Math IS Real Life -- January Edition

Welcome!  It is our first time linking up with some fabulous fellow math bloggers,  4mulaFun, The Teacher Studio, Teaching to Inspire in 5th, AND MissMathDork for Math is Real Life.

Many moons ago, I posted a little sign in my third grade classroom that read, "Become a USER of math, not just a DOER of math." This was after endless conversations about why we learned all the things we did in our third grade math classroom.  I have memories of telling the kids they would not be walking about in the grocery store and have someone hand them a worksheet with problems to solve, and they would not open a cookbook with a recipe they want to double and see a multiple choice question in the margin.  Yes--we learn to do a lot with math, but if we are not able to USE it for a purpose all the things we know how to DO are no good to us at all. The foundation of our explorations back then, and always will be---understanding the purpose for what we are learning and how it helps us maneuver in our daily lives.

I would like to share one of my second grade students' recent explorations...

A few weeks before Christmas break, I was browsing the holiday items at Farm & Fleet, and I happened upon a beaded ornament kit that I knew well--those infamous pipe cleaner beaded wreath ornaments.  Well, I had to get them, as they brought back memories from my own childhood and I knew my kids would enjoy making them.

  
I got the two kits home, sat down at the kitchen table, and took a closer look at the directions to help determine how I should divide the beads and pack them into individual baggies for my kids. I am always wanting to do things to make things easier in the long run when it comes to prep of materials.  I looked at the diagram and figured out how many green beads and red beads I needed to put in each baggie.  I got through one kit that made enough for 16 ornaments when I asked myself--"What am I doing? I should have the kids doing this!"  I stopped midway and left my nice little prep behind.

I took the other ornament kit to school that same week and shared it with my kids. I told them how I picked up the ornament kits and they would have to help out with prep before we could make them as a class.  I showed them the big bag of  green beads, and the small bag of red beads, and told them there were enough beads to make 16 ornaments. I posed the same questions I asked myself at home (replacing the "I" with "we"):

• What do we need to do? (separate the beads)
• What do we need to know to be able to do it? (how many green and red beads are needed for each ornament)
• How are we going to figure it out?

The kids were very quick to answer the first two questions.  They needed more information to go further.  One student said loudly, "Why don't you just look at the directions, Mrs. Masters?" Ha! Smart cookie!  So we looked at the directions, and I knew he was expecting the directions to tell us exactly how many of each bead we needed to make an ornament.  NOPE! Here's what we found.

We discussed what we saw--number of each color of bead in the kit, number of pipe cleaners in the kit, a diagram showing how to feed the beads onto the pipe cleaner, and a diagram showing how to bend and tie.  Did the directions show us what they needed to know? Well, yes, but they had to do some work.  None of the kids chose to focus on the total number of beads in the bag, but their attention WAS drawn to the diagram.  BWT this was also a perfect example of using informational text features for a purpose.

Quite a few hands went up when I asked how what we saw could help us.  In our discussions we decided to just count the red beads in the diagram, that was easy--we needed 8 of them for one ornament.  Then we saw that each group of green beads had 4 beads, and we needed to have 7 groups of green beads to make an ornament.  I asked the kids if they had enough information to help them answer their question, and they said yes. It was time to go to it! Some kids worked together, and some went on their own, to determine how many green beads were needed to make one ornament.  No directions were given except for the fact that they needed to show their thinking.  Here are some examples of their thinking...

Each group/individual showed their thinking, explained, and we asked ourselves if what was shared was reasonable.  After discussions began, two girls went back to their seats to do some revision.  One student in particular noticed this and drew attention to the fact that they left.  I asked them why they went back, and they said it was because their answer didn't make sense.  I stressed how important it was that the girls realized this and went back to rework.  As we say, the trip (journey) is just as important as the solution. We, of course, had some discussions of how repeated addition of equal values is multiplication and how each section of the ornament was a group.  Only a few students wrote 7 x 4 or 4 x 7.  This exploration was a perfect application of skills learned and served as a foundation for new knowledge as well (multiplication).  Not to mention, we had a good-ole'-time making the ornaments and taking them home to put on our trees. Something to remember!

Thanks to  4mulaFun, The Teacher Studio, Teaching to Inspire in 5th, AND MissMathDork for the opportunity to link up! 

ALSO--Just a reminder, starting January 11th, we will be joining Tara, The Elementary Math Maniac, for her book study of Number Talks: Helping Students Build Mental Math and Computational Strategies (K-5) by Sherry Parrish. The text is well worth the investment, and we hope you will join us!

Smiles!

What are the other kids doing? Wednesday Linky - Reading & Writing About Math

Coming to you a little late in the day for our linky, What are the other kids doing?  It's a linky dedicated to sharing independent practice activities that you use with your students that make it possible for you to meet with small guided math groups.  Many teachers call them math centers or workstations--whatever you call them, these activities are designed to engage students in meaningful practice away from the teacher. For details about linking up, click here! We'd love for you to join in the sharing!

Today's topic---reading and writing about math!

