Monday, October 28, 2013

Monday Math Freebie - Be a Number Detective

Classroom Freebies Manic Monday
I've been working on number sense riddles for some time now. Today I'm sharing my first set for the numbers 1-32. Each card has 3 or 4 clues and ends with the question "What number am I?" In general, these cards are designed to help develop number sense and thinking flexibly about numbers and how they are used and represented in our world. Terms such as multiple, factor, even, odd, prime and composite are used.

If you want to use these in a math center, I have included a poster. Here's what the cards and poster look like.

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

Wednesday, October 23, 2013

Instructional Conundrum: 100 Board or 0-99 Chart?

In my work with preservice teachers I find myself thinking a lot about the language of math and the models we use. Today I want to discuss the differences between the 100 board and 0-99 chart.

In some circles, the 0-99 chart is also called a 100 board. In old-school language it is called a counting chart. I don't particularly like either of these names. Here's why.
  1. Even though 100 numbers are represented on the 0-99 chart, it does not extend to 100. To be called a 100 board, it should include this number.
  2. A counting chart should begin with the first counting number, which is 1. Zero is not a counting number. Therefore, a chart that begins with 0 should not be called a counting chart.
I know these are really minor points, but they speak to the issue of precision and the language we use to describe mathematical tools. 

Beyond the semantic issues of what we call these charts, I have greater concerns about the use of 100 board (and the 120 board we now see to support Common Core standards).

Our system of numeration is a base-10 system. This means we have 10-digits (0-9) and that every number can be made using one or more of these digits in combination. Ten and powers of ten are used to construct the system.  Larger numbers are built by repeatedly bundling ten: 10 ones make one ten, 10 tens make one hundred, 10 hundreds make one thousand, and so on. In simpler language, every time we reach ten of a particular unit, it is regrouped and renamed. Here's what the tens column looks like on these charts. Note the placement of each.

This is where my problem with the 100 board comes in. When we reach 10 ones on a hundred board, they still remain in the ones row (or column, depending on how the chart is arranged), but they belong at the beginning of the next decade. On a 0-99 chart all the numbers in a decade appear in the same row. For example, on a 100 board, the decade row for thirty begins with 31 and ends with 40. On a 0-99 chart, the decade for the thirty row begins with 30 and ends with 39. 

This representation on the 0-99 chart is much clearer and more accurately represents the way our number system operates. 

The other idea the 0-99 chart makes explicit is that zero is an even number. Even though we don't begin counting with 0, placing it on the board shows students that one less than 1 is 0 and that zero IS a number! On a 100 board we recognize numbers ending in 0 as even, but because zero does not appear, students don't view it as a number (just a placeholder) and often question its classification, wondering if it is even, odd, or neither. The 0-99 chart can help students overcome these misconceptions.   

In the final analysis, both charts can be used for developing skills in counting up and counting back, skip counting, finding one more/one less and ten more/ten less than a number, recognizing patterns, place value, addition, subtraction, finding multiples, prime numbers, and more. However, the 0-99 chart does this while helping students work within the structure of our base-10 system.

Now that I've articulated the reasons that I feel the 0-99 chart is a better tool than the 100 board, here's a set of charts for you to use. One is a traditional 0-99 chart (oriented horizontally), while the other displays the numbers vertically.
Download 0-99 Charts.

What are your thoughts about the difference between the 100 board and the 0-99 chart? Which do you prefer and why?

Tuesday, October 22, 2013

A Halloween Treat - Math Freebie

Commercially produced math manipulatives (Unifix cubes, base-10 blocks, etc.) have become so expensive that I am always looking for cheap alternatives. The Dollar Tree and Dollar Spot at Target have supplied many of the materials I use these days (particularly cute mini-erasers). Last summer (2012) I started using sand timers, rubber animals, foam beads, and more from Oriental Trading Company.

Here's the Halloween set I'm using for counting, graphing, patterning, multiplication, fractions and more. You get 500 of these beads in a package for $6.00. (That's about 1.2 cents each!) There are 5 shapes and each one comes in a large and small size.

Here are the pages I created to go along with them.

If you don't have these shapes and still want to do the activity, here's a page with an assortment of images you can use. 

These activities can be used to meet a number of following Common Core Standards including:
  • K.MD.3. Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.
  • 1.NBT.1. Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.
  • 2.MD.10. Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put- together, take-apart, and compare problems using information presented in a bar graph.
  • 3.NF.1. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

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

**BTW** - Faith over at 1st Grade Fantabulous has a terrific post on how she uses the fall foam beads and has some freebies for you! Here's what those pieces look like.
I hope you'll head over and check out her post entitled Winners and Fall Centers.

Monday, October 21, 2013

Monday Math Freebie - Dots and Boxes Games

Classroom Freebies Manic Monday
While searching for resources for teaching scientific notation I came across a middle school version of the dot game where students were required to simplify exponents and record numbers in scientific notation. I loved this idea and wrote to the author asking if I could adapt his idea for the elementary classroom. My thanks to Kevin Koch for giving me permission to create these resources!

