# Archive for October, 2011

## Big Ideas in Math

It is really important that teachers understand **the Big ideas and Enduring Understandings** in mathematics. We need to teach from a **framework** of the Big Ideas and Enduring Understandings. NCTM stated that:

*Teachers need to understand the big ideas of mathematics and be able to represent mathematics as a coherent and connected enterprise. (NCTM, 2000, p. 17)*

I travel around the country and I see people just teaching from lesson to lesson. We have got to stop doing that. Math comes out as this disconnected set of happenings, that usually makes no real sense in the big picture. It’s just another time we set aside in the school day.

In general, we as teaching force, (and I mean everyone involved, teachers, administrators, math coaches, support personnel, consultants and teaching assistants too) need to learn about, discuss, understand and be able to articulate what the BIG IDEAS and ENDURING UNDERSTANDINGS in math are so that we can make sense of the math we are teaching and plan accordingly. We need to plan with them in mind, teach with them in mind and assess with them in mind. What a difference a BIG IDEA can make!

Randall Charles wrote a landmark article on the BIG IDEAS in math in 2005. It is a must read. SEE IT HERE. I highly recommend that schools do grade level planning for math with the BIG IDEAS as a frame.

Let me know what you think!

Happy Mathing,

Dr. Nicki

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## Geometry and Math

Here is a great interdisciplinary geometry lesson! Go beyond the book! Make real life connections. Here is a great lesson on Mondrian and the math in his paintings.

Happy Mathing,

Dr. Nicki

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## Math Problem Solving Posters

Here are some great posters that use the Acronym ACE.

Poster 1

See the write up on this page. Scroll down to Constructed Response Resources for Mathematics.

Happy Mathing,

Dr. Nicki

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## More Problem Solving Rubrics: Teach to the Whole Class, Review in Guided Math Groups

Math Word Problem Solving Rubrics give students an opportunity to see where they are and where they need to go. Rubrics should be used as part of a conversation. They should provide some specific feedback about what’s great and what’s still in progress. Ideally, once students receive the feedback they get a chance to incorporate it as part of their learning journey. In other words, they should get a chance to fix what they got wrong:) You can discuss specific problems and errors in individual conferences or in small guided math groups. Gather students together who have made the same errors and discuss how to correct those errors. Here are some examples of word problem rubrics:

Example 3

Example 4: Click here (if it doesn’t download then Google this term *Word Problem* PTA (Scoring *Rubric*)

Happy Mathing,

Dr. Nicki

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## Exemplar Math Tasks

Here is a great resource for some math writing tasks. You have to scroll down and the math tasks are listed by grade level on the right. What do you think of these tasks? How would your students do? Notice the emphasis on precise language, representation and perseverance through the problem.

Happy Mathing,

Dr. Nicki

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## Word Problem Solving Rubric: Teach to whole class, review in guided math groups

Here is a great word problem solving rubric! I would discuss this and make examples with the class so everyone understands all the elements. I would also make individual copies so students would have it as an “up and close” reference. They could keep it in their problem solving notebooks. I would go over their story problems in small guided math groups, guided by the rubric.

Happy Mathing,

Dr. Nicki

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## Math Resources

Here is a great math methods website with some excellent resources!

Happy Mathing,

Dr. Nicki

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## Math Talk: Getting Started in Whole Class and Small Groups

What is math talk? Math talk involves rigorous, engaging, accountable discussions about math. Math talk is a structure that is integrated throughout the math workshop. It happens in whole class settings as well as small group settings. You want your students to be engaging in it in math centers with partners and groups. Math is a language. We learn a language by speaking it. So, let’s get to talking. Here is some springboards about it to get you thinking and talking about how to do it in your class.

http://www.eduplace.com/math/mthexp/pdf/mathtalk.pdf

http://www.hmheducation.com/mathexpressions/pdf/kfauthor-mathtalk.pdf

http://www.trianglehighfive.org/pdf/007_math_talk.pdf

http://www.edu.gov.on.ca/eng/studentsuccess/lms/MathTalk.pdf

http://blog.tomsnyder.com/math-hub/bid/51966/Generating-Math-Talk-That-Supports-Math-Learning

http://www.mathsolutions.com/documents/0-941355-53-5_L.pdf

Math Talk in Action:

http://www.schooltube.com/video/0bab0ba73caf41019251/Math-Talk

Action Planning Templates:

http://www.edu.gov.on.ca/eng/studentsuccess/lms/math_talk_learning_community.pdf

Happy Mathing,

Dr. Nicki

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## Multiplying Fractions: Guided Math and Center Activities

Here are some great examples of multiplying fractions that can help students to illustrate what they are doing. The CCSS states that students will be able to illustrate and explain what they are doing. We have often stressed the algorithm with no explanation. You should definitely have students illustrating the multiplication of fractions in small groups and in centers. They should talk out their understanding to each other as they are doing these activities. Here are some tools to help build conceptual understanding:

http://zerosumruler.wordpress.com/2011/06/15/multiplying-fractions-a-visual-tour/

http://www.coolmath4kids.com/fractions/fractions-14-multiplying-fractions-01.html

http://www.youtube.com/watch?v=rvTdhb2pybQ

http://www.youtube.com/watch?v=7QITX4evxTA&feature=related

http://www.youtube.com/watch?v=_X2nqjj_Q5E&feature=related

http://www.youtube.com/watch?v=NBFS3KW_aIY&feature=related

http://www.youtube.com/watch?v=8p-XwgBfFmI&feature=related

http://www.youtube.com/watch?v=0k_VJICaFiE&feature=related

Happy Mathing,

Dr. Nicki

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## Beyond Answer Getting: Guided Math Group Work

Here is a must see video by Phil Daro on the need to teach our students more than “answer-getting” (click on the second tab at the top). Guided math groups is a space to help students really talk about the math they are learning. You want to guide conversations, guide conceptual understanding, guide procedural fluency and guide strategic competence building in a small, comfortable, academically rigorous learning situation. Three key elements of guided math group work:

1. Time to talk (each person gets to explain their mathematical thinking and their understanding of the thinking of others)

2. Time to listen (each person gets an opportunity to focus and try to comprehend the math that we are speaking about)

3. Time to practice (with the help of each other and the teacher, students will practice the math)

Whether you are working at the concrete, pictorial or abstract level, students need to know what the math is that they are working on. This should be explicit. We all have to seriously consider what it means to teach math and not answer-getting.

Happy Mathing,

Dr. Nicki

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