Math Must Read Mentor Texts

Teachingisagift is again linking up with Stacia and Amanda at Collaboration Cuties for Must Read Mentor Texts.  I love how writing these posts makes me think about my favourite books and then write about how I use them in my classroom!

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Many years ago I came across the book "A Grain of Rice" by Helena Clare-Pittman.  I was intrigued by the story and I loved that it linked to mathematics.  

The book is a simple variation on the old grains on a chessboard example of exponential growth.  As a reward for concocting a potion which saved the life of the princess, humble farmer Pong Lo asks for the Emperor's daughter's hand in marriage.  The Emperor is willing to offer Pong Lo anything he wishes, except for the hand of his daughter, the princess.  

Pong Lo then surprises the Emperor by making a basic request. He asks for a single grain of rice doubled every day for 100 days. The Emperor is baffled, yet he complies.  He soon discovers that Pong Lo uses his math skills and ingenuity to make all his wishes come true.

From Helena Clare Pittman's website:

"The peasant, Pong Lo, falls in love with the princess, Chang Wu, presenting, of course, the problem of class, for starters. But this peasant is "more than a little" clever, gifted and determined. With the conviction of love in his heart he defies tradition and common sense, becoming indispensable to the workings of the emperor's palace, and dear to emperor's love of good food and to his daughter's heart. The story unfolds from there and rests on Pong Lo's wit, and knowledge of arithmetic progression. This book has been in print since 1986, used in school curriculums since 1994, and is a love story on a royal scale."

This story is a great introductory lesson to the patterning and algebra strand in the Ontario Curriculum for mathematics.  I also like to use it prior to this lesson I wrote about INTERACTIVE MATH NOTEBOOKS.  The mathematical focus for this lesson the exponential growth of the powers of 2.

Prior to reading the story, I ask the students to consider this question: "Would you rather have $0.10 each day for 10 days or would you rather receive a penny on the first day and double that amount everyday for 10 days?   I allow students to think about the question but not give me any responses at this point.

I then begin to read the story and stop on the page where Pong Lo asks for a grain of rice which will double every day for one hundred days.

I then revisit the question I posed about the money.   With a partner I ask the students to determine how much money they would receive, depending on which decision they made.  We debrief the strategies used, and the answers the students come up with.  I like to use this as a bit of a diagnostic assessment of strategies students use.

I then ask the students to determine how much rice Pong-Lo would have at the end of 100 days. Again they work with their partners.  I like to use the KWC (Know, Want to Know and Conditions) model to have students work on the problem in partners.  I have them go through each step included in the table you see below.

K:  What do I KNOW?  Based on the problem, I know that...

W:  What do I WANT to do, find, or figure out? I am trying to find or figure out...

C: CONDITIONS.  Are there are special conditions? (e.g. that Pong Lo requests a single of grain rice which doubles each day for 100 days)

Next I use the APEC sheet to have students work through the process to come up with a reasonable answer.  

There is no right or wrong way for the students to use the table, but they must fill out all sections.  I find that gifted students often are able to come up with the correct answer but they cannot show how they know they are correct, and they have trouble explaining their thinking and/or making connections.  Using APEC gets my students thinking about the entire problem solving process and how the concepts they have been learning about connect to other math concepts, to themselves and to the world around them.

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Prior to finishing the story but after the students are finished working on the problem they share their thinking, discuss the process and the answer.

I then finish reading the story to the students and we talk about what that much rice would look like. How would Pong Lo store it all?  What could he store it in?   Exploring a variety of measurement concepts are a natural extension to these questions.

Another extension I have used with my students is to have them create their own story related to the concept, powers of 2.  This can be used as an excellent cross curricular connection to language arts, visual arts and technology.

Head over to Collaboration Cuties now to read about more great Must Have Mentor texts!

Math Survival Guide

Let me start this post by telling you that I do not use regular math textbooks or math work books.  I realized after trying to use the board approved text book for one year of teaching gifted students that it just didn't work...for them or for me. 

I use a variety of hands-on, minds-on teaching strategies such as those found in the Ministry of Education's Guides to Effective Instruction in Mathematics.  I find these activities to be much more engaging for the students I teach.  I also use the dynamic geometry software Geometer's Sketchpad (GSP) for teaching the majority of the geometry concepts I cover in grade six.

That being said, I do think that students need to record their learning, so I created the Math Survival Guide.  Students use these throughout the year as we cover each of the strands.  I started my first math class by having the students make their own "survival guide".  I gave each student half of a file folder...I try to be environmentally conscious and reuse ones the main office doesn't want any longer.  I cut the file folders in half using a paper cutter.

Start with an old file folder.

Cut the file folder in half.  Now you have TWO covers.



Open one half like this with the "fold" in the middle.

Each student glues a large piece of quad paper face up to one half of the open file folder.  You may need to trim off the holes and a few rows from each side of the quad paper to make it fit.

Students fold the paper into eighths.

Make sure all the creases in your fold are nice and "crisp".  Students can use a straight edge such as a ruler to get nice, clean folds.

Students continue to fold until they have the right fit.

Add a cover.  (My students do a much better job than I do!)

Students use four squares of the quad paper for each entry.  They must include the word/concept, a written definition and a picture, diagram or symbol.

