*[Photo by bumeister1 via flickr.]*

Welcome to the ** Math Teachers At Play** blog carnival — which is not just for math teachers! We have games, lessons, and learning activities from preschool math to calculus. If you like to learn new things and play around with mathematical ideas, you are sure to find something of interest.

Scattered between all the math blog links, I’ve included highlights from the Common Core Standards for Mathematical Practice, which describe the types of expertise that teachers at all levels — whether in traditional, experimental, or home schools — should seek to develop in their math students.

Let the mathematical fun begin…

## TRY THESE PUZZLES

By tradition, we start the carnival with a couple of puzzles in honor of our 52nd edition. Since there are 52 playing cards in a standard deck, I chose two card puzzles from the Maths Is Fun Card Puzzles page:

- A blind-folded man is handed a deck of 52 cards and told that exactly 10 of these cards are facing up. How can he divide the cards into two piles (which may be of different sizes) with each pile having the same number of cards facing up?
- What is the smallest number of cards you must take from a 52-card deck to be guaranteed at least one four-of-a-kind?

The answers are at Maths Is Fun, but don’t look there. Having someone give you the answer is no fun at all!

1. Make sense of problems and persevere in solving them.

- Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution.
- They analyze givens, constraints, relationships, and goals.
- They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution.
- Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem.
- Mathematically proficient students continually ask themselves, “Does this make sense?”

## EARLY LEARNING ACTIVITIES

**Bon**plans for mathematical fun with a Birthday Party Fibonacci Style!**Kristen**and her daughters play with possibilities in How Do You Count a Dozen Ducklings?- Have you collected a stash of math-related picture books?
**Cindy**offers advice on Organizing Your Children’s Math Library. - Your students will enjoy Tens Concentration or Math War with
**Jennifer’s**free Printable Ten Frame Cards. **Tricia**shares a free “I have, who has?” card game in Monday Math Freebies – Numbers to 20.**Julie’s**students play Concentration with her free, downloadable Place Value Practice cards.- Did you enjoy How to Train Your Robot from last month’s MTaP carnival? Here’s a great follow-up:
**David**posts two examples of Kindergarteners programming.

2. Reason abstractly and quantitatively.

- Mathematically proficient students make sense of quantities and their relationships in problem situations.
- They pay attention to the meaning of quantities, not just how to compute them.
- They knowing and flexibly use different properties of operations and objects.

## ELEMENTARY EXPLORATION

- Have you thought about how important talking is to math? After a discussion with his niece,
**Timon**ponders Language and Conceptual Understanding. **Amber**shows us her method for Making Math Tactile for My Auditory/Kinesthetic Left-brained Learner (A Math Lesson In Pictures.)**Malke**entertains a tough audience with Scissor Stories: Tales of Transformation.**Christopher**demonstrates how much easier it is for elementary students to explain their answers (and to self-correct) through conversation: If you keep at it, it will pay off…**Maria**discovers Some online measuring games.**Crewton**teaches Long Division With Base Ten Blocks.**Phyllis**explores averages and more in Oreo Learning and Fun.- And here on
*Let’s Play Math!*blog, I continue my study of what it means to profoundly understand elementary math in PUFM 1.4 Subtraction.

3. Construct viable arguments and critique the reasoning of others.

- Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments.
- They justify their conclusions, communicate them to others, and respond to the arguments of others.
- Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

## MIDDLE SCHOOL MASTERY

**Donna**offers printable cards to teach Multiplying and Dividing Decimals Using Number Sense. Note: “Because that’s what the rule says” does not count as justification!**Patrick**shares a multiplication game in Great Gift for a Math Dad.**Alexander**tackles the summer doldrums in Word Problems with Percents for the Summer Break.**William**encourages middle school students to play with Square number snakes and rings. (Can your kids spot the error?)**Julie’s**students explore the Volume of 3D Shapes with Play-doh.**Mathcounts Notes**shares a couple of “beginner level” puzzles: Counting and Painted Cubes.**Jen**wraps up a year of math journaling with a Culminating Mind Map.

4. Model with mathematics.

- Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life.
- They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas.
- They can analyze those relationships mathematically to draw conclusions.

## ADVENTURES IN BASIC ALGEBRA & GEOMETRY

- Can your students explain Why do you Flip the Inequality when Multiplying by a Negative? Check out
**James’**video! **Tom**adapts a lesson he found online to give algebra students a different way to think about slope: Feed Your Students a Hot Cup of Alphabet Slope.- What topics
*must*algebra 1 students master?**Sophia**sends out a Call for help! Algebra 2 Teachers! - Algebra students should learn to write simple proofs, as
**Erlina**demonstrates in Proofs of sum of two even numbers is even. **Fawn**shares a variety of puzzles and activities in Last Math Lessons.**Pat**highlights a couple of Nice Old Geometry Problems.

5. Use appropriate tools strategically.

- Mathematically proficient students consider the available tools when solving a mathematical problem.
- They are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations.
- They detect possible errors by strategically using estimation and other mathematical knowledge.

## ADVANCED MATH ENDEAVORS

**John’s**students apply geometric series to a 1792 Penny.**Druin**demonstrates how to take Cornell Notes in Math Class.**Grace**asks for help in creating a visual connecting high school math concepts.**Trever**offers a creative introduction to vectors as units of movement in Vector Dancing.**Terrance**shares his “Exponential and Logarithm Functions” version of the Review game: Trashketball.**Shaun**explains What are Limits in Calculus? Subsequent posts discuss additional concepts related to limits.**Kalid**gives his take on How To Understand Derivatives: The Quotient Rule, Exponents, and Logarithms.**Sam**wraps up the school with some real-world math in Wealth Inequality! A Calculus Investigation.**Rachel**explains how math is used to keep track of offenders and undertake search and rescue operations in Conic section hide and seek.- And don’t miss the Carnival of Mathematics 88!

6. Attend to precision.

- Mathematically proficient students try to communicate precisely to others.
- They try to use clear definitions in discussion with others and in their own reasoning.
- They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately.

## PUZZLING RECREATIONS

**Shecky**offers a new version of a classic logic puzzle that is easy enough for elementary students.- In The List, My Shirt, and Taking a Break from a Problem,
**Rodi**reminds us that some math problems need to be pondered. - MAA MinuteMath delivers a new puzzle every day from the AMC-8, AMC-10, or AMC-12 competitions.
**Dave**dips into history to challenge us with Puzzler: a squarable region from Leonardo da Vinci.**Guillermo**shares a symmetry puzzle in One and Palindromes.**yofx**offers a Pythagorean puzzle: Scharezade + Math.**Fawn**shares several wonderful puzzles from her Math Teachers’ Circle.**David**poses the eternal question: How long until we “Pig Out”?

7. Look for and make use of structure.

- Mathematically proficient students look closely to discern a pattern or structure.
- They also can step back for an overview and shift perspective.
- They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects.

## TEACHING TIPS

- What did your students learn in math this year?
**Kate**shares a printable mini-journal called Top Ten Things… **Heather**poses the riddle, How is a Homeschool Mom Like a Mathematician?**Sue**ponders the difficult task of Teaching for Understanding.- What are the roots of math anxiety?
**Dave**considers how to protect (or regain, if possible) his sons’ Mathematical Innocence. **Colleen**links to several resources encouraging teachers to ask Rich Questions in Mathematics.**Guillermo**warns us about Deceptive and Misleading Mathematical Patterns.**Dan**attempts to assemble An Incomplete History Of The Math Edublogosphere. Help him out — go add your data!**Mr. Honner**shares a few insightful Reflections: Students in Math Class.**Pat**continues to provide a wonderful resource for teachers with his On This Day in Math series.

8. Look for and express regularity in repeated reasoning.

- Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts.
- As they work to solve a problem, they maintain oversight of the process, while attending to the details.
- They continually evaluate the reasonableness of their intermediate results.

## FINAL COMMENTS

That rounds up this 52nd edition of the ** Math Teachers at Play** carnival. I hope you enjoyed the ride.

The next installment of our carnival will be posted at Motion Math Blog in August. If you would like to contribute, please use this handy submission form. Posts must be relevant to students or teachers of preK-12 mathematics. Old posts are welcome, as long as they haven’t been published in past editions of this carnival.

Past editions of the carnival can be found on our MTaP archive page.

**We need more volunteer hosts!** Classroom teachers, homeschoolers, unschoolers, or anyone who likes to play around with math (even if the only person you “teach” is yourself) — if you would like to take a turn hosting the ** Math Teachers at Play** blog carnival, please leave a comment below or email me directly.

*[Photo by bumeister1 via flickr.]*

### LEGAL FOOTNOTE

Common Core Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

The NGA Center for Best Practices (NGA Center) and the Council of Chief State School Officers (CCSSO) hereby grant a limited, non-exclusive, royalty-free license to copy, publish, distribute, and display the Common Core State Standards for purposes that support the Common Core State Standards Initiative. These uses may involve the Common Core State Standards as a whole or selected excerpts or portions.

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