.  Some teachers went higher!

Changing the task to "Make a picture with a value of 100" really changed it.  It was way more difficult to reach the sum AND be creative.
If I were doing this with children, I would have used more (and better) colors.  We grabbed what was close by.  I think it shows the idea well.  The children also would label the picture, using the names of the shapes and their values.  FUN!!

Why Teach Math?

I just spent two days with Dr. Yeap Ban Har.  I've been in his sessions before but never a two-day intensive workshop.  Here are some of the ideas he shared that really hit home with me.

• The math we teach isn't as important as the thinking skills we teach.  We need to be comfortable and familiar with information and data--how to take it apart and make sense of it.  
• Some people are good and this is easy.  Some people will struggle and may need more help.  But we will work and will all be successful.
• Visualization is a key skill.  It's the minds' ability to see things that are not obvious. 
• Math is an excellent vehicle for the development and improvement of a person's intellectual competencies.  
• It's the conversations (questioning) and natural language we have during math lessons that will make the math come alive and make sense for the child.
• If you have to repeat (reteach) material each year, you won't have time to teach that year's material.
• Howard Gardener listed many intelligences.  The ability to memorize and the ability to follow procedures aren't among them,  They just take an inordinate amount of practice.  
• The goal of a math lesson is the leave knowing more than you started with,

Thanks Ban Har.  I'm tired but it's a happy tired.

Singapore Math Intensive Institute

I've just finished an amazing week at SDE's National Conference for Singapore Math.  I met teachers who are so devoted to finding ways to reach their children and teach them conceptually.  By Thursday, our brains were full, but we pushed on.  I was so sorry to miss the sessions on Friday, but my niece's wedding is Sat. and missing any part would have created major family drama.  I've heard Jana Hazekamp hit her lesson out of the park.  I haven't heard about Char Forsten's lesson yet, but I know Char well enough to know it was great.

The next big event is with Dr. Yeap Ban Har.  He'll be in Houston on Aug. 2-3, and the Chicago area on Aug. 6-7.  Ban Har is from Singapore and has served in a variety of roles there, including training their teachers and, currently working for Marshall Cavendish, the Singapore Math publisher.  I've had the pleasure of learning with him before.  If you have the chance to attend, grab it.  He teaches in depth and with intention.  You'll think about what you learn from him for months, if not years.  You will be changed and it will impact your teaching.

I know this is short notice....so if you can't make it, think about our National Conference in Las Vegas for 2013!  He'll be there for 2 days (and it's at the Venetian again!)

Number Bonds and Improper Fractions

Fractions are so challenging to our students.  We need to make sure we teach conceptually from the beginning and take our time.  This is a lesson I've taught many times with 4th graders who already know about number bonds.  It really helps them learn about how to turn improper fractions into mixed numbers.

Fifth Grade Model Drawing

This problem came to me from some friends.  It's got a "hidden question" that you have to answer before you can answer the stated question.  I also show the array model of multiplication here instead of the traditional algorithm.

I do lots of professional reading, in lots of forms.  I read blogs, professional journals, spend way too much time on Pinterest, and even tear myself away from my ipad to read real books.  I'm so excited about Small Steps, Big Changes.  Chris Confer and Marco Ramirez have written a very practical book about some ways to make changes in school cultures.  This book, written from the perspective of a teacher, an administrator, and a math coach, would make a meaningful book study for leadership teams, district (math) coach teams, or even a whole school.  It's an easy read, highlighting eight practices:

• Keep the end in mind
• Understand the problem
• The stance of a researcher (Making tough decisions)
• The 80/20 rule (Making decisions for the good of 80%)
• Patterns of talk (in the classrooms, the halls, and the teachers' lounge!)
• Patterns in Content
• Patterns in Instruction
• Intentionality

While this book focuses on math, it's really about change.  It's a great book to pick up over the summer.  I promise you'll be pondering these important ideas.

How I Justify Spending Time on Pinterest

I admit it.  I spend way too much time on Pinterest!  BUT it's usually time pretty well spent.  I use the search tool to look for fractions, division, or Singapore Math.  And there's lots of good content out there.  Pinterest is a way of bookmarking good websites to the cloud--with a visual and social component!  You can follow my boards (lots of them are math related!) as a way to get started.  If you get bored, look at the Humor and Wisdom Board!!

Summer Math Ideas

In Houston, the thermometer is already pushing 90 and it's beginning to feel a lot like summer.  I love the blog Mind Shift and first read this NY Times blog article on that site.  These are great ideas for summer OR sparks for ideas using current events during the year, especially after testing.  Enjoy!

http://learning.blogs.nytimes.com/2012/04/25/these-days-are-numbered-eight-summer-math-ideas/

How Would You (or your class) Draw This?

David weighed 240 pounds on Earth and 40 pounds on the moon. How much would Steven weigh on the moon if he weighs 180 pounds on Earth?

This problem was presented to an 8th grade class.  I think model drawing makes it much more accessible to students in a lower grade.  Here's how I solved it!  

A Model Drawing Schedule

Model Drawing, also called Bar Modeling, is the most commonly used problem solving strategy in Singapore Math.  Our students struggled with it in the beginning.  When we reflected on our teaching, we decided they needed more practice with one model before we moved on.  This is a sample of what our schedule looked liked as our students became more successful.  I mention in this video that we wrote 10 versions of each problem.  In a two-week span, we used 6-7 of them.  The rest were saved to be review problems other weeks.

Working on Math Facts

Trying to solve problems without knowing your math facts is like trying to read for comprehension and having to sound out every word!  However, our kids need strategies to learn their facts and lots of games to practice them.  If we depend on flash cards and parents, it's not going to happen.  Here's how I teach kids to learn their facts...and as an added bonus, how to simplify fractions using a multiplication chart!

Model Drawing with Rate and Speed

Before break, a participant asked me to show how I'd use model drawing to show rate and speed problems.She was good enough to send examples.  Thanks!!

  Since the unit bar is labelled with Mrs. G's time, I put her miles above the bar.  I could have done a running total below the bar, but chose to do an ellipsis instead.  It's a great tool to use when the numbers are larger.

This problem clearly shows the relationship to multiplication.  After all, model drawing is turning a word problem into a visual representation so the student can find what to do next.

For more explanations, I recommend Char Forsten's Step-By-Step Model Drawing for grades 1-6
step-by-step-model-drawing

Or Lorraine Walker's Model Drawing for Challenging Word Problems for grades 6-Algebra 1.
Model-drawing-for-challenging-word-problems

Check out my Livebinder!

Live Binder is a great way to keep your bookmarks "in the cloud."  I love my Livebinder.  First, I installed the widget on toolbar so if I find a site I like, I just click on it and it adds it to my livebinder.

Check out my livebinders!

http://www.livebinders.com/edit?id=133702  Ricky Mikelman's Singapore Math Live Binder

http://www.livebinders.com/edit?id=195368 Math and Technology

Happy New Year!