Saturday, March 30, 2013

Math Freebie - Moo-ve It Games (+/x)

Here are two different adaptations of a game I found several years ago on the NC DPI web site

Version 1: Moo-ve It Addition! - In this game players roll two dice, determine the sum, and cover one occurrence of the sum on the game board. Players can bump each other's markers off the board to make room for their own. The first player to get three markers in a row is the winner.

Version 2: Moo-ve It Multiplication! - In this game players roll two dice, determine the product, and cover one occurrence of the product on the game board. Players can bump each other's markers off the board to make room for their own. The first player to get three markers in a row is the winner.

I hope you get a chance to use these in your home or classroom. Please let me know if you try them and how they work! 

Paperless Math Strategies

The blog TeachPaperless began in 2009 as way for a teacher to detail his experience working in a paperless classroom. Then in 2011 it became a "collaboratively written blog dedicated to conversation and commentary about the intertwined worlds of digital technology, new media, and education." While surfing today I read through some interesting posts. Here's one you might like.

The strategies are grouped into before, during and after instruction. Each one also describes the preferred grouping and optional tech tools. There are many terrific ideas here for mental math, vocabulary, critical thinking, and more. If you have some time, do check it out!

Tuesday, March 26, 2013

Decimal Place Value Strips

This week my class is working on pedagogy for teaching fractions and decimals. Tonight we are going to explore decimal place value strips.

In this file you'll find three variations of the strip sets so that you can use them to differentiate. The first form includes the words for place value on the strip (ones, tenths, hundredths, and thousandths). The second form includes numbers to show the value of the digit in a particular place. The third form includes no additional information. Each set includes whole and decimal numbers from ones through thousandths and comes in both color and black and white versions.

Here's a peak at the file.
These strips were designed for use in activities that meet the following Common Core Standards for Math:
4.NF.7. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

5.NBT.3. Read, write, and compare decimals to thousandths.
  • a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). 
  • b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 
5.NBT.4. Use place value understanding to round decimals to any place.

I hope you get a chance to use these in your home or classroom. Please let me know if you try them and how they work! 

Monday, March 25, 2013

Monday Freebies - Vocabulary Booklets

Classroom Freebies Manic Monday
I've been working on interactive notebooks with my students over the last few semesters. In thinking about how they might be used in the classroom, we spend quite a bit of time talking about strategies for vocabulary.

I thought it might be fun to create some strip booklets for students to use in math or science, either over the course of the year or for each major unit of instruction. Each booklet includes pages identified by letter of the alphabet. Most letters are given a single page, but the pages for Q/R, U/V, W/X, and Y/Z are shared. On each page there is a space for the word, a picture, and definition.
Here's what they look like.

I hope you get a chance to use these in your home or classroom. Please let me know if you try them and how they work!

BTW, if you're looking for strategy ideas for teaching academic vocabulary, here are a few resources I like.

Monday, March 18, 2013

Monday Math Freebie - Place Value Game

Classroom Freebies Manic Monday
Today I have two versions of a game designed to help students understand how the position of a digit in a number changes its value. In each version of the game students roll dice and determine whether the numbers rolled will be used to make tens or ones. The goal is to be the player closest to 100 at the end of five rounds.

Here are a few pictures.

This activity meets the following Common Core Standards for Math.
1.NBT.2 - Understand that the two digits of a two-digit number represent amounts of tens and ones.

1.NBT.4 - Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

Download Closest to 100.

I hope you get a chance to use these in your home or classroom. Please let me know if you try these and how they work! 

Thursday, March 14, 2013

A Visual for Pi Day

Pi Day is Today!

Photo © Mykl Roventine.

Today, March 14th, is Pi Day. No, that's not a typo. It is Pi day, as in 3.14159... you get the idea. The first Pi Day celebration was held at the San Francisco Exploratorium in 1988.

What is pi anyway? I'm sure you remember it from math in some formula you memorized, but do you really know what it is? Pi represents the relationship between a circle’s diameter (its width) and its circumference (the distance around the circle). Pi is always the same number, no matter the circle you use to compute it. In school we generally approximate pi to 3.14 in school, but professionals often use more decimal places and extend the number to 3.14159.

One activity I loved doing with students was to ask them to bring in a can and lid that would soon be recycled. I always brought in a few extras so that there would be a variety of sizes. Each student was given a lid and directed to measure the diameter and circumference. Students then divided the circumference by the diameter. We recorded the results on the overhead and discussed them. Most were amazed to find that the results were nearly the same, allowing for some margin of error in measurement. This is a quick and fun and provides a meaningful way to introduce the concept of pi.

