# Archive for January, 2012

## Great Posters for Talking About Math: Questions for whole class and Guided Math Groups

Mrs. Shannon has put up some fantastic guided math resources.  Here are three of my favorites!

Question prompts – These are great to get at the mathematical practices.  I would add one that asks: How did you model your thinking?

Guidelines for Discussion

Guided Math Checklist

See all of her resources here!

Happy Mathing,

Dr. Nicki

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## Problem Solving Across the CCSS Content Domains: Practice in Guided Math Groups

There is a big emphasis on problem solving across the curriculum in the new Math Common Core.  We find a great deal of problem solving in operations and algebraic thinking but it is also heavily woven throughout measurement and data as well as fractions and place value domains.   What are you doing to make sure that your students are problem solving across the curriculum?  Have you mapped it out to ensure that you solve different types of problems throughout the week?  If you do a Do Now or a Problem of the Day routine…what do these problems look like?  Are you doing money, time, graphs, fractions, mass and volume problems often, depending on your grade level?  Here are a few examples from the CCSS Domains listed below:

2.MD.8. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies…

2.MD.10.  Solve simple put-together, take-apart, and compare problems1 using information presented in a bar graph.

3.MD.1. . Solve word problems involving addition and subtraction of time intervals in minutes…

3.MD.2.  Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units…

• 4Nf3Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators…
• 4NF4Solve word problems involving multiplication of a fraction by a whole number…
• 5.NF.2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators…
• 5.NF.3. Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers…
I would do problem solving as an ongoing class routine, in guided math groups and in problem solving centers.
Let me know how you’re doing!
Happy Mathing,
Dr. Nicki
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## Beyond Just Add a Zero to the End: Guided Math Activities that Tackle Working with the Power of Ten

Teaching students to multiply and divide by the powers of ten is often reduced to just do something with that zero.  So students often say things like if you are multiplying, “just remember to add a zero on to the end.”  What does that mean?  Do they really understand what they are doing?  Do we teach it with place value in mind?  Here is a great model for teaching this concept…the number slides!  Try it and teach your students the place value behind multiplying or dividing by zero.  Teach the students how to use these rulers and then facilitate discussions about multiplying and dividing by powers of ten in small guided math groups.

Happy Mathing,

Dr. Nicki

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## Fraction Resources and More: Great to Use in Guided Math Groups

Here is a great math resource.  The sidebar on the left has folders for different topics.  Just open a folder and click the icon down and several resources on that topic will appear. Here is the fraction page.  There are different games and manipulatives to use to practice.  For example, the fraction folder has cards, numberlines and tiles.  Check it out!  These are the types of activities that are aligned with the Math Common Core.  Students should be able to draw their own illustrations of fractions and numberlines. In order to do this, they must have several experiences working with these types of materials.  Have the students use these things to make up story problems as well.  They is a big emphasis in the CCSS on problem solving across the domains.  Students should practice telling stories with visuals, numberlines and manipulatives.  Have the students work on these activities in centers as well as use them when working in small guided math groups.

Happy Mathing,

Dr. Nicki

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## More Math Exemplars: Great for Guided Math Centers

Here is an exemplar.

Resource 1 -http://www.ontla.on.ca/library/repository/mon/5000/10305062.pdf

Happy Mathing,

Dr. Nicki

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## Some great math exemplars: Guided Math Group Work

Here are some great exemplars.  I think it is good to do them in small guided math groups, so you can see what students are doing and they can talk through their approaches.  When you are looking at exemplars, you want to notice if the students are meeting the content standard as well as the mathematical practices.  Set up some criteria for the students.  Practice doing a bunch of exemplars together and then also have the students do them in partners and groups.  You want to scaffold the learning and give students a sense of success.

Resource 1

Resource 2

Resource 3

Let me know what you are doing with exemplars:)  Do you do them daily, weekly, monthly?  Does your school have a plan?  Does the grade level have a plan?  Do you do exemplars across the content domains?  Let me know and send me examples of the great stuff you are doing out there!

Happy Mathing,

Dr. Nicki

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## Mathematical Reasoning: Developing, promoting and expanding thinking in whole group and small group

Mathematical Practice 2 is about students learning to “make sense of quantities and their relationships in problem situations.” It involves students being able to “contextualize” and ” decontextualize” numbers.  Are your students able to put words to numbers?  For example, can they tell you a story that makes sense about 2.5 x 10? Also, can they take apart and discuss the numbers in a problem?   Do they reason quantitatively  by “creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects[?]” —CCSS
NCTM (2000) says that reasoning involves:
• Recognizing reasoning and proof as fundamental aspects of mathematics
• Make and investigate mathematical conjectures
• Develop and evaluate mathematical arguments and proofs
• Select and use various types of reasoning and methods of proof

What does all this really mean?  Well in the next few posts I would like to explore this.   I believe reasoning is taught over time and reinforced through our daily practices.  It involves questioning, prompting, listening, challenging, proving, giving evidence, thinking out loud, thinking with a partner, thinking by yourself, thinking in a group, and thinking publicly to name a few things.  Teachers set up environments where this happens.  We set students up to reason or not to reason.  We set them up to publicly prove what they know or not.  We teach them specific reasoning skills or we don’t.

