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December 3, 2009

Problem-Solving Strategies

By Victoria Jasztal

    Once upon a time, math was... cut-and-dry. I remember being in either fourth or fifth grade and having to solve multiplication or division problems in front of the class using the "one and only" method our teacher taught us. I felt eyes bore into my head as I thought to myself, D-M-S-B- divide, multiply, subtract, bring down, don't forget, don't make a fool of yourself in front of the class. When I solved the problem correctly, I felt a great sigh of relief. Yet when I didn't "match" the teacher's solution, I felt embarrassed.


    I was the typical non-conventional learner in math, always sketching pictures and color-coding problems so I could understand them. As I teach a new generation of mathematicians, times have changed. Now students are encouraged to find a variety of methods to solve word problems!

    Two days ago, I received an email from a person, who viewed either my Teachingvision.org site or the grades 3-5 blog here at Scholastic. I want to share her comment with you:

    I was wondering if you could give me some more information about your Glue It and Do Its. You had mentioned it in one of your Scholastic posts and I took the idea and tried it in my classroom. I was wondering if you could give me any more information about how you use it in your classroom. As part of my professional grown plan, I created a blog where I report on things I am doing in my classroom to help other teachers. You can check it out to learn how I have used your idea in my room. The link is http://www.teachertweet.blogspot.com. I would love to hear more about how these notebooks enhance your math instruction.

    Thank you for loving what you do and sharing with others!


    My PowerPoint Presentation

    As a result of this email, I want to share the lesson plan I have written for tomorrow's observation. It  begins with a short PowerPoint presentation that I will reference below.



    You need to know that not just one method of problem solving works! You and your partner in class may both solve a problem correctly; it is perfectly acceptable to complete the problem in different ways. Our lives are full of problem-solving moments; we just may not realize it at times. For example:
    • Having $250.00 to spend during the holiday season, think about whether you want to splurge for an iPod or purchase several inexpensive gifts instead.
    • How much money do I need for gas if I need to drive to Chattanooga, Tennessee? I know that Chattanooga is about 12 hours away and I have a 13-gallon tank. Gas is $2.60 per gallon. Think of how many times I will stop for gas and how much I will spend each time I stop.
    • My father works about 40 hours a week. He earns about $12.00 an hour. How much will he be making this week?
    • When my family eats at a restaurant and spends $46.00 for the family, how much should they tip the waitress if a tip is at least 15%?

    Today, I am going to show you what you have learned over the course of this year. You have completed “Glue and Do” problems, where you have had to write explanations with numbers, words and pictures.

    Why Don't we Just Write the Number Explanation?

    When you ask your family to help you out at home, do they just point to numbers without explaining to you in words about how they solve the problem? Sometimes you may also learn from others when pictures are drawn out- most people are visual learners.

    On the next page, you are going to see an example of a problem I solved using two different ways. Both ways are correct. I’ll be showing the papers to you in just a few minutes. What I want you to notice on the next page are the words and pictures. (Pictures of a problem about volume will show up briefly; please reference the photo at the beginning of this post.)

    You may have noticed that in my second picture that part of the cubes were red and the other parts were orange. In volume problems, you just try to find how many cubes fit into the shape that is shown.
     
    Here are some excellent strategies you may want to use as problem solvers:

    •    Highlight important words in your word problem.
    •    Color code your pictures when solving your math problems.
    •    You may want to draw out diagrams or group things together when solving specific problems.
    •    Don’t worry if you cannot think of a picture for the problem you are solving. Not all problems require a picture, but remember that many people in the world are visual learners and pictures “stick” in people’s minds.

    Now you are going to see a few examples and non-examples before solving specific problems with the group you are working with today.

    I will also show a non-example that does not have an appropriate explanation with words, numbers and pictures. The non-example below does not share a concise method on how to solve the problem:

    IMG_4640

    How many ways can this problem be solved?
    Students will see a few methods that can be used to solve two kinds of questions. One is a long multiplication question; the other is the volume questions shown. 

    Words, Numbers and Pictures:
    Students will receive a packet of three questions and complete them, “Glue and Do” style where they will solve the problem with words, numbers and pictures. Once they have completed their problem, they will gather with those in the class who have been given the same cards as them. (Hint: These questions were differentiated for each group.)

    *I found the questions through problems several students missed on a ThinkLink math assessment, the 2005 FCAT released math assessment for fourth grade, probes I created through ThinkLink, and my own thinking.

    Four-Minute Intermission:
    Measurement Rap From Mr. Duey - We are learning about measurement right now in class, so before students learn how to write their own multiple choice problems, they will listen to a rap song about centimeters, meters, inch and perimeter. They will be given the lyrics prior to listening to the song.

    Coming Up With Your Own:
    Students will now write two of their own multiple choice word problems, and see my examples first. They will receive a sheet with topics for their questions. We may then move on to problem-solving games in the five groups before completing the lesson. The games will be differentiated for the five groups.


    *Make sure when students work on their "Glue and Do" questions that they use words, numbers and pictures to solve their problems. You can make a page on Microsoft Word for this observation that has room for illustrating and writing beneath the word problem.

    Expand the Lesson

    The lesson can be expanded by students visiting Math Maven's Mysteries, where problems can be completed online as well as printed out. 