In this version of the dot game, students draw line segments and form boxes as usual. When they complete a box, they earn one point. However, if they complete a box with a number sentence, they must say the number sentence aloud and give the solution. Answering correctly earns a player extra points. Once all the boxes have been made, players total their scores. The player with the highest score is the winner.

The two versions I have today are for practicing basic facts, one in addition and one in multiplication. 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 these and how you like them! 

Monday, October 14, 2013

Monday Math Freebie - Fall Themed Multiplication Games

Classroom Freebies Manic Monday
In honor of fall I have created two new multiplication games and "dressed up" some old game boards for practicing basic facts in multiplication.

Here's what you'll find in this packet.

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

Saturday, October 12, 2013

Resources for Teaching about Extinction

I'm preparing to teach controversial issues in the classroom. As I plan for discussions of geologic time, evolution, extinction, and climate change, I'm sitting on the floor of my office, pulling books from the shelves, papers from the file cabinet (yes, I am "old-school" in some ways!), and searching for web resources on my iPad while thinking about how to put them all together. I thought this might be a good time to share a few excerpts and some of the resources I'll be using in my lessons.

Resources for Teaching about Extinction

written by Martin Jenkins and illustrated by Vicky White

The world's quite a big place,
you know. But it's not that big,
when you consider how much
there is to squeeze into it.

After all, it's home not just to billions of people, but
to the most amazing number of other kinds of living
things, too. And we're all jostling for space.

We humans have changed the world a lot over the
years, to make room for ourselves and to produce the
things we need.  We've turned forests into farmland,
dammed rivers, and built towns and cities to live in.
Some of the other animals and plants that we share
the Earth with have coped with the changes very
well.  But some haven't.

In fact, some have coped so badly that they're not here

They're extinct.

Text ©Martin Jenkins. All rights reserved.

written by J. Patrick Lewis and illustrated by Christopher Wormell

The 20 poems in this book pay tribute to species that have disappeared since crossing paths with humankind. The book opens with these disturbing words.
More than ninety-nine percent of all species that have ever lived are now extinct.
. . .
On Earth, six animal species die every hour, many of the most recent due to climate change, habitat destruction, or human greed, carelessness or indifference.
A timeline runs across the bottom of the pages, with the poems ordered by when a species became extinct. You'll also find its scientific name and where it once lived. The first poem is to the aurochs, a species from which modern cattle descended that died out c. 1627. The last poem is to Miss Waldron's red Colobus monkey, a species that died out in 2000. In between you'll find familiar and unfamiliar animals, like the dodo and the blue buck.
The Arizona Jaguar

Description: Loner; nightfall eyes;
Coat of spots on spots (disguise);
Once the New World's largest cat;
Mountain, grassland habitat;
Fed on any kind of meat;
Stumbled down a one-way street;
Color of a jealous sun.
Status: Nowhere. Future: None.

Poem ©J. Patrick Lewis. All rights reserved.
The book concludes with a series of endnotes describing each animal in further detail.

Here's another poem about extinction that is particularly powerful.
The Animals are Leaving
by Charles Harper Webb

One by one, like guests at a late party
They shake our hands and step into the dark:
Arabian ostrich; Long-eared kit fox; Mysterious starling.

One by one, like sheep counted to close our eyes,
They leap the fence and disappear into the woods:
Atlas bear; Passenger pigeon; North Island laughing owl;
Great auk; Dodo; Eastern wapiti; Badlands bighorn sheep.

Read the poem in its entirety.

After watching this, check out this LiveScience article entitled 

Hands-On Activities/Simulations

The Mammoth Extinction Game

Scholastic Lesson Plan - Learning the Causes of Extinction

Web Sites

Scholastic Study Jams - Population Growth

Discovery Science - Top 10 Extinct Species

Animal Planet - Extinct Animals

Oxford University Museum of Natural History - Learning Zone: Extinct and Endangered

Other Books to Keep on Hand

written by Jerry Pallotta and illustrated by Ralph Masiello

written by Sandra and William Markle and illustrated by Felipe Davalos

I hope you found this list helpful. If you have any terrific resources for teaching about extinction, I hope you'll share them.

Tuesday, October 8, 2013

Fall Books and Resources

It's supposed to be fall, though you wouldn't know it here. Until recently our temperatures were still in the 80's and our leaves were barely changing color. But yesterday we got some rain and this morning finally have some cooler temperatures. Pumpkins are dotting the landscape, the squirrels in my yard continue their frenzied gathering of acorns, and the sounds of geese have me convinced that fall is finally here. There are many, many good books about the seasons, and fall in particular. I know I cannot name them all, so instead, here are some of my favorites.