My point is students don’t just start reasoning.  This is a “habit of mind” that is developed, practiced, promoted and expanded over time and throughout the years.  Schools have to think about how they develop a culture of reasoning.  Grade levels should come up with some benchmark routines that promote reasoning.  You should think about how reasoning is interwoven throughout the day, week, the month and the year.

Here are some sample weekly routines:

What’s the problem routine?  You give the students some numbers, say 10 x 30 and ask the students to make up a story about this.

Convince me paper:  You give the students something that they have to convince you about:  Convince me that ….. (1/2 is greater than 1/3)

True or False essays:  You give the students a statement and they have to decide and defend whether it is true or false.  For example: Anytime you multiply a number by 0, you get 0.  True or False?  Defend your answer with 3 examples.  Show your thinking.  Explain your thinking.

Teachers can do these at any grade level with the appropriate content.  These are great thinking prompts that work across grade levels.  It’s important to think about access for all. I encourage teachers to develop different graphic organizers for the responses so that they are tiered and give different entry points. I recommend that you  process them in small guided math groups so that you can hear the thinking.  I also think there should be some whole group sharing, so that the entire mathematical community in your class can engage together.  There are benefits to facilitating both types of conversations and there should be a balanced approach.

Happy Mathing,

Dr. Nicki

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## Gummy Worm Math: Measurement Never Tasted So Good!

Have you ever wondered how long a gummy worm can really be stretched?  Did you know that a gummy worm can grow if you put it in water?  Do you know how many pennies a gummy worm can hold up under? Well gummy worms are great to explore this and other measurement topics (width, length, weight, volume) as well as to graph the data that is collected.  These activities allow your students to hypothesize, experiment, observe,  analyze and interpret data and have FUN the whole while doing it!  Here are some links to get you started:

Gummy Worm Math Resource 1

Gummy Worm Math Resource 2

(Love this rubric – “commendable”, “acceptable”, and then…. “see the teacher”)

Gummy Worm Math 3

Gummy Worm Math 4

Gummy Worm Math 5

Gummy Worm Math 6

Gummy Worm Math 7

Gummy Worm Math 8

Gummy Worm Math 9 (Task Card)

Gummy Worm Math 10

Happy Mathing,

Dr. Nicki

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## More Resources for Teaching Capacity

Students struggle with measurement.  They need more experiences actually exploring the measurements they are learning about.  I definitely recommend hands-on, minds-on workstations where students can go and actually figure out that there are 4 quarts in a gallon.  As we plan units of study, we should use Multiple Intelligences as a framework for setting up a variety of experiences with the content.  Imagine if your students visited the topic through song, through a hands-on activity, through a poster, and through a story.  The more encounters they have with the content, the more they retain.

Remember that planning for the talk around the experiences is just as important. Scaffolded questions and writing prompts are an essential part of the process.  Graphic organizers should be used throughout the unit as advanced organizers, lesson entrance and exit slips, and study guides.  When we have students listening, speaking, writing and reading about the content, it has more opportunities to stick.  You can differentiate many of these types of learning opportunities so that everyone is working in their zone of proximal development.

Here are a few more capacity resources:

Resources 1: Story: The Royal Land of Gallon (Scroll to the middle of the page to see) This is more a mnemonic scaffold.

Resources 2: A Capacity Rap

Resources 3: NCTM Gallon Man Lesson

Resources 4:  Great Capacity Power Point

Resources 5: Another Power Point Lesson on Capacity

Resources 6: Worksheet: Capacity Video showing Real World Items

Resources 7 – A Detailed Plan

Always follow up conversations in small guided math groups because that is where everyone gets a chance to talk! Let me know how it goes!

Happy Mathing,

Dr. Nicki

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## Gallon Man: Great Ways to Teach Capacity

Gallon Man is a great way to teach capacity. Here are a variety of ideas for using Gallon Guy or Gallon Girl.  Some have templates for students to cut out and others show students using construction paper folded different ways to make a Gallon Man.   Gallon Man is a cousin to Fraction Man!  These hands-on activities help students to internalize the knowledge and have a frame of reference for capacity.

I would have the students make the figure in a math center and then I would have them bring it to a small guided math group to discuss.  During the discussion, they can refer to their graphic organizer to come up with problems and answer questions.

Here are a few of my favorite examples:

Resource 1– Gallon Man

Resource 2 – Students Making a Gallon Man

Resource 3 -Gallon Man Bulletin Board Activity

Resource 4- Another Gallon Man Bulletin Board

Resource 5 – A Very Colorful Gallon Man

Resources 6- Gallon Man Template

Resource 7- Colorful Gallon Man Template

Resource 8- Digital Gallon Man

Resource 9 – Hand Drawn Gallon Man

Resources 10 – Gallon Man Song

Resource 11- Another Gallon Man Song

Resource 12 – Class Singing Gallon Song

Resource 13 –  Class Drawing and Singing Gallon Man

– Teacher explaining Gallon Girl

Resource 15– A Display of Gallon Man and Liter Lady

Happy Mathing,

Dr. Nicki

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