## 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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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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## Common Core Math Progressions: Detailed Guided Math and Center Activities

The Common Core folks have put up Math Progressions, which describe each domain in detail.  They only have progressions up for Operations and Algebraic Thinking and Place Value right now. There are pictures, diagrams and lots of good information. This is a must read for everybody!

Operations and Algebraic Thinking Progressions

Place Value Progressions

Happy Mathing,

Dr. Nicki

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## Math Riddles: Great Critical Thinking Activities for Small Guided Math Groups

Riddles are a great motivation for learning math.  Here are several links to place value riddles that can get your students thinking.  Definitely allow your students to use concrete materials for solving the problems.  After much work with the riddles, move the children to becoming problem posers as well as problem solvers

Resource 1

Resource 2

Resource 3

Resource 4

Resource 5

Resource 6

Resource 7   (great article for scaffolding riddles by grade level)

Happy Mathing,

Dr. Nicki

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## Dividing Decimals at the Pictorial Level – Making it Visual in Guided Math Groups

Something everybody needs to know how to do!  Here are some great resources that I am encouraging everybody (including the primary teachers) to look at.  We all have to step up our game.  Every elementary teacher needs to know and be comfortable with solving math problems at least through 8th grade math!!!:)  Notice the modeling—this is key.  The idea that we conceptually illustrate what is happening is of utmost importance. We need to take this idea of conceptually modeling the math…and do it with whatever we are teaching.  Watch how well this is done in the following videos!

Resource 1

Resource 2

Resource 3

Resource 4

Resource 5

Resource 6

Resource 7

Happy Mathing,

Dr. Nicki

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## Dividing Decimals at a Concrete Level: Great Guided Math Lessons

The new Math Common Core states that 5th grade students will

## Perform operations with multi-digit whole numbers and with decimals to hundredths.

5.NBT.7. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

So, we need too make sure our students understand decimals thoroughly.  We need to teach it at a concrete, pictorial and THEN abstract level.  This is the first post of a series that deals with decimals.  Here are some resources to teach dividing decimals at a concrete level.

Resource 1

Resource 2

Happy Mathing,

Dr. Nicki

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## More Base Ten Block Magic: Building Understanding One Block at a Time in Guided Math Groups

See these great resources to teach operations with base ten blocks in small guided math groups!

Visualizing Algorithms

Exploring Decimals

Visualizing Multi-digit Multiplication

Picturing Multiplication

Happy Mathing,

Dr. Nicki

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## The Magic of Base Ten Blocks: Develop Conceptual Understanding in Guided Math Groups

This is  a great site that shows you how to use base ten blocks to develop conceptual understanding of the operations.  I would do all of these activities with the students in small guided math groups with real base ten blocks. I would then hold small guided math sessions at the computer so I could use this site to teach at the pictorial level.  Finally, I would have the students work with this site during center time.

Happy Mathing,

Dr. Nicki

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## Base Ten Blocks Part 2: Center Ideas and Guided Math Group Lessons

Base ten blocks are great manipulatives for practicing place value.  Here are 10 of my favorite virtual base ten sites! I would use these in three ways.  First, I would use them as whole group instruction on an interactive board.  Second, I would have the students work on them during center time at the computers. Third, I would pull small groups to the computers and hold some guided lessons there using these sites.

1. http://www.learningbox.com/base10/BaseTen.html ( I like this game, especially the drumroll and how everything reinforces place value)

2. http://www.learningbox.com/base10/CatchTen.html (this is fun but I never can seem to get the bear to catch ten!)

