Saturday, August 29, 2015

Fly on the Math Teacher's Wall: Personalized Math Notebook Covers

Here's an idea for getting your math year off to a great start...

When I posted about Math Journals & Notebooks, I mentioned that I loved the idea of having children make covers relating math to themselves as Courtney shares at A Middle School Survival Guide. Ideally, I'd begin the lesson by reading aloud a book that relates math to everyday life. (I mention several suggestions here.)

When I first considered what might go on a cover, I didn't have a lot of ideas. I just thought about # of siblings or children, year of birth or age, height or weight, etc. But the more I considered, the more ideas multiplied! I'd definitely want to do this as a brainstorming activity with students rather than giving them a list. See what your collective brain energy can come up with! How is math related to our daily life? Here are some of the things we thought of:
  • time you wake up/go to sleep
  • # of favorite ____________ (sports, colors, hobbies)
  • # of years _____________ (teaching, being a student, playing an instrument or sport)
  • time each day that you ___________ (exercise, go to school, watch tv, read, play video games)
  • # of _____________ that you own (pets, video games, books)
  • # of years until you (finish school, turn 21, want to get married or have kids)
  • cost of your favorite (restaurant meal, soda, candy bar)
  • amount you spent per week on (lunch, snacks, coffee)
The possibilities are endless!

These covers then become a fabulous jumping-off point for PROBLEM SOLVING.

After students finish their covers, have them generate several problems on 3x5" notecards that use the information they created. For example, on my cover, I posted the following:

I went ahead and wrote my problem on the cover itself, but would have students write on cards. My question, "How many hours do I sleep each night? Each week?" could then be posed to other students. In the classroom, I could put my cover under the document camera and ask students to answer the question posed on my card(s). They could then share a variety of strategies for solving the problem. In a homeschool setting, children could write problems for siblings or parents to solve. Problems could be written at a wide variety of levels, making them grade and age appropriate.

At the Northwest Math Conference I went to a workshop entitled, "Taking the Numb Out of Numbers" by Don Fraser (Ontario, Canada). He began by telling the group of 30 of us, "Did you know that in a group of 23 or 24 there is a 50% chance that at least two people in the group will have the same birthday?" He then gave us a graph showing us the probability of sharing the same birthday in groups of varying sizes. In a group our size--30 people--the likelihood was 70%. We graphed the days/months for birthdays in the room. Interestingly enough, none of us shared the same birthday...we were in the 30%. After looking at the data, Don asked us to come up with problem solving questions--real life questions--based on the information we'd collected. It was amazing to see how many questions we could generate, at all different levels of mathematical knowledge and proficiency.

Don encouraged us to begin each day by reading a "story" and having kids make up a question/word problem. Going back to the math notebook covers, imagine the possibilities if you put ONE child's notebook cover up each day and asked kids to generate questions from the "stories" found there. The problem solving possibilities are endless!

Do your students make personalized math notebook covers? What interesting stats have they included? Comment below with your stories and then visit Mrs. Balius and read what she has to say about setting up daily math routines!!! :)

Saturday, February 21, 2015

Fly on the Math Teacher's Wall: Squashing Fraction Misconceptions

The irony is not lost on me. Fractions, the math concept I most struggled with in elementary school, is now one of my favorites to teach. In this Blog Hop, my math blogging friends and I will be exploring fraction misconceptions. Here we go...

After years of operating with whole numbers, it's new territory to see fractions and understand the what numerator and denominator mean. What do each of those numbers really mean?

In this example, we'll look at an egg carton. First, we'll consider what the whole this case the whole is the entire egg carton.

Look at the following examples and ask yourself:

1. What does the string show?
2. What do the tile show?


The string shows how many parts our whole is divided into (our denominator) and the tile show how many of those parts have been filled (our numerator.)

A common misconception results when students look at the pieces in the model without taking the meaning of numerator/denominator into consideration. For example, in the first photo above, a student might say that they have 6 pieces, so it's 6/2. Most students, however, can readily tell you that the top example shows one-half, so a bit of probing (Where do you see the 1 in 1/2? Where do you see the 2 in 1/2?) helps to reestablish context.

In a similar example, I've heard students struggle with the question, "What fraction of a dollar is a nickel?"

Many students will answer "one-fifth" because they are thinking of 5 cents; if it has a 5 in it, it must be 1/5.

I like to pull out Money Value Pieces and again revisit the concept of numerator and denominator. We first talk about what our "whole" is: 100 cents.

I might ask, "What does 1/5 look like on our model?" Since we've explored numerator and denominator, they know that the whole would be broken into five portions:

It doesn't take long for someone to say, "One-fifth of a dollar is 20 cents!" (They can check this using the dime piece, a ten strip.) Then, using the nickel model, they explore how many pieces it would take to cover the dollar. "Twenty! So a nickel is 1/20 of a dollar!"

