# Archive for August, 2011

## 5 Subtraction Algorithms: Great to do in Guided Math Groups

We are continuing our discussion about the need to teach our students a variety of strategies and algorithms.  Remember that two of the Common Core Standards that discuss algorithms are

• 3.NBT.2. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

4.NBT.4. Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Here are some great resources for Subtraction Algorithms:

1) Use the Number Splitting Strategy for Subtraction

Resource 1

Resource 2

Resource 3 : How does this scaffolded organizer teach and shape thinking?

Resource 4 :  The common core wants students to be able to discuss whether problems are mathematically true or false beginning at first grade

2) Open Number line Strategy for Subtraction (See this blog for several resources)

Resource 1

Resource 2

3) Subtraction Using the Counting Up Strategy

Resource 1 (As you watch this video, think about how the graphic organizer scaffolds students thinking about the traditional algorithm).

Resource 2 (What can we tell about Mattie’s sense of place value by the way she discusses the problem?)

Resource 3  (Watch this video and then think about what strategies the teacher uses to get across the concept.  Is she building conceptual understanding?  What purpose does the poem serve?  Does the poem help to build conceptual understanding or is it just a great mnemonic device?)

So, what do you think of these strategies and algorithms?  How many of them do you use?  Which ones would you introduce first and why?  You should definitely discuss these in small guided math groups so that students get to discuss what they are doing and listen to others.  This ties right into the mathematical practices that state that students should be talking and listening to each other discuss math.

Happy Mathing,

Dr. Nicki

P.S. Be sure to read the other posts on algorithms.  We will be discussing all four basic operations during this series.

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## Printable Math Strategy and Algorithm Posters: Great to Discuss in Guided Math Groups

Be sure to hang  up as reference posters in your classroom.  You might also also have them nearby when you are talking about different strategies and algorithms in your small guided math group.  These serve as scaffolds (in the form of cues) so that students can remember what they are learning. See some here…

Happy Mathing,

Dr. Nicki

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## More about algorithms: Be sure to teach them in Guided Math Groups

Here is a variety of great resources that show different addition and subtraction algorithms.

Resource 1

Resource 2

Resource 3

Resource 4

Be sure to encourage math talk.  It is not enough just to have students doing it different ways.  They should be explaining their ways to each other.  The first mathematical practice from the New Math Common Core states that:

Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

How are we making sure that this happens in our classroom?  What kind of culture of “talk” are we fostering? What are we doing well and what can we do better?

HAPPY MATHING,

DR. NICKI

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The New Math Common Core states that children will understand how to “add and subtract (depending on the grade level the number range varies)…using strategies and algorithms based in place value, properties of operations and/or the relationship between addition and subtraction.”

We have to really think about what does this mean in action? How does it look in the classroom?  How do we get fluent as a teaching community ourselves, so that we can teach this way.  I think one way to start is to have grade level discussions about how to operationalize this.

I do think that we should use small guided math groups to discuss different strategies because you want to give the students a chance to talk about their thinking.

Here are some examples of teaching partial sums.

Video

What do you think of the way the teacher frames the method?

How does it make it more student friendly by saying we are going to “break-down” the parts.

What do you think of the way that the teacher uses different colored pencils to highlight the parts of the problem?

In this next video notice how Eli is solving the problem by drawing out the base ten blocks.  What does this tell us about his understanding of place value?

Now look at this video of a teacher using technology to teach the partial sums method.

How does this instructional strategy of representing it differ from using the concrete base ten blocks?  Do you see how it clearly shows the relationship of place value while moving towards just the abstract representation – but using the pictures as the ongoing scaffold.

Look at these next two videos:

Video 1

Video 2

What do you notice about the way that the teacher is talking about the numbers?  Notice how he says “5 tens or 50 ones.” Also notice the very step by step process that he uses to scaffold learning of the strategy.

Here is a Partial Sums Poster.

I wanted to share these videos because they offer different perspectives and nuances on teaching this algorithm.

