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!

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