Playful Math Snacks: Proofs Without Words

From Denise:

The July “Let’s Play Math” newsletter went out yesterday to everyone who signed up for Tabletop Academy Press math updates. This month’s issue focuses on math proofs without words. What fun!

If you’re not on the mailing list, you can still join in the play:

And remember: Newsletter subscribers are always the first to hear about new books, revisions, and sales or other promotions.

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sloyd square

Math Snack: Proofs Without Words
Playful, no-preparation math activities for all ages

Our first proof is a diagram from Paper Sloyd. Fold a square in half diagonally, both ways. Unfold. What do you see? Can you say anything about the shapes, lines, or angles? How do you know? Now, fold in the four corners of the paper square so they meet at the center. What new relationships can you find?

When using proofs without words, don’t try to force your kids in a particular direction. What I see here is that the tilted square (formed by connecting the midpoints of each side) has exactly half the area of the larger square—‌but your students may find something else. The point is to have a good discussion. Begin with Annie Fetter’s key questions: “What do you notice? What do you wonder?” or similar idea-generators: “What is going on? Have you seen something like this before? Are there other ways of looking at it?”

Here’s another picture with squares…


Playful Math Snacks for May 2015

From Denise:

The May “Let’s Play Math” newsletter went out Monday morning to everyone who signed up for Tabletop Academy Press math updates. This month’s issue focuses on math games for all ages. What fun!

If you’re not on the mailing list, you can still join in the play:

And remember: Newsletter subscribers are always the first to hear about new books, revisions, and sales or other promotions.

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Math Snack: Two Math Games
Playful, no-preparation math activities for all ages

Math games pump up mental muscle, reduce the fear of failure, and develop a positive attitude toward mathematics. Through playful interaction, games strengthen a child’s intuitive understanding of numbers and build problem-solving strategies. Mastering a math game can be hard work, but kids do it willingly because it is fun.

The easiest no-prep strategy game for all ages is the finger game Chopsticks. You don’t need any equipment, so it’s a great game to keep in mind for when you and your kids are stuck in a line or waiting room. Math concepts: counting up to five, thinking ahead.

And one of my all-time favorite games is…


Playful Math Snacks for April 2015

From Denise:

AprilMathCalendar

The April “Let’s Play Math” newsletter went out Monday morning to everyone who signed up for Tabletop Academy Press math updates. If you’re not on the mailing list, you can still join in the fun:

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Math Snack: Math Treks
Playful, no-preparation math activities for all ages

Created by Maria Droujkova, a Math Trek is a “virtual reality” game, played at the intersection between the real world and your imagination. Participants explore their towns and communities, start noticing mathematics everywhere, and grow their math eyes.

Math Treks are like scavenger hunts for math. Gather a group of friends, choose a topic, and go for a walk to see how much math you can find. Take pictures to share and compare. My math club families have enjoyed a Multiplication Trek (looking for things in groups and arrays) around our local library and a Symmetry Trek through the woods.

If you have time for a little preparation, Maria posted several Math Trek game sheets you can download and print. …


Playful Math Snacks for March 2015

From Denise:

The March “Let’s Play Math” newsletter went out this morning to everyone who signed up for Tabletop Academy Press math updates. If you’re not on the mailing list, you can still join in the fun:

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Math Snack: Why Pi?

Photo by KaCey97078 (CC BY 2.0) via Flickr.
Photo by KaCey97078 (CC BY 2.0) via Flickr.

In math, symmetry is beautiful, and the most completely symmetric object in the (Euclidean) mathematical plane is the circle. No matter how you turn it, expand it, or shrink it, the circle remains essentially the same. Every circle you can imagine is the exact image of every other circle there is.

This is not true of other shapes. A rectangle may be short or tall. An ellipse may be fat or slim. A triangle may be squat, or stand up right, or lean off at a drunken angle. But circles are all the same, except for magnification. A circle three inches across is a perfect, point-for-point copy of a circle three miles across, or three millimeters…


Playful Math Snacks for February 2015

From Denise:

The February “Let’s Play Math” newsletter went out this morning to everyone who signed up for math updates. If you’re not on the mailing list, you can still join in the fun:

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by Ξ at 360 blog
by Ξ at 360 blog

Math Snack: Fractal Valentines

What better way to say “I love you forever!” than with a pop-up fractal Valentine? My math club kids made these a couple years back, and they turned out great.

To make your card, choose two colors of construction paper or card stock. One color will make the pop-up hearts on the inside of your card. The other color will be the front and back of the card, and will also peek through the cut areas between the hearts. Fold the papers in half and cut them to card size.

Set the outer card aside and focus on the inside. The fractal cutting pattern is simple: press the fold, cut a curve, tuck inside, repeat…


Playful Math Snacks for January 2015

Denise author colorFrom Denise:

I just sent out my first newsletter to everyone who signed up for math updates. If you’re not on the mailing list, you can still join in the fun:

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Math Snack: Calendar Patterns
Playful, no-preparation math activities for all ages

A new year is a great time to investigate patterns on the calendar. If you don’t have a printable planner, then download your favorite calendar style. Let’s play…

Young children can use the calendar as a number line to do addition and subtraction beyond what they might normally handle. Look for addition and subtraction patterns. 3+5=? Now go to 13+5, and 23+5. What do you notice? What do 11-7, 21-7, and 31-7 have in common? Take turns finding and describing patterns.

Older children can practice their times tables. Mark the numbers you hit when you count by 2. What pattern do they make? Make the counting-by-3 pattern, or mark the 7s, etc. Which counting-by patterns are your favorites? What happens if you start at a weird number, like counting by 6s but starting at 5?

Try some of Cynthia Lanius’s algebra calendar puzzles. Can you explain why they work? What other patterns can you discover?


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