Happy Mathing,

Dr. Nicki

Partial Sums Poster

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## Math Strategies and Algorithms: Great to Teach in Guided Math Groups

The new Math Common Core stresses the use of different strategies and algorithms.  I am going to be writing about this for the next few days because it is crucial to the new NBT Domain.  Let’s start by talking about strategies and algorithms.  A strategy is an approach to doing something.  An algorithm is a step by step procedure for doing something that often involves repeating the steps throughout the process.

I think it is important to note that there is no one way to do something but there are efficient and inefficient strategies.  According to the new Math Common Core, students should know BOTH – strategies and algorithms.  And teachers should know both:)   AND STUDENTS SHOULD LEARN A VARIETY OF STRATEGIES BEFORE THEY LEARN THE TRADITIONAL ALGORITHM…AHA…How many strategies and algorithms do you have to teach the 4 basic operations in your pocket right now?  You should have at least 3 for each operation.

I strongly recommend that you allow students to discuss their different approaches in guided math groups so that you can scaffold approaches and really get to listen to students talk about their mathematical thinking.  There is a long going debate about whether to teach them or let them emerge.  I think you should do both.  I think you should elicit strategies from students as well as share strategies with them.

Here is a well written  paper on algorithms. (PLEASE READ IT.  IT IS A VERY INFORMATIVE DISCUSSION AND DISCUSSES MUCH OF THE RESEARCH).

MUST SEE VIDEOS FROM THE SCHULTZ CENTER!

We will look at a variety of resources throughout the week.

Happy Mathing,

Dr. Nicki

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## Doing Productive Work

On mathtv.com there is a video that says “Never mistake activity for achievement.”  I like this because sometimes I see really busy classrooms, but I am left wondering what the students are learning.  Busy should be productive. Busy should be fruitful.  Busy should be standards-based, rigorous and engaging.

Busy, alone can be dangerous.  It can be dangerous because we see our students working but we have to always ask ourselves, “Are they learning?”   Being engaged is necessary but not sufficient.  Being engaged in standards-based, rigorous and exciting activities can lead to amazing achievement.

Happy Mathing,

Dr. Nicki

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## Scaffolding is the Key! Small Guided Math Groups is the Place!

Josh Rappaport wrote an excellent piece on scaffolding.  He notes that

“No one would attempt to climb Mount Everest in a day. But when we teach math, we often expect something similar from students. We expect them to learn a complex, multi-step process in one lesson, in one hour. We expect them to go from no awareness of the process, to awareness to competence to mastery. And we don’t take account of the fact that many math process[es] require a long ladder of thought steps. In edu-jargon, this process of taking all of the little steps into account — and teaching each step individually — is called “scaffolding.” ”

This is a brillant metaphor.  See his whole post.

Guided math groups are an essential part of the “scaffolding” process.  In a guided math group you can listen to students talk, you can watch them do the math and give immediate feedback and you can do some direct instruction as well.

I encourage us all to think about “How tall are those ladders we are using in math class?”

Happy Mathing,

Dr. Nicki

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## Mathematical Proficiency for Everyone!

Is it possible to do something in your math class this year, so that everybody develops proficiency?  David Borenstein raises this question and others in his NY times article about math. What happens if we truly believe that everyone can learn math, and that we have the keys to that?  How does the paradigm for teaching and learning math then switch?  How would things change IF we had no doubt that everyone can, will and must do math proficiently?  And we really believed it was possible with some instructional interventions, masterful scaffolding and appropriate math tools? Think about it, seriously and read the entire article here.

Happy Mathing,

Dr. Nicki

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## 48÷2(9+3) = ? Great Critical Thinking and Debate Question!

NCTM tweeted that 98% of the people got it wrong!  What do you think?  Do the math, explain your thinking and then check your answer!

Happy Mathing,

Dr. Nicki

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## Math Video Resource Library

Here ia a great free 4th grade math video resource library!  It is by Envision math but you don’t have to have the program to use the videos!

Happy Math,

Dr. Nicki

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