3. http://www.learningbox.com/base10/Estimation.html (great for estimating amounts)

4.http://ejad.best.vwh.net/java/b10blocks/b10blocks.html (be sure to read the instructions at the bottom of the page…great for smartboard teaching)

5.***** http://ulm.edu/~esmith/nctmregional/blocks.htm (this is an excellent resource for teaching operations with virtual base ten blocks)

Virtual Library Resources:

7. http://nlvm.usu.edu/en/nav/frames_asid_154_g_2_t_1.html?from=category_g_2_t_1.html (base ten block addition)

8. http://nlvm.usu.edu/en/nav/frames_asid_155_g_2_t_1.html?from=category_g_2_t_1.html (base ten block subtraction)

9. http://nlvm.usu.edu/en/nav/frames_asid_154_g_2_t_1.html?from=category_g_2_t_1.html (base ten block decimals)

Happy Mathing,

Dr. Nicki

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## Using Base Ten Blocks to Teach Guided Math Lessons and Do Math Centers

Throughout the month of November we have been discussing different mathematical manipulatives.  I am going to start a series of posts on Base Ten Blocks.  These are great mathematical manipulatives to use when working in small guided math groups. They are one of the most important manipulatives we have to teach place value, number sense, addition, subtraction, multiplication and division. Yet, they are very underutilized.   These  3-dimensional blocks come in a variety of materials (plastic, wood, magnets) and colors.  They are divided into cubes /units(one’s place) rods /longs(ten’s place) flats (hundred’s place) and blocks (thousand’s place).

I want to start by giving an example of the base ten centers that I set up for students in the primary grades when we are exploring representing numbers and their values.  I will begin each lesson with a mini-lesson either using magnetic base ten blocks, overhead base ten blocks or an interactive base ten block game on the Smartboard. Then, I send the students to centers where they explore numbers.

I differentiate the centers by readiness- meaning I have students exploring different numbers.  So for example, in the stamp center, the novices might have blocks through the hundreds and the apprentices and experts might have blocks through the thousands.  I also use tic tac toe menus and dot cards during the place value unit (see   http://daretodifferentiate.wikispaces.com/Choice+Boards   and  http://www.iu29.org/resources/Documents/ThinkDot.pdf ).  Finally, after student activity time, I always end with a share where we make an entry in our class math journal about the math that we did for the day.  We don’t just talk about what we did, but we talk about what the math was that we were practicing.

1. Magnetic Base Ten Blocks – Partner A pull a card; Partner B show the representation on the white board with magnetic blocks
2. Stamp Base Ten Blocks – Work as Individuals- Pull 2, 3 or 4 cards (depending on the group); Make the largest number possible and stamp it out; Then, make the smallest number possible  and stamp it out
3. Regular Base Ten Blocks – Pull a card (numbers are written in expanded form); Show the number
4. Paper Base Ten Blocks – Roll a number (2, 3 or 4 digit based on group); Write the name, the number, the expanded form and show the number by gluing down the paper Base Ten Blocks.
5. Base Ten Block Flashcard Set –This is a great set that I bought at Lakeshore.  I like it because it has 4 representations of the number and you can give the experts all 4 cards to match up and the novices two.  There is a picture, expanded form, standard form and word form.  The students love to play this in groups.  It is a cooperative game, where everybody is helping each other to find all the pairs.
6. Computer Base Ten Block Game (various games)
7. Draw out the number in Base Ten Block Representation (roll a number and represent it by drawing out the base ten blocks).
8. Place Value Match Up Self Checking Puzzles (bought at Lakeshore)

Base Ten Block Mats:

http://www.didax.com/support/manipulatives/base_ten_blocks/2-5195_pg45.pdf

http://www.didax.com/support/manipulatives/base_ten_blocks/2-5195_pg46.pdf

Base Ten Block Paper

http://mason.gmu.edu/~mmankus/Handson/b10blocks.htm

http://wps.ablongman.com/wps/media/objects/778/796754/17.pdf

http://www.ablongman.com/vandewalleseries/Vol_3_BLM_PDFs/V3%20All%20BLMs.pdf

http://lrt.ednet.ns.ca/PD/BLM/table_of_contents.htm (scroll down to the base ten materials)

Be sure to look for the upcoming posts on using Base Ten Blocks!

Happy Mathing,

Dr. Nicki

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