I use this technique to activate prior knowledge.  I put the math vocabulary for the task/unit/activity we are exploring on the overhead, or I make up cards with the names on them.  I ask the students to copy each term onto a four by four box.  After they have copied all the terms and concepts, I ask them to try and write something in each box.  They are to use a variety of words and pictures/symbols.  If they do not know a term or concept I allow them to talk with their "elbow" partners and see if they can add some ideas.  If they are unsure about their idea, I recommend that they use the small size Post-It notes to write on.  Gifted students often don't want to record something if they don't KNOW for sure it is correct.  The Post-Its allow them to "guess" and then "check" as they go about completing the task/activity.  These notes fit perfectly, and students can then "confirm" or change their initial thinking and put a final entry in the box when they are satisfied.

This activity is great for me at the beginning of any new unit/task/activity because I get to walk around and see what the students know and don't know.  It is not as intimidating as always giving a "diagnostic" pre-test.  Students seem more willing to show what they know, and I am not sure they even realize that I am collecting diagnostic data at this point.

As the unit/task/activity continues, students go back to their survival guides and revise/edit their initial entries or they confirm their thinking.  At the end of the unit/task/activity the students can use the information to help them study for any quiz or test I might administer.

By the end of grade 6 they have a complete math dictionary divided into the five strands of the Ontario Curriculum. We also add a section on problem solving strategies as we work through our Problems of the Week each week.  The teachers in grades 7 and 8 often tell me that my students keep their survival guides and bring them to junior high school with them. 

This is only part of how I run the math program for my gifted students, but it is a great way to start the year, and to start any new unit/task/activity!

Daily Math Routine

I do not want to bore my students (or take a lot of time out my math program as I find there are not enough hours in the day to cover the HUNDREDS of expectations in the Ontario curriculum). One day while browsing at the local Chapters bookstore, I found a book called "Daily Math" and had a quick scan through it. The book is made up of practice sheets and each day of the week is devoted to a different strand from the curriculum. Each day (except Friday) has 5 questions. I thought to myself..."Well for less than $15.00 what do I have to lose?"

I don't know about you but my students are also "dawdlers" in the morning. They have nothing to motivate them to get to their desks and get working while waiting for announcements and O'Canada to play. In my school there is usually a lag of about 10 minutes before morning exercises. I really cannot afford to lose the time, nor can I stand trying to corral almost 30 pre-teens every morning.

This lead me to using Daily Math as a morning motivator! Each evening, a student has the job to put out the next days "Daily Math" on the top of each student desk UPSIDE DOWN. They do this only after all the other students have left the room. I usually find that I choose a mathematically strong, motivated student who wants to hand out the papers and I keep an eye open to see if he/she looks at the question...so far none have!

When students arrive in the morning they need to "hustle" to get their "Daily Math" done. They only have until the announcements and O'Canada come on to complete the 5 questions. They may not work with a partner, but I do let them use calculators or manipulatives.

Once they have finished the 5 questions, the students line up in front of my "stool" (really a perch for me during lessons etc.)  I have a clipboard with the answer sheets and a recording sheet on it.  I mark the student work until I have 5 student markers (these are students who scored a perfect mark and have shown their work).  

Each student who becomes a marker gets to take a mini pylon cone from my little stash, and a RED PEN.  (OH YES, they LOVE those red pens let me tell you!)  These students place the cone on their desk and then as the students finish they go to a marker to have their work checked.   Once their work is marked, students hand in their Daily Math and prepare for the day ahead.

This process allows me to finish taking "silent attendance" and to record (on a class list on my clipboard) the marks of the students who have finished. I collect the questions from each student and review each student's work in detail. I make note of students who are struggling, and those who are making common errors.  Sometimes this leads me to an immediate "mini lesson" if the whole class or a large percentage of the students seem to be struggling with a question or concept. Other times, I can teach a small group lesson at my desk to a few students who have the same issues, or I can work with an individual one on one.

Student papers are kept clipped together in another bin behind my desk. Each Friday there are two extra questions for the students to complete. These are called "Brain Stretch" and they are often problem based. I sometimes give the students an extra few minutes to complete the work on Friday.  As part of our Friday routine, the students also get all the work from the week back and they do a self reflection on a sheet I have created for them. They record their mark each day out of /5 at the top of the page, then total the mark out of /25 for the week ( I don't count the brain stretch on Friday as part of the total). I have also taught the students how to convert the mark out of 25 to a percentage.  Below these calculations, they write a reflection on what they did well that week, what they found challenging, and how they are going to address any areas of difficulty.  I ask them to be very SPECIFIC about their plans for improvement (e.g. I am going to use flashcards to practice my multiplication tables, I am going to use the Math Frog website to practice the concept, I am going to use Geometer's Sketchpad to review my geometry concepts, etc.)

This process helps the students set goals for the following week and to reflect back on areas or concepts they are finding challenging.  I also have a"Parent Signature Requested" rubber stamp which I stamp on the reflection sheet. The students must have their parents review their work and return it to me on Monday signed by a parent.

Each student who returns their signed work on Monday gets a ticket for a weekly draw. The draw prizes are classroom privileges such as "swap your desk", "listen to your tunes", "super supplies bin".  I still expect all the students to return their work...but only those who return it on Monday morning get a ticket for the draw.  By the end of the year I had 100% of my class returning their work on Monday morning...I don't think it was because of the draw though...I think they just didn't want to hear me comment about it not being in on time.  I also track everything the students do, and I follow up with both students and parents, so I think that most in my class realized it was just better to have the work in on time.