Welcome to the 144th edition of the Playful Math Education Blog Carnival — a smorgasbord of delectable tidbits of mathy fun. It’s like a free online magazine devoted to learning, teaching, and playing around with math from preschool to high school.

Bookmark this post, so you can take your time browsing.

There’s so much playful math to enjoy!

By tradition, we would start the carnival with a puzzle/activity in honor of our 144th edition. But this time, I want to take a peek back at the history of our carnival.

For children, learning always begins with play. This is how they wrap their minds around new ideas and make them their own.

“There should be no element of slavery in learning. Enforced exercise does no harm to the body, but enforced learning will not stay in the mind. So avoid compulsion, and let your children’s lessons take the form of play.”

—Plato, The Republic

If we want our children to enjoy learning math, our first job is to establish an attitude of playfulness.

This is especially important for anyone working with a discouraged child or a child who is afraid of math. The best way to help a discouraged child is to put away the workbook. Try something different, fun, and challenging.

Far too many people find themselves suddenly, unexpectedly homeschooling their children. This prompts me to consider what advice I might offer after more than three decades of teaching kids at home.

Through my decades of homeschooling five kids, we lived by two rules:

Do math. Do reading.

As long as we hit those two topics each day, I knew the kids would be fine. Do some sort of mathematical game or activity. Read something from that big stack of books we collected at the library.

Conquer the basics of math and reading, then everything else will fall into place.

“What is the best curriculum for my children? They are four and six years old, and I’m afraid of letting them fall behind.”

I remember being a young parent, eager to start homeschooling. I used to get mad (without letting it show, like a true introvert) when people told me, “They are young. Just let them play.”

Now I see the wisdom in it.

The most important thing for your children right now, by far, is for them to enjoy learning. The joy of learning is a child’s natural state. As a parent, your primary job is to keep yourself from stomping it out.

But our parental fears can push us into joy-trampling before we realize it.

And our own experience of school makes it hard for us to see how much of our children’s play really is learning. We expect education to look like schoolwork, but natural learning looks nothing like that.

One of the most common questions I get from parents who want to help their children enjoy math is, “Where do we start?”

My favorite answer: “Play games!”

And in this time of pandemic crisis, it’s even more important for families to play together. So my publisher agreed to make my ebook Let’s Play Math Sampler: 10 Family-Favorite Games for Learning Math Through Play free for the duration.

Math Concepts: number symbols, numerical order, thinking ahead. Players: two or more. Equipment: one math deck of playing cards (remove face cards and jokers), or a double deck for more than four players; additional cards to use as train cars.

Set-Up

Give each player four to six miscellaneous cards (such as the face cards and jokers you removed from the card deck) to serve as the cars of their number trains.

Lay these cards face down in a horizontal row, as shown. Shuffle the math card deck and spread it on the table as a fishing pond.

How to Play

On your turn, draw one card and play it face up on one of your train cars. The numbers on your train must increase from left to right, but they do not need to be in consecutive order. If you do not have an appropriate blank place for your card, you have two choices:

• Mix the new card back into the fishing pond.

• Use the new number to replace one of your other cards, and then discard the old one.

The first player to complete a train of numbers that increases from left to right wins the game.

Variations

House Rule: Decide how strict you will be about the “increases from left to right” rule and repeated numbers. Does “1, 3, 3, 7, 8” count as a valid number train? Or will the player have to keep trying for a card to replace one of the threes?

For older players: You can adapt Number Train to play with more advanced students:

It’s a short book with plenty of great stories, advice, and conversation-starters. While Danielson writes directly to parents, the book will also interest grandparents, aunts & uncles, teachers, and anyone else who wants to help children notice and think about math in daily life.

“You don’t need special skills to do this. If you can read with your kids, then you can talk math with them. You can support and encourage their developing mathematical minds.

“You don’t need to love math. You don’t need to have been particularly successful in school mathematics. You just need to notice when your children are being curious about math, and you need some ideas for turning that curiosity into a conversation.