Students need many opportunities to explore the concepts of numerator and denominator using a variety of manipulatives and visual models. (More love2learn2day examples here.) I ask them to record their thinking in a variety of venues: math notebooks, class anchor charts, and video productions. In this ScreenChomp example, you'll hear a pair of students explain the meaning of numerator and denominator; notice that they use more than one visual to explain their thinking.

To continue on the Fraction Misconceptions Blog Hop, please visit my friend Jamie at Miss Math Dork!

Sunday, January 4, 2015

Measuring & Graphing with an Amaryllis

Our family received an Amaryllis kit from Grandma for Christmas. Today, the kids and I planted the bulb and got ready for a little measuring & graphing activity. Want to join us? Here's how:

1. Purchase an Amaryllis kit from a local store. In winter, they are widely available.

2. Plant the bulb according to package directions. (If yours, like ours, arrives with a hard disk of "plant medium," you might want to have a discussion about how much the peat changes by volume after water is added.)

3. Place an anchor in the soil to support your rulers. We used chopsticks.

4. Tape the ruler to the anchor so that it aligns with the top of the bulb's neck.

5. Measure. Our bulb already had green growth, albeit at a weird angle. We just measured straight across at the top so as not to break the plant. I told the boys that we'd measure our plant the same way I measure the tippy top! My 12yo is measuring in centimeters and had to scale a blank graph to go with his estimate for ultimate growth. My 8yo is measuring in inches, to the nearest half inch.

Here are a variety of options for graphing amaryllis growth.

***This activity was created to say THANK YOU for your support this past year. I appreciate you!

Tuesday, December 23, 2014

iHeart Math Holiday Hop

Happy MATH-y Holidays! I'm hosting the final day of the iHeart Math Holiday Hop. The entire advent calendar (see bottom of post) has now been unlocked; you can now go back and download freebies--23!--from ALL of my math blogging friends. Some of the activities are seasonal and you'll want to use them when you return to school in January. Others can be saved until next Christmas. Some, like mine, can be used any day of the year!

Stocking Stuffer #1 - Giving Back: Favorite Math Books & Games

It's no secret that I'm obsessed with math-related children's literature. Even if your Christmas shopping is finished, you still have plenty of time to grab the gigantic list and head to the library to check out a stack of favorite books to share with a child.

Since we are a big game family, I've also compiled a list of favorite Math Toys, Gifts, and Games. Chances are, some of these are in your closet. Why not pull them out to enjoy over holiday break? In the interest of minimalizing, you could pass around a set of games amongst friends.

In addition, this free Math Game List handout can be passed along to teachers, parents, and homeschoolers who are interested in enriching children's math experiences at home through simple card and board games. This list, which also includes a few game-like activities, could be used in a variety of ways:
  • letter home to families at end of school year
  • math center ideas for school or homeschool
  • early-finishers list
  • a checklist for summer fun

    Stocking Stuffer #2 - Math Tip: Gingerbread Math

    Here's a timely online activity for young mathematicians. On Topmarks Maths: Gingerbread Man Game, students can choose from the following:
    • matching written numbers to dots
    • ordering #s of dots by quantity
    • counting
    • sequencing numbers
    • counting with one-to-one correspondence
    Teachers can use the full-screen function and project the activities for transition times. So fun!

    You know you have a hit when you demonstrate the new homework assignment and the class collectively says, "Oooooooh, COOL!"

    Since we've been using clocks as a model for learning fractions, I thought it might be fun to make Flip this case, mini books in which fractions appear to move, getting either bigger or smaller (depending upon the order in which you compile the pages.)

    The pdf comes with 3 pages of "clock friendly" fractions. (23 fractions with an extra blank one, just in case.) At right, you see several samples of Flip Book cards.  The assignment asks students to:
    1. Color each given fraction. The cards come with numbers and blank clocks.
    2. Cut out the cards.
    3. Sequence the cards. They are purposely printed out of order. The set includes equivalent fractions that must be placed sequentially.
    4. Staple into a Flip Book.
    The pdf is FREE in my Teachers Pay Teachers  and Teachers Notebook Stores. The pdf was revised to improve "flip quality." Grab your revision if you downloaded before then! ;) The clocks are now on the right side, so the opposite of what you see in the video below.

    One of my students made a little stop action video to demonstrate...AKA, the "Separatists' evil clock plans..."

    Visit all 23 of these math bloggers for fabulous tips and freebies! Just click on the calendar squares to link to individual blogs. Happy Holidays!

    Image Map

    Thursday, December 11, 2014

    Fairy Tale Favorites!

    Fairy tales invite students to think about short stories in new, exciting, and creative ways. Here are some of our favorite activities that focus on character in grades 4 and up.

    Poetry & Art: Character
    I invite students to create diamante poems that either show the changes in a single character or contrast two characters. After writing a poem, students create background displays. Here's how...

    First, think of a prominent feature from the book that is fairly easy to define in an chunky outline, like a beanstalk (right) or stars (left.) Then, make shape templates out of cardboard scraps and use teeny pieces of tape to mount them on background paper.

    Spray them with tempera paint that has been watered down just slightly...enough so it will go through a spray bottle. (Test this ahead of time and remind students that less is more. Too much spray will give you "lake effect poetry.")

    When dry, remove templates and write the poem. A couple colored construction paper cut-outs help the artwork to "pop" and give it more depth. I use this tempera spray art for a variety of poetry-art projects. Students always love it!

    Character Study Sheets

    "Character analysis"'s not a phrase that brings students running. But what if you change it up a bit? How about scoring characters on report cards? It's so much fun to consider...

    What grade might you give Red Riding Hood for "follows instructions?"
    How about Cinderella's stepsisters? What grades might they receive for "gets along well with others?"

    Character Report Card

    Character: Adjective Scale
    Throw in a few adjectives--and their opposites--and you've got the makings of more creative character analysis.

    On a scale of 1-10, how might you rate each of the three pigs for lazy versus industrious behavior? How would Hansel and Gretel score on impulse control? The possibilities are endless...

    Casting Characters
    Finally, what if you got to cast characters in a movie production? Can you describe each character and cast a famous actor or actress in the roles?

    I love teaching short story through folk and fairy tales! Read more about our unit adventures here and here.

    You can also preview the character analysis sheets here.

    Thursday, December 4, 2014

    Christmas Art & Poetry: Winter Art from the Heart

    I spent the morning with an incredible group of (almost 30!) second graders, creating winter scenes.

    In preparation for their scenes--and for poetry writing--we brainstormed nouns, verbs, and adjectives that they might find in a book with the subject of "winter." They came up with fabulous lists.

    I am tickled with how these turned out. On another day, they'll complete poems to go on the back of each winter scene. Here are a few to share...

    Wisemen, angel, Mary & Joseph

    Notice the "naughty" list?

    Love the reindeer.

    Wreaths on the fence are a nice touch.

    So much detail. Love the colored birds.

    Now THAT is an angel! (And what a Rudolph!)

    Check out the Grinch!

    Frozen comes to life! The kids started singing spontaneous carols--and the Frozen tunes--while they worked!

    Penguin habitat!

    Tree is all decorated.

    Angel AND Santa!

    Displays for a class of 30 kids takes up a lot of counter space! :)
    You'll find the updated lesson here. (If you've already purchased it, please download your free revision with winter scenes.)

    Wednesday, December 3, 2014

    Math in Real Life: Brownies for a CROWD!

    I love exploring "real life" math with students. Today I'm excited to be linking up with:

     A monthly REAL WORLD math blog link-up hosted by

    A month ago, my family attended an annual camp retreat. When I walked in the kitchen and saw this...

    ...I knew it was time for real life math. My sister, the baker, was in the process of preparing brownies for 150. Here's her recipe:

    Thankfully, a computer program converts a standard brownie recipe to serve 150. But the question do you convert fractional parts of quarts, gallons, tablespoons, etc.? And what does that equal in portions that bakers are likely to find friendly? For example:
    • How many cups of cocoa power, sugar, and flour are needed?
    • How many sticks of butter?
    In the kitchen, this chart is posted on a nearby cabinet. 

    Using that chart, she made some delicious brownies! Can you figure out exactly how much of each ingredient she used?

    What other "real life" math moments do you see in this activity?

    Monday, December 1, 2014

    December Sale, Calendar, & Events!

    So much going on this month! Sales, freebies, math hops and more!

    Today kicks off TPT's Cyber Monday & Tuesday sale. Save up to 28% by using the promo code TPTCYBER at checkout.

    In my store you may want to check out the "Presents."

    Presenting...Multiples & Factors
    These little factor and multiple flap book "presents" require students to write the definition of "factor" and "multiple" and list 5 multiples for 2-10 and all the factors for 6, 7, 8, 9, 10, 12, 18,  24, 36. Blank versions are also included for teachers or students who want to use their own numbers. Great for use in math notebooks!

    Presenting...Powers of Ten (pictured below)

    Color, cut, and glue these little "present" flap books to review place value and decimal patterns when multiplying or dividing by powers of 10. On each sheet students solve nine problems and write descriptions of the patterns they observe. Blank versions are also included for teachers or students who want to use their own numbers. Revised **TODAY** to almost double the content! If you've previously purchased the product, you can download the revised file for free!

    December Math Calendars
    As always, the NRICH site is sharing online math holiday calendars...a problem each day for the days leading up until Christmas.  Visit them here, by level:

    Primary Calendar (British Stages 1-2*)
    Secondary Calendar (British Stages 3-5)

    iHeart Math Holiday Hop!
    23 math bloggers have joined up to offer a season of mathematical tips and freebies!You can begin today by visiting Mr. Elementary Math.
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