# Math Teachers at Play #52

[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

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

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

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

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.

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

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

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.

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.]