## 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?