Apples and Pumpkins by Anne Rockwell - This text describes the joy of visiting a farm in fall to pick the reddest apples and the perfect pumpkin. 
Autumn: An Alphabet Acrostic by Steven Schnur - This is one book in a seasonal series featuring acrostic poetry. In this installment, you will find one acrostic poem for each letter of the alphabet, from acorn to zero. How does zero fit with fall? You'll have to pick up the book to find out!

Autumn Equinox: Celebrating the Harvest by Ellen Jackson - The book introduces the history of the Autumn Equinox and describes how many ancient cultures celebrated the harvest.

Autumn Leaves by Ken Robbins - As with his other works, Robbins' photos are gorgeous and show 13 different leaves in actual size and wearing their fall colors. The book ends with an explanation of why trees lose their leaves in fall.

Autumnblings by Douglas Florian - One in a series of seasonal poetry, this book contains a variety of inventive poems about fall.

Fletcher and the Falling Leaves by Julia Rawlinson - The change of seasons is coming, and Fletcher the fox doesn't understand why the leaves are falling. Text and illustrations come together beautifully in this moving tale.

How Many Seeds in a Pumpkin? by Margaret McNamara - This is a terrific book for examining pumpkins. Read my review, with lots of ideas for instruction, here.

I Know It's Autumn by Eileen Spinelli - In rhyming text, a young girl describes all the signs that tell her it is fall.

In November by Cynthia Rylant - This is a lovely poetic text that captures the mood and feel of November. It's also a wonderful book for thinking about the seasons with your senses.

It's Fall by Jimmy Pickering - One in a series on the seasons, this one follows Sally and Sam (a dog) through an apple harvest festival, hayrides, Halloween and more.

Leaf by Leaf: Autumn Poems by Barbara Rogasky - This book contains 25 poems on fall accompanied by beautiful photographs. Here you will find poems by Yeats, Whitman, Poe, and more.

Leaf Jumpers by Carole Gerber - Beautiful colored linoleum prints and rhyming text showcase the leaves and events of the fall season. Eight leaf types are identified for children who want to try some identification on their own.

Leaf Man by Lois Ehlert - Made of leaf collages, leaf man must go where the wind takes him. Along the way he will meet ducks, rabbits, and many other animals composed of collections fall leaves.

Leaves by David Ezra Stein - A young bear becomes concerned when the leaves begin to fall from the trees. This is a beautiful, quiet story that captures the feeling of fall.

When Autumn Falls by Kelly Nidey - Illustrated with beautiful cut-paper collage, poetic text describes many fall events, like bobbing for apples, selecting pumpkins, and jumping in leaves.

Why Do Leaves Change Color? by Betsy Maestro - This book in the Let's Read-and-Find-Out Science nicely explains what happens to leaves in the fall.

Nancy Elizabeth Wallace has created two terrific books for fall. Both feature cut paper collage illustrations that hold hidden facts and riddles. There is much to be found in a close examination of the pictures.
  • Pumpkin Day - Follow the rabbit family on a trip to Pumpkin Hollow Farm where they select pumpkins for cooking, decorating, and carving.
  • Apple, Apples, Apples - Follow the rabbit family on a trip to Long Hill Orchard as they learn about how apples grow before picking their own.

Here are some poems touching on the theme of fall to round out your study. I have included the first few lines of each, along with a reference to the book where you can find the poems in their entirety.
  • October by John Updike, in A Child's Calendar.
    • The month is amber,
         Gold, and brown.
      Blue ghosts of smoke
         Float through the town,

  • November by John Updike, in A Child's Calendar.
    • The stripped and shapely
         Maple grieves
      The ghosts of her
         Departed leaves.

  • Bullhead in Autumn by Marilyn Singer, in Turtle in July.
    •    in autumn
      I settle
         belly down in the shallows
      above me
            red and yellow

  • Why do leaves change colors? by Amy Goldman Koss in Where Fish Go in Winter And Answers to Other Great Mysteries
    • The oak tree always lets me know
         When autumn has begun.
      But why do its dark green leaves
         Change colors one by one?

  • Moon of Falling Leaves by Joseph Bruchac and Jonathan London in Thirteen Moons on Turtle's Back.
    • So, each autumn, the leaves
      of the sleeping trees fall.
      They cover the floor
      of our woodlands with colors
      as bright as the flowers
      that come with the spring.

  • Fall by John Frank, in A Chill in the Air: Nature Poems for Fall and Winter.
    • Fall sets fire
      To the tips of trees,
      And fans the flames
      With an icy breeze.

I have just scratched the surface here of some wonderful books and poems that celebrate autumn. You will notice that I have not included books that cover the full change of seasons (year), or those that cover life cycles of plants. I know that The Seasons of Arnold's Apple TreeFrom Seed to Pumpkin, and Red Leaf, Yellow Leaf are missing (among others).

In addition to these books, you'll find a range of free resources on my Pinterest boards. Here are a few screenshots with links directly to the fall-themed teaching boards.

I hope you find all these resources helpful. If I've missed a great resource for teaching about fall, please let me know!

Infographic on Endangering Animals

Source: National Geographic Newswatch