“In nearly all circumstances, our conversations grow organically out of our everyday activity. We have not scheduled “talking math time” in our household. Instead, we talk about these things when it seems natural to do so, when the things we are doing (reading books, making lunch, riding in the car, etc) bump up against important mathematical ideas.

“The dialogues in this book are intended to open your eyes to these opportunities in your own family’s life.”

Today we have a guest post from Lucy Ravitch, author of the new Kickstarter picture book Trouble with Monkeys: A math concept story of place value. She’s sharing a few ideas from her Math Activity Thursday (M.a.Th.) video series. Enjoy!

Hello, math fans and enthusiasts! Each week I try to give you and your family a fun math activity to try. Two months ago I posted this video with ten ways to turn play dough into an engaging activity for lower and upper elementary math.

If you want to make your own dough from scratch here are a few simple recipes. I encourage you to let your children play freely at first, before trying these activities.

Below I have identified some of the math concepts that your kids will experience as they play.

1. Toss It

Practice counting. With older children, record your results and make a graph of the data.

How many times can you catch it in a row? What’s your average number of tosses?

Talk about attributes. Does the size or color of the play dough balls make a difference?

How high are you tossing it? Talk about measuring systems. Do you use feet and inches, or meters and centimeters?

If you know how to juggle, time how long you can keep the balls going.

2. Smash It

Make several small balls or pieces. Then play as you smash them.

Play a NIM game: Make 10-15 small play dough balls. Take turns. On your turn, you can smash one ball or two. Whoever smashes the last ball wins the game.

Or smash your math facts: Choose several equations for your children to practice. Write each answer on a 3×5 card. Lay out each card next to a play dough piece. As you call out the equations, kids smash the play dough next to the correct card.

3. Shape It

Have fun molding your play dough. Roll it out to cut shapes.

Try making 3D shapes while practicing your math vocabulary. MathisFun.com has a great section about solid geometry. Can you find three math terms that are new for you?

Roll out the dough and cut 2D shapes. Discuss their attributes. Can you cut your shape in half to be symmetrical?

4. Hide Things in It

Find small objects around the house and enclose them inside play dough.

Take turns hiding small objects in play dough. Optional: Give a one-minute time limit to guess before opening it. This gives you and your kids a chance to talk about size, shape, or other attributes.

Have challenges to use the least amount of dough to hide identical objects. Two players have two minutes to hide an object in as little play dough as possible. The object must be completely concealed within the dough. What methods will you use?

5. Make Imprints on It

Show off your design skills and observe textures.

You can practice counting as you poke and press your fingers or objects into the dough. Older children can discuss the distance between impressions and/or the pressure applied.

As you and your kids make designs, talk about what you notice: Is your design symmetrical? What tools did you use (toothpicks, pencils, marbles, fingers, toy cars)? Which objects make interesting textures?

6. Cut It

Use a butter knife or the edge of a ruler to cut your play dough. Discuss findings as you play and explore.

In the video, I posed the question: how many sections do you get if you make only three cuts? Try it and see.

Does the number of pieces change if you use a shape other than a flat circle?

Discuss making straight cuts that will intersect or be parallel. Bring in more geometry terms.

Experiment with a different number of cuts.

7. Weigh It

Pull out a kitchen scale or balancing scales to use with dough.

Older children can make conversions between ounces to grams. They can make calculations about doubling or multiplying the measured weight. With younger kids, try using balancing scales. Compare the weights between pieces.

Try making two pieces that weigh exactly the same. This is harder than it sounds! For small children, this gives them the opportunity to see that the mass (weight) of an object can come in different shapes.

8. Measure It

Use a ruler or measuring tape while you play. There are several ways you can measure your dough — height, width, and length.

How long can you extend one ounce of dough? Pick your own size/weight of play dough and see who can get the longest. What fraction of a yard or meter is it?