We would like to share some things we already do and some plans for the future. :0)

 
Class Math Books

This summer, Sarah and I participated in a reading/writing professional development workshop. The speaker was fabulous, and we got a lot of great ideas from her. One thing that she discussed was creating class books. Now this is something I have done many, many times throughout my teaching life, but what stuck out was she mentioned writing math books.....WHAT?!?!   How simple, but yet how difficult for me. When I've done class written books before they typically were by month and each book had a theme with a prompt the students wrote about. They also focused on English/Language Arts.

So my thoughts are this could easily be done during small guided math groups (in which each group writes their own books, or parts of a whole class book), or it could be done as a rotation/station.

Now, I am admitting that I have not done this yet, but wanted to put it out there for anyone to help me out with, or brainstorm with me:) so I have no pictures to share.  If anyone out in the wonderful world of teaching would like to share how they have created math class, I would love to hear your ideas and how they worked in your classroom.  I plan to come back and let you know how they worked in mine....once I get it all figured out!

Over the years, I have tried to engage my students in writing about math in different ways.  Here are some questions/prompts that I have used with third and fifth grade during independent work time while working with small guided math groups. I have tried to organize some of the most effective prompts/ideas I have used into categories in list form.

Reflecting

• Explain what you learned today.
• How can what you learned today be used in your life outside of school?
• What "I wonders" do you still have about what you have learned?
• Create an illustration showing what ______________ means.  Then write a caption to go with your illustration. (various vocabulary terms/concepts)
• Make a list of the steps you learned today.
• Describe the attributes of ___________________. (geometry)
• Describe something you learned from a classmate today.
• Why is it important to know how to ___________________? (many possibilities)

Problem Solving

• Explain the strategy you chose.
• How is this problem like another you have solved?
• How did you and your partner's strategy differ? (partner problems)
• What was easy for you? Difficult?
• Would you choose to solve this problem or a similar one the same way? Explain.
• How does this problem relate to real-life? 
• Write a similar problem.  Take this problem and make it your own.
• What worked well? Did not work well?

**I have also used many of the questions on my problem solving discussion fans as prompts for written reflection.  Check them out here--the download is free!

Vocabulary (insert words/concepts of choice)

• What is the meaning of _______________?
• Define _________________.
• Describe _________________.
• How are ________________ and _______________ different? Similar?
• What is ____________________?
• Illustrate __________________. Then write a caption to accompany your illustration.
• _____________ is to ______________ as ______________ is to _______________ (analogies--used this with older students)
• Create and label a model to show the meaning of __________________.

**For more vocabulary ideas--you might be interested in our previous post.  Another freebie is included!

Some additional writing activities that my students have enjoyed--some quick and others done over time.

• writing math riddles
• creating math comic strips
• creating "teaching" mini-books (My fifth graders created mini-books to teach concepts to someone else younger than them.  They had to use language they would understand--could not make any assumptions.  This was a great project--challenging for some.)
• math PowerPoints to illustrate concepts/key vocabulary (I am sure there are many other formats for creating these today--it was quite a few years ago that my fifth graders did this.)
• writing math poetry or songs (Multiplication is... {two-word poetry}, Sing a song of ___________. {use familiar tunes as basis}, acrostics, shape poems)

Something I have especially like to use with ALL grade levels is list making.  Here are some examples...

• Make a list of ways to make 20.
• How many different things could you buy with $5?
• Find at least 6 items in the room that are about one foot long.  Write them in a numbered list.
• How many ways can you show/represent 100?
• Make a list of real-life times when you need to add.
• Look around the room.  Make a list of as many object as you see that are arrays. (love to do this one with my second graders--you would be surprised at the number of arrays in your classroom)
• List all of the math words you know. (This is quite telling!--do at various times throughout the year.  I let my kids use the resources around the room.  They must know what each word means.)
• Write some examples of how you can use measurement (of length) in your life outside of school.
• List the skills you need to figure the area of a garden.

Math Picture Books

Using picture books during rotations/independent work time is something I have started doing more of in the past few years.  Most of the texts I use are those that I have used as mentor texts, so students have knowledge of the texts before exploring them during independent work time.  You can click here to see some of the texts I have used.  I have just started adding to this page of our blog, so additional texts and reflection sheets will be include in the future.  One of the texts my students liked most last year was The Big Buck Adventure by  Shelley Gill.  You can read more about how I used the text in a post on our Hoots N' Hollers blog.  This particular text was actually used during guided reading rotations.  You will also be able to download the free reflection sheet!

Please feel free to link up your reading and writing ideas for independent work time.  We love it when you share!  Don't have a blog--please share in a comment!

All the best for the rest or your week!

An InLinkz Link-up

What are the other kids doing? ---- Problem Solving

Welcome to the third installment of our new linky--What are the other kids doing?  It's a linky dedicated to sharing independent practice activities that you use with your students that make it possible for you to meet with small guided math groups.

Today's topic is problem solving!  We will be sharing some things we already do and some new things we are looking forward to trying.

Allowing students to independently problem solve as individuals, with a partner, or in small groups is essential.  Creating the problems is something I find myself doing on a daily basis.  I do not plan ahead a week in advance---I am continually considering my students' current understanding of concepts, the skills they have learned, how they are progressing in guided math groups, and the standards.

Three different problems may be provided for students on a given day.  For example, we may be working with adding on with the start unknown. Some students are able to work with greater numbers (three-digit) while others are adding 2 digit numbers.  The problems may be identical with differing numbers.  There may also be a group of students having difficulty writing an equation to match a start unknown addition word problem.  Those students may continue working with a result unknown problem in the independent setting and further work will be done with guidance in a small guided math group with start unknown problems.  I simply number the bags that house problems so students know exactly which problem they will be solving.

Some problems include a checklist to help guide students, while others may not---this depends on the needs of students.

A checklist example:

• Carefully read the problem.
• Label what is known (K) and unknown (U).
• Write an equation to match the problem situation.
• Solve the problem using a strategy of choice.
• Write your answer in a sentence with words.

Whatever problem students are given, one thing remains constant---students must decide what strategy they will use to solve.  The strategy (pathway) is just as important as the solution.  The discussion that students are allowed to have with one another gives them the opportunity to see multiple pathways for solving the same problem as well.

Problems do not always have one solution, and students don't always solve the problems they are given.  Here are two examples:

• 25 trick-or-treaters went into the haunted house.  Some were brave enough to go upstairs, and the rest stayed downstairs. How many went upstairs? How many stayed downstairs?

• 16 students went into the library.  Two students sat on each beanbag.  How many beanbags were used?  What strategy would you use to solve this problem? Be prepared to tell why you would use this strategy. 

No matter how well problems are planned, there are times when students get stuck.  Pam from Pam's Place came up with a wonderful idea to help instill perseverance in her students---Need a Hand?  Click here to read more about Pam's fabulous idea! 

Below are pictures of the hands that students will be able to use during independent work time while I am meeting with small guided math groups. 

Suggestions on hands include:

• Use tools to model.
• Reread the problem.
• Try a different strategy.
• Label what is known (K) and unknown (U).
• Picture the problem situation in your mind.
• Look back to your journal for a similar problem. 
• Problem solve any words you do not understand. 
• Draw a picture.
• Ask yourself what you have learned that can help you.
• Look for a pattern.
• Act out the problem silently or with a partner.
• Talk about the problem with a classmate. 
• More will be added as the year progresses...

Something else I would like to try this year is group problem solving with roles.  This idea was shared in Dr. Nicki Newton's book Guided Math in Action (Chapter 8). While students work collaboratively to solve the problem, each has a special role. 

She suggest the following four roles:

• Reader--reads the problem and translates for the group
• Illustrator--draws a model to show the group's thinking about the problem
• Number Cruncher--writes an equation to show the numbers in the problem 
• Checker--Solves the problem in a different way to check the original solution

We will spend needed time understanding expectations and practicing before students are expected to work independently.

Finally, I would like to recommend a couple of great resources for problem solving---one I have had for years, and a new one.  Check them out!

• Introduction to Problem Solving: Strategies for the Elementary Math Classroom by Susan O'Connell (Now available in K-2 and 3-5 editions)
• Problem Solving with Math Models by Dr. Nicki Newton (available for grades K-5)

I have also worked with students using model drawing (Singapore Math) as a fifth grade teacher for many years.  Here is a resource I recommend!

• Step-by-Step Model Drawing by Char Forsten

A few years ago I discovered these cards from Edupress. I purchased them at our local school supply store for about $10 a piece. Inside are 40 cards (front and back).

Please excuse the bad iPhone picture...I looked and looked for the grade 2 cards on websites but could only find the Addition and Subtraction cards for grades 2-3. I could only find the problem solving cards starting at grade 3. You can find those here.

What I like about these cards is that they can be done in small groups, or as a workstation. I have used them as both. One year, I had a "Brain Blaster of the Week". I would display the card and the students would try to problem solve what was on the card for that week. I had a bucket for them to put their work in. They could just use a slip of paper to show how they problem solved. That was a requirement. I wouldn't just take answers written on a slip, a strategy had to be shown. I would then draw a few papers from the bucket. If they were right, or close, using a strategy matched the problem, we would discuss it as a class. I would then give a fuzzy (part of our classroom management system). Some of the kids were baffled that someone could be rewarded for getting an answer wrong. I like to reinforce the idea that mathematicians are not always right, and need to practice, practice, practice!

I then would go through the rest of the bucket when the kids where gone, and I would assess who is on track and who needs more guidance. This was addressed duirng small guided math group times. We would break down the problem and discuss strategies that could be used to solve the problem.  These cards are a great assessment tool, too!

We would love to hear your problem solving ideas and how you use them with your students!  Feel free to link up or share in a comment!  Click here for details about linking up...

AND---If you haven't already, visit a fabulous blog hop--Math Books That Will Change Your Teaching! You can enter to win some HIGHLY RECOMMENDED math resources!!

An InLinkz Link-up