Are you doing anything special for Pi Day? Perhaps you could make a pi necklace or a pi bracelet. Can you find your birthday in pi? My birthday begins with digit number 7669! Since any day is a good day for poetry, you could try reading some pi poems. If you're looking for more ideas, visit the Exploratorium pi site or try this middle school math newsletter.

Learn more about pi at Ask Dr. Math FAQ: About Pi.

Not a fan of pi? Check out my post entitled Pi Day is Tomorrow! But Should We Celebrate It? for a bit of information on the pi/tau wars.

Monday, March 11, 2013

Monday Math Freebie - Multiplication BUMP!

Classroom Freebies Manic Monday
My class has just finished multiplication and division. Here's a set of BUMP boards I made to practice basic facts. You'll find boards for facts from 1-12. Students roll a 10-sided die and then multiply by the factor on the board.

There are two versions available. They are both pictured below.

If you don't have 10-sided dice, you can download a really nice set of dice templates from the Twinkl web site. Please note that you must sign up for a free account to download.

If you prefer to use spinners instead of dice, here is a set of 1-10 number spinners. In this file you'll find one large spinner, two medium-sized spinners, and four small spinners.
Download 1-10 Spinners.

I hope you get a chance to use these in your home or classroom. Please let me know if you try these and how they work! 

Thursday, March 7, 2013

Two Great Finds for Interactive Whiteboards

Don't you love the way you stumble across things you aren't expecting while searching the web? While looking for dice nets today I came across two sites that will be great for use on interactive whiteboards.

Sign up for a free account to access a random student name generator, score board, dart board selector, timer, and more!

What interesting resources have you stumbled upon lately?

Wednesday, March 6, 2013

Encouraging A Love of Math

Encouraging and nurturing the love of mathematics can be a challenge both at home and in the classroom. Here are some of the things I do to support reluctant math lovers of all ages.

By puzzles I mean not only logic puzzles and Sudoku, but jigsaw and geometric puzzles. Jigsaw puzzles help develop skills in orientation and visual discrimination. Geometric puzzles also help students to think deeply about the orientation of shapes in space and how they can be put together to make new shapes. Here are some of the puzzles I like to provide.
  • Tangrams - Tangrams are 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. The linked site provides a good description of tangrams. When I use these I actually solve the puzzles, trace the outline of the finished shape on cardstock, and then laminate. For younger students, these outline shapes help them fit the pieces into the puzzle. Once students are comfortable with using them, I use the shapes to teach areafractions and angle measure. Try them out online at Cyberchase Math Games. Then fold your own set or print a set and try to build some shapes. You can also print some tangram puzzles as well as shape outlines for young children. Here's another good resource.

    You can pair this puzzle with the books Grandfather Tang's Story: A Tale Told With Tangrams by Ann Tompert and The Warlord's Puzzle by Virginia Pilegard. Both are stories that use tangrams in a way that encourages kids to build along with their own set of tangrams as they read.

  • Pentominoes - A pentomino is a polyomino composed of five congruent squares connected edge to edge. Can't picture them? Look to the right. You can download a set of your own or try out this terrific starter activity online. Since the area of all twelve pieces equals sixty squares, a challenging puzzle is to try and cover a 6×10 rectangle. Pieces can be flipped and rotated, but this isn't as easy as it seems, and that's surprising given that there are actually more than 2000 solutions! Students can then try to fill rectangles of similar areas (5x12, 4x15, and 3x20). I regularly use pentominoes to teach area and perimeter.

    The book Chasing Vermeer by Blue Balliett is filled with pentominoes. When a Vermeer painting is stolen in transit from the National Gallery in Washington D.C. to the Chicago Institute of Art, Petra and Calder become intent on finding the painting and solving the mystery. 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! Learn more about the book, the author, and the other books in the series at the Scholastic site

  • Geometric Puzzles - I own a number of puzzles created by Kate and Dick Jones, owners of Kadon Enterprises. They are all challenging and extremely well made. You can even try some online before you buy. All puzzles come with books explaining the math and offering many variants on play.

You can find more resources for dissection and shape puzzles on my Pinterest board for  Tangram/Pentomino/Shape Puzzles/Mazes.
  • Sudoku - If you like puzzles and numbers and haven't tried sudoku, you're missing out. For kids  just starting out, try a scaled version of the puzzle (4x4, 6x6, etc.) or something more concrete, like a sudoku board. If you want something even more kid-friendly (less abstract) to develop reasoning skills, try a version with pictures. Go ahead and try an online version of Picture Sudoku.

  • Kakuro and KenKen Variations - Whether you try Kakuro or KenKen/Mathdoku, these games all take the basic rules of sudoku and add in the element of calculation. In Kakuro puzzles (also known as Cross Sums) the numbers 1-9 are used in combination with addition. In some vairations multiplication is used. Here's a good basic guide for solving Kakuro puzzles. In KenKen or Mathdoku, the puzzles can focus on a single operation or all 4. To get started, check out these guidelines for helping kids learn to solve KenKen puzzles.

  • Logic Puzzles - You know the ones I'm talking about here. John, Karen, Tim, Ellen and Sam attend a party. The gifts they bring include a car, a giraffe, a watch, walkie-talkies and blocks. The information keeps coming and it is your job to figure out what each person wore, brought and ate. Phew! These can be great fun! Here's an introduction to logic puzzles and how to solve them. You can begin by solving some simple logic puzzles

You can find several boards devoted to number and logic puzzles at my Pinterest site.

Two great sites with a wide range of number puzzles (printable and online) are Krazydad and Conceptis Puzzles.

Using art in math class is one way to develop visual and spatial skills, as well as pattern recognition and basic geometry skills.
  • Origami - Paper folding is a great way to develop spatial reasoning abilities. It's also fun! You can get great paper at Origami Corner. Try making an origami crane or origami frog. If you have trouble reading origami directions in print, try following along with the videos from Origami-Fun or the Origami Instructor's channel on YouTube. For inspiration, visit the site of artist Robert J. Lang and check out his origami compositions. I'm crazy about his arthropods. Better yet, check out his TED Talk.

    While you're folding you may want to check out The Origami Master by Nathaniel Lachenmeyer and Lissy's Friends by Grace Lin (both picture books), as well as Fold Me a Poem by Kristine O'Connell George (poetry). All these books focus on origami. 

  • Spirograph - If you haven't seen a real spirograph, look here. Kids love making art with these kits. Klutz has simple Spiral Draw book/kit that includes 4 plastic drawing wheels and directions to get you started. Or you can try this Hypotrochoid Art Set. Once a few designs are made, consider the ways to color the design so that a pattern emerges.

  • Tessellations - Tessellations are all around us in the natural world. Here are few examples. If you like the art of M.C. Escher, then you already know all about tessellations. Creating them from cut paper or drawn shapes can be challenging and fun. The Can You Believe THIS Is Math? project has a good introductory set of directions on making tessellations. has a terrific gallery of examples, as well as a lengthy section with detailed directions on different ways to make tessellations. Tessellations can be used to study the types of symmetry in a plane.

Playing games is a great way to develop problem-solving skills as well as practice skills in arithmetic. I had a game corner in my classroom where students could play games when their work was finished. We also had game day on Friday for 20-30 minutes if we'd had a good week. While I know most of these can now be played electronically, there is something to be said for actually sitting down on the floor with kids, rolling dice, and moving pieces around a board. Some of the games on my shelf include:


I've already mentioned a number of books that connect to the ideas shared above. Using children's books is a great way to explore math with kids. Here are some titles that include mathematical content or challenging puzzles 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. If you are a fan, check out The Annotated Phantom Tollbooth.

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. After reading the books, try your hand at solving the puzzles in The Mysterious Benedict Society: Mr. Benedict's Book of Perplexing Puzzles, Elusive Enigmas, and Curious Conundrums. You can also play games for the gifted at the Mysterious Benedict Society site.

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. Titles include:
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

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. You can download puzzles from the Winston Breen books to try them out. There are two sequels to this book, The Potato Chip Puzzles and The Puzzler's Mansion that are also highly entertaining.

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.

Alright, that's it for now. I hope you'll find these ideas helpful in your classroom or at home. If you have a great idea of your own for encouraging a love of math, please share!

Monday, March 4, 2013

Monday Math Freebie - Function Machine Fun

Classroom Freebies Manic Monday
I've been trying to find a fun way to practice basic facts while working with patterns and function machines. I think this idea works well.  Player 1 draws a Function/Rule card and hands his/her partner the number cards that correspond to the input numbers. Player 2 selects one of the input numbers and places it on the inbox of the function machine mat. Player 1 reads the rule on the Function/Rule card and places the correct output number on the outbox of the function machine mat. Player 2 records the information on an Input-Output Chart and tries to determine the rule. Play continues in this fashion until the rule is determined or the player runs out of recording spaces. After each player has taken four turns guessing the rule, players total their scores (total number of guesses needs) and the lowest score wins.

Here are a few sample images.

I hope you get a chance to use this in your home or classroom. Please let me know if you try it and how it works!