Discuss height and what it takes to make dough stand vertically. How tall can you get three ounces to stand? Can anything help make it taller?

9. Roll It

Make sure you have plenty of room for this activity. Playing outside or on smooth floors works best.

With one push how far does your play dough roll? Is there an ideal size for a piece? Is there an ideal weight for rolling?

Is the ground sloped? What effects does the rolling surface have?

Why do some shapes roll easily while others don’t? Can you create a not-round shape that will roll?

10. Compare It

Compare similarities and differences between dough colors and types. Consider comparing the previously listed activities

If you made your own dough, compare consistency between batches. Is homemade dough denser or lighter than store-bought dough?

What are differences between the dough you played with and the dough that has not been touched?

Which of these activities do you think will take the shortest amount of time? The longest? Or put the activities in order based on how much dough you will need — least to greatest.

May you and your students have fun as you play with dough!

About the Author

Lucy blogs at kidsmathteacher.com and is the author/creator of Kids Menu Books. The first book in that series is The Pancake Menu, an interactive book that lets kids practice math as they play restaurant.

And be sure to visit Lucy’s Kickstarter project! She’s teamed up with artist Trav Hanson to create the delightful picture book Trouble with Monkeys: A math concept story of place value.

I love it when a plan — or rather, a series of math thoughts — comes together.

On Monday, Emily Grosvenor (author of the Tessalation! picture book) asked me how parents who are insecure in math could help their children learn through play, and I responded with this quote from my Let’s Play Math book:

If you are intimidated by numbers, you can look for patterns of shape and color. Pay attention to how they grow. Talk about what your children notice.

But I wasn’t entirely satisfied with that answer. So many adults have come away from their own school experience thinking math is only numbers. Even with shapes, isn’t it the numbers about them — how many sides, what size of angles, calculate the the area or perimeter — that are important? That’s what school math tends to focus on.

Those of us who are comfortable with math know that there are many more things to notice and think about than just numbers. We know that it’s this noticing, thinking, and wondering that is at the heart of math. And that just playing with shapes can build a powerful foundation for future math learning.

The ability to create, and maintain, and manipulate shapes mentally — that’s the goal. Just like kids who can put numbers together in their heads, kids who can rotate, flip, and think of how shapes fit together in their heads have a powerful tool to analyze not only simple shape puzzles, but dividing up an area that’s a more complex room shape … to look at a piece of artwork … or look at a building … For these kids, all the world around becomes a playground to use mathematical ideas.

Of course, pattern blocks are good for much more than just filling in worksheet pictures. But I love this peek into how a child’s understanding grows, in bits and spurts — without any numbers at all — until the world itself becomes a playground for mathematical ideas.

Want more?

You know what? Children like mathematics. Children see the world mathematically … When we do a puzzle, when we count things, when we see who’s got more, or who’s taller … Play and mathematics are not on opposite sides of the stage.

You could say that Tessalation is a book about tessellations (repeating tiled patterns), but it is really a children’s picture book about discovering order in a chaotic world.

— Emily Grosvenor

Seeing Math in the World

In taking a playful approach to mathematics, I hope to open children’s eyes to math in their world. Schooly math lessons have led many of my math group kids to think a “pattern” has to be a strictly repeating (and rather boring) series of shapes or colors.

But in the real world, patterns are so important that American mathematician Lynn Arthur Steen defined mathematics as the science of patterns.

“As biology is the science of life and physics the science of energy and matter, so mathematics is the science of patterns,” Steen wrote. “We live in an environment steeped in patterns — patterns of numbers and space, of science and art, of computation and imagination. Patterns permeate the learning of mathematics, beginning when children learn the rhythm of counting and continuing through times tables all the way to fractals and binomial coefficients.”

Tessa Truman-Ling’s delight in patterns is contagious. And it will provide a wonderful jumping-off point for a variety of math activities.

Visit Grosvenor’s Kickstarter page to find out more about her lovely book: