Monday, May 2, 2016

Connecting Math and Art to Teach Multiplication

In October of 2011, one of my students, now a highly successful classroom teacher, created an annotated bibliography on connecting math and art in the teaching of multiplication. I've updated that information and included a number of new resources. My thanks to Christine Mingus for the original post.
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In the interest of finding new and artful ways to help teach children about multiplication, this post highlights resources that use art to enhance math instruction, increase student motivation and engagement, and help students tap into fun and creative ways to think about math concepts.

Visual learners, and even ELL students, benefit from making projects that allow them to explore mathematical concepts in new ways -- and art is all about looking at the world from multiple perspectives.  Art simply feels like play for elementary aged students, and using it to explore multiples and place value helps foster their confidence in their math abilities and definitely works to keep a multiplication lesson percolating.  Many children see art as a non-threatening subject matter, and using it to ground a lesson is a great way to generate ideas and excitement among your young mathematicians.  Getting them to see the visual and creative aspects of math can go a long way in teaching the algorithms of multiplication and can create a lot of math-positive, math-rich dialog in the process.

In third grade, students begin to explore basic multiplication by utilizing strategies, algorithms, and appropriate methods of computation.  As they progress beyond simpler whole number operations into this new realm of mathematical thinking (learning the multiplication tables through the twelves), art can lead the way and ease the transition into higher level reasoning and problem-solving.

Web Resources
Artful Connections With Math: Multiplication Array Prints -  In this lesson, students explore positive and negative space and create a stamp on top of a watercolor wash. They repeatedly print the stamp as an array representing a fact family of multiplication and division number sentences. The video below provides additional information about this lesson.

Multiplication City Art - See how one teachers helps her students learn array multiplication by creating city blocks where the buildings are created by differing arrays of windows.

Art Inspired Math - This brief article by Michael Naylor describes some activities that will get students looking for mathematics in artwork and also creating their own artwork to show off geometric ideas.

Fooling Around With Math and Art - Here's a description of an interesting art project that morphed into a cool way to look at array multiplication.

Origami Multiplication Flash Cards - If cootie catchers aren't your thing, you may want to make these basic origami shapes and encourage your students to do the same.  These are found on Rick Morris's New Management website, and you can use them with his multiplication triangle tests (downloadable as a PDF file at the bottom). 

Math Art: Hands-On Math Activities for Grades 2, 3, and 4 - This is the web page that accompanies Zachary Brewer's book (see below).  Here you will find pictures and descriptions of various projects throughout the book, including his lesson on common multiples and his lesson on multiplication arrays.

String Art and Math:  A Project in Multiplication - While I normally associate string art with bad 1970s home decor, I think this is a really interesting way to play artfully with multiplication.  Instead of using nails to create the string art, students will have to be advanced enough to know how to use embroidery thread and needles to pull the thread through cardstock printed with the design template.  This could be a good art/math center activity for those students with strong fine motor skills, and could produce very colorful work for display in the classroom.  (The sample worksheet is downloadable as a PDF file at the bottom of the page.)

National Gallery of Art:  NGA Kids - While this is just a wonderful arts site for kids to create their own artistic compositions, you can bookmark this at your classroom computer center and invite students to create online works that demonstrate multiplication concepts.  Basic multiplication can be expressed through art through image repetition, and here kids can try all kinds of cool programs: BRUSHTER (an interactive painting machine); NGAkids Photo Op (an introduction to digital photography and image editing); the Collage Machine; Mobile Maker; FLOW (a remarkable interactive motion painting program); and Wallovers (which uses a 6 x 4 grid for students to create symmetrical compositions and can reinforce the interrelatedness between multiplication and addition).  Students can create the multiplication masterpieces and then write out what kinds of images are multiplied in their work (and express them as equations).  

Books for Teachers

Mathematical ART-O-Facts: Activities to Introduce, Reinforce, or Asses Geometry & Measurement Skills by Catherine Johns Kuhns. (2008). Crystal Springs Books (978-1934026113). Gr. 3-6.

This book contains 22 different math activities focused on geometry and measurement, though multiplication and division concepts can be found woven throughout the lessons. Fun and engaging, all of these activities promote mathematical thinking and creativity through problem solving.


Math Art:  Hands-On Math Activities for Grades 2, 3, and 4 by Zachary J. Brewer.  (2010).  Create Space (1453636439).  Gr. 2 - 4.

This book shows you how to successfully integrate arts into any elementary math curriculum. Each of the math activities ultimately result in an aesthetically-pleasing project that reinforces a basic math concept.  Inside are two great projects to help teach multiplication to third grade students:  a project about multiples (p. 14 - 17), which demonstrates how to skip count and how to tell the difference between common and uncommon multiples, and another that shows how to represent multiplication facts as arrays (p. 26 - 27).  All the lessons list teaching objectives, what materials are required, full project descriptions, and black line masters of reproducible assessment sheets (which require students to explain their mathematical thinking in writing).

Comic-Strip Math:  Problem Solving: 80 Reproducible Cartoons with Dozens and Dozens of Story Problems That Motivate Students and Build Essential Math Skills by Dan Greenberg.  (2010).  Scholastic Teaching Resources (0545195713).  Gr. 3-6.

This is such a brilliant idea - what a fantastic way to blend art, math, reading,and writing.  Using comics to explore math encourages students to use their visual, verbal, spatial, and logic skills in interpreting situations.  While most of the multiplication exercises in the book incorporate multi-step problems (some of which also ask children to take the next step into division), there is a nice section in the book with lots of fun activities for them to solve (p. 12 - 19).  Each lesson features a comic at the top, which concludes with a "figure it out" question, and then the follow-up questions listed below take on a more-familiar worksheet format.  There are "super challenges" at the bottom of each page to help students extend what they've learned and some encourage them to create their own pictures, diagrams, charts and models.  Consider setting up a math/art center for students to make their own multiplication comic strips. You could use graph paper to help them better design the more traditional story-board layout, or take larger paper and fold it to create frames for students to draw in. Encouraging them to think about and ask multiplication problems through art and humor and then asking them to share them with classmates could be incredibly fun for everyone.

MathART Projects and Activities by Carolyn Ford Brunetto.  (1999).  Scholastic Teaching Resources (0590963716).  Gr. 3 - 5.

This book is full of good ways to connect math to simple art projects, and inside there are two very fun multiplication projects:  multiplication constellations (p. 38 -41), and my favorite idea, multiplication houses to reinforce basic multiplication facts for numbers 1 to 12 (p. 40 - 41).  Using the template, students can create their houses - or if you are more artistically inclined, you can encourage them to create their own houses (or skyscrapers, or other buildings).  For example, if a student creates the house of nine, the number 9 would be written on the door. The numbers 1 to 12 would be written on the house's twelve windows. When you open the window to any given number, you see the product of nine and that number revealed.  Creating these houses for kids to use as lesson guides would be very enjoyable, and if you made large ones for your classroom, you could create your own Multiplication Neighborhood that your students could look at for review.  

Quick and Easy Math Art:  Dozens of Engaging Art Activities That Build and Reinforce Essential Math Skills and Concepts by Deborah Schecter. (2011). Scholastic Teaching Resources (0439199425).  Gr. 2 - 4.  

Here is another great art-math resource offered by Scholastic, chock full of great, inexpensive, and simple projects that anyone can do.  There are a number of very cute multiplication activities (p. 14 - 22):  Be Mine! Multiplication (which you can see in color on the cover of the book), Multiplication Menageries, Fall Factor Trees, and Teeny-Tiny Times Table Books.  The author makes it clear that educators should test out these projects before introducing them to the class - as any art teacher can tell you, figuring out how to do them on your own first can help you determine exactly how you need to model instruction, what steps are important to emphasize, and will help you figure out how complicated (and possibly time consuming) it is going to be.  Many of these multiplication projects would be suitable to use at math centers. 

Monday, February 1, 2016

Connecting the Curriculum - Feathers

Each semester I teach a course entitled Content and Pedagogy for Science and Social Studies. While we focus on best practices for instruction, we also focus on subject specific methods. In the introductory weeks we look at a wide range of texts and I model how they can be used in science and social studies instruction.

I love this class, but it's sometimes hard to convince my students that these subjects can play nicely together. (I'll admit this isn't ideal. I'd love a course devoted to each of the subjects.) Since my class focuses on two seemingly unrelated curricular areas, I thought that this would be a good time to start a new series of posts that highlights the ways in which they can be connected.

I'm launching this series today with the theme of FEATHERS.

Feathers are a unique physical adaptation found only in birds. But what are they? What are they used for? You'll find these answers and much more in this terrific informational book.
written by Melissa Stewart and illustrated by Sarah S. Brannen

Melissa has a Pinterest board with lots of teaching ideas and resources for using the book in the classroom. You'll also find a Teacher's Guide on her web site, as well as a Readers Theater script, math activity, and more.

You can pair Melissa's book with this podcast from BirdNote. This just-under two minute segment describes how down feathers serve to keep bird's warm (insulate them) in very cold weather.

This podcast mentions how "People learned years ago how well goose-down insulates and began stuffing comforters, sleeping bags, and clothing with it." This use of feathers as a natural resource provides a connection to economics and another book.
written by Carmen Agra Deedy and illustrated by Laura Seeley

In this story, Agatha explains to a young boy visiting her shop that “everything comes from something”—silk from silkworms, cotton from cotton bolls, wool from sheep, and linen from flax. She tells him:
"Everything comes from something,
 Nothing comes from nothing.
 Just like paper comes from trees,
 And glass comes from sand,
 An answer comes from a question.
 All you have to do is ask."
That evening, a group of naked geese wake her from her sleep and remind her that “everything comes from something,” and that her new feather bed is made from their feathers. (Please note that I am not endorsing the use of down, just highlighting it as a historically accurate use of a natural resource. Please read Can Down Be Ethical or Green to learn about ethical options to down feathers. )

Peachtree Publishing has a helpful Teacher's Guide for this book.
KidsEconPosters has a page on the book that explores how it can be used to teach economics concepts that include natural resources, goods & services, economic wants, productive resources, capital resources, and human resources.
You might want to consider making an "Everything Comes From Something" resource kit so students can see the natural resources used to make everyday items. You can also try this lesson from Virginia's Ag in the Classroom program entitled Resource Round-Up.

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There you have it, feathers as a theme for connecting science and social studies. I hope you found this helpful. If you have ideas or resources to contribute, please share them in the comments. I'll be back next week with another post on Connecting the Curriculum.


Saturday, January 23, 2016

Teaching for Conceptual Understanding

My math classes focus on teaching math for understanding, not rote memorization of processes. For sure knowing basic facts and how to compute is important, but understanding strategies and why procedures work is just as valuable.

In the post 5 Tips To Help Students Develop Conceptual Understanding In Math, Crystal Morey describes her approach to inquiry-based instruction and the ways in which she develops students' conceptual understanding.

This quote highlights one problem teachers using this approach run into.
"Since I’ve begun to focus on the development of conceptual understanding, I’ve run into some challenges. Students and parents alike want me to teach short cuts and algorithms. Yet, when I hear students talking and thinking mathematically, I’m certain that this struggle will prepare them to be risk-takers, not only in my classroom but in their daily lives, too."
It's a post worth reading. You can also see her in action teaching students about inequalities, with a focus on concepts FIRST and notation last.


Click on the video title to be taken to Teaching Channel for a transcript of the lesson, copy of the lesson plan, and more.

Monday, January 18, 2016

What Color Were Dinosaurs?

Based on fossil evidence, how can scientists know what color dinosaurs were? In this TEDEd lesson, Len Bloch shows how making sense of the evidence requires careful examination of the fossil and a good understanding of the physics of light and color.

In this terrific video you'll learn a bit about the microraptor, a four-winged carnivorous dinosaur with iridescent black feathers, as well as the work that scientists do in determining how dinosaurs actually looked.
You can find more resources at How Do We Know What Color Dinosaurs Were?

Friday, September 25, 2015

Books for Math Storytelling Day

September 25th is Math Storytelling Day. Today (every day!) is the perfect opportunity to encourage and nurture the love of mathematics through reading about math. There are many terrific books that include mathematical content or challenging puzzles to solve. Here are some titles that will encourage children to stretch their mathematical muscles in a different way.

The Phantom Tollbooth by Norton Juster - Take a journey with Milo, a young boy who drives through a magic tollbooth into the Lands Beyond and embarks on a quest to rescue the maidens Rhyme and Reason from exile and reconcile the estranged kingdoms of Dictionopolis and Digitopolis. This is a great book for kids enamored of words and/or numbers.

Grandfather Tang's Story: A Tale Told With Tangrams by Ann Tompert and The Warlord's Puzzle by Virginia Pilegard are both stories that revolve around an ancient Chinese puzzle made from a large square cut into seven pieces. The seven shapes include a small square, two small triangles, a medium-sized triangle, two large triangles and a parallelogram. Kids can read the stories and follow along with their own set of tangrams!

The Number Devil: A Mathematical Adventure by Hans Magnus Enzensberger - With full color illustrations, this book tells the story of a twelve year old boy and math hater named Robert, who meets the Number Devil in his dreams. Over  the course of twelve nights, the Number Devil illustrates different mathematical ideas using things like coconuts and furry calculators. Along the way he also takes Robert to Number Paradise where he meets different mathematicians.

Chasing Vermeer by Blue Balliett - Petra and Calder are preoccupied with Vermeer. When a Vermeer painting is stolen in transit from the National Gallery in Washington D.C. to the Chicago Institute of Art, they become intent on finding the painting and solving the mystery. Clues and mysteries abound.
  • Calder carries a set of pentominoes in his pocket at all times, so be sure to print your own set to use while reading this one!
  • Play pentominoes online.
  • Learn more about the book, the author, and the other books in the series at the Scholastic site
Brown Paper School Math Books by Marilyn Burns - Don't let the publication dates fool you into thinking these are out of date (one was first published in 1975!). These are great books for helping kids see that math is fun and for everyone.

The Book of Think: Or How to Solve a Problem Twice Your Size
The I Hate Mathematics! Book
Math for Smarty Pants

The Mysterious Benedict Society by Trenton Lee Stewart - Eleven year-old Reynie Muldoon is intrigued by an ad in the paper that asks “Are You a Gifted Child looking for Special Opportunities?” Reynie and dozens of other children show up to answer the ad and take a mind-boggling series of tests, but only Reynie and three others are left at the end. Puzzles and mysteries abound in this adventurous tale. Sequels include The Mysterious Benedict Society and the Perilous Journey and The Mysterious Benedict Society and the Prisoner's Dilemma.

Books by Greg Tang - Greg Tang has written a series of books that encourage children to look for patterns in math and find more "economical" ways of solving problems.

The Best of Times: Math Strategies That Multiply
Grapes of Math: Mind Stretching Math Riddles
Math Appeal
Math Fables: Lessons That Count
Math Fables Too: Making Science Count
Math for All Seasons: Mind-Stretching Math Riddles
Math Potatoes: More Mind-Stretching Brain Food
Math-terpieces
    The Man Who Counted: A Collection of Mathematical Adventures by Malba Tahan - Orginally published in 1949 as O Homem que Calculava, this book of mathematical puzzles was written by Júlio César de Mello e Souza and published under the pen name Malba Tahan.  The book is an enjoyable  series  of "Arabian nights"-style tales, with each story built around a classic mathematical puzzle. In each tale, Beremiz Samir uses his mathematical powers to "settle disputes, give wise advice, overcome dangerous enemies, and win for himself fame and fortune."

    The Puzzling World of Winston Breen by Eric Berlin - Winston sees puzzles everywhere. Imagine his dismay when he gives his sister a box for her birthday, only to learn that it has a secret compartment containing four wood sticks with puzzle clues. Readers will solve puzzles right along with Winston and his sister Katie as they try to solve the mystery. The sequel to this book, The Potato Chip Puzzles, is also highly entertaining.

    Books by Theoni Pappas - Written in the same vein as the Brown Paper School Books, Pappas has written many books about math, my favorites of which are those where a cat explores the math in and around his house.

    The Adventures of Penrose the Mathematical Cat
    Further Adventures of Penrose the Mathematical Cat

      The Origami Master by Nathaniel Lachenmeyer, Lissy's Friends by Grace Lin (picture books), and Fold Me a Poem by Kristine O'Connell George (poetry) are all books about origami. Paper folding is a great visual and spatial puzzler for kids and adults. It's also fun!

      Do the Math: Secrets, Lies, and Algebra by Wendy Lichtman - Tess is an eighth grade girl experiencing typical middle school problems--friends breaking promises, peers cheating on tests, the boy that may-or-may not be interested--as well negotiating some drama at home. Tess examines everything logically and views her world through the lens of mathematics.
      "The way Sammy spoke about her mother made me think of what Venn diagrams look like when the two sets have nothing in common--like, for example, the set of odd numbers and the set of even numbers. Their intersection is called an empty set, because there's nothing in it. There's not one number that can be both odd and even. I didn't like thinking of Sammy and her mother like that--like an empty set." (p.49)
      While the book isn't necessarily about math, Tess has many interesting mathematical insights and how they relate to the world we live in. 

      That's it for now. Do you have a favorite book that offers something mathematical to puzzle over? If so, please share. I would love to add your ideas to this list.

      Thursday, September 24, 2015

      The Science of Story Time

      Last week on Science Friday there was a segment entitled The Science of Story Time. While it begins with a discussion of a study that shows reading with kids has positive effects ranging from increased vocabulary to greater success reading independently, it ends with experts and callers sharing favorite books for science-curious kids.

      Visit the Science Friday site for a list of books discussed.

      Monday, September 14, 2015

      Informal, Math-Rich Experiences - The Richmond Math Salon

      This is an old (2010) video, but I keep returning to it because I love the notion of a math salon. 
      A while back I wrote a post describing the components of elementary school homework I believed were important. Here's a description of one of those components.
      Puzzle - When was the last time you sat down to solve a puzzle and did it for fun? I do this all the time. Sudoku, crossword puzzles, jigsaw puzzles, logic problems, tangrams ... I could go on. Puzzles are good for the brain. They develop critical thinking and problem solving skills. They teach kids to persevere, guess and check, collaborate with others, and try a whole host of new strategies. Can you think of a better training ground for mathematical thinking than puzzling? Now imagine if your teacher encouraged you to do this for homework. 
      This is exactly the kind of think happening in this math salon--kids exploring ideas in meaningful ways that just happen to touch on aspects of mathematical thinking. Just imagine what you could do with this idea in a classroom.

      You can read more on my views about homework in the post entitled Elementary School Homework and Reading in Math and Science.