    Here is one last thing I would like to share with you:

    IMG_4625

    Think of everything you can in your classroom as a potential word problem. Let's say the parents in my class sliced 90 slices of turkey together for our recent Thanksgiving feast. If there are 23 students in the class and 10 parents attended, how many slices of turkey could each person receive at the most?

    IMG_4631
    One class mom baked three delicious fruit pies for our feast.

    • How many slices were there between the three pies if each pie was cut into eight slices?
    • If students ate X out of eight slices of one pie, what fraction of the pie was eaten? What is that fraction expressed as a decimal and percent?

    I thank every person who has asked me about problem-solving strategies this year, and I hope to share more with you as the year progresses.

    Once upon a time, math was... cut-and-dry. I remember being in either fourth or fifth grade and having to solve multiplication or division problems in front of the class using the "one and only" method our teacher taught us. I felt eyes bore into my head as I thought to myself, D-M-S-B- divide, multiply, subtract, bring down, don't forget, don't make a fool of yourself in front of the class. When I solved the problem correctly, I felt a great sigh of relief. Yet when I didn't "match" the teacher's solution, I felt embarrassed.


    I was the typical non-conventional learner in math, always sketching pictures and color-coding problems so I could understand them. As I teach a new generation of mathematicians, times have changed. Now students are encouraged to find a variety of methods to solve word problems!

    Two days ago, I received an email from a person, who viewed either my Teachingvision.org site or the grades 3-5 blog here at Scholastic. I want to share her comment with you:

    I was wondering if you could give me some more information about your Glue It and Do Its. You had mentioned it in one of your Scholastic posts and I took the idea and tried it in my classroom. I was wondering if you could give me any more information about how you use it in your classroom. As part of my professional grown plan, I created a blog where I report on things I am doing in my classroom to help other teachers. You can check it out to learn how I have used your idea in my room. The link is http://www.teachertweet.blogspot.com. I would love to hear more about how these notebooks enhance your math instruction.

    Thank you for loving what you do and sharing with others!


    My PowerPoint Presentation

    As a result of this email, I want to share the lesson plan I have written for tomorrow's observation. It  begins with a short PowerPoint presentation that I will reference below.



    You need to know that not just one method of problem solving works! You and your partner in class may both solve a problem correctly; it is perfectly acceptable to complete the problem in different ways. Our lives are full of problem-solving moments; we just may not realize it at times. For example:
    • Having $250.00 to spend during the holiday season, think about whether you want to splurge for an iPod or purchase several inexpensive gifts instead.
    • How much money do I need for gas if I need to drive to Chattanooga, Tennessee? I know that Chattanooga is about 12 hours away and I have a 13-gallon tank. Gas is $2.60 per gallon. Think of how many times I will stop for gas and how much I will spend each time I stop.
    • My father works about 40 hours a week. He earns about $12.00 an hour. How much will he be making this week?
    • When my family eats at a restaurant and spends $46.00 for the family, how much should they tip the waitress if a tip is at least 15%?

    Today, I am going to show you what you have learned over the course of this year. You have completed “Glue and Do” problems, where you have had to write explanations with numbers, words and pictures.

    Why Don't we Just Write the Number Explanation?

    When you ask your family to help you out at home, do they just point to numbers without explaining to you in words about how they solve the problem? Sometimes you may also learn from others when pictures are drawn out- most people are visual learners.

    On the next page, you are going to see an example of a problem I solved using two different ways. Both ways are correct. I’ll be showing the papers to you in just a few minutes. What I want you to notice on the next page are the words and pictures. (Pictures of a problem about volume will show up briefly; please reference the photo at the beginning of this post.)

    You may have noticed that in my second picture that part of the cubes were red and the other parts were orange. In volume problems, you just try to find how many cubes fit into the shape that is shown.
     
    Here are some excellent strategies you may want to use as problem solvers:

    •    Highlight important words in your word problem.
    •    Color code your pictures when solving your math problems.
    •    You may want to draw out diagrams or group things together when solving specific problems.
    •    Don’t worry if you cannot think of a picture for the problem you are solving. Not all problems require a picture, but remember that many people in the world are visual learners and pictures “stick” in people’s minds.

    Now you are going to see a few examples and non-examples before solving specific problems with the group you are working with today.

    I will also show a non-example that does not have an appropriate explanation with words, numbers and pictures. The non-example below does not share a concise method on how to solve the problem:

    IMG_4640

    How many ways can this problem be solved?
    Students will see a few methods that can be used to solve two kinds of questions. One is a long multiplication question; the other is the volume questions shown. 

    Words, Numbers and Pictures:
    Students will receive a packet of three questions and complete them, “Glue and Do” style where they will solve the problem with words, numbers and pictures. Once they have completed their problem, they will gather with those in the class who have been given the same cards as them. (Hint: These questions were differentiated for each group.)

    *I found the questions through problems several students missed on a ThinkLink math assessment, the 2005 FCAT released math assessment for fourth grade, probes I created through ThinkLink, and my own thinking.

    Four-Minute Intermission:
    Measurement Rap From Mr. Duey - We are learning about measurement right now in class, so before students learn how to write their own multiple choice problems, they will listen to a rap song about centimeters, meters, inch and perimeter. They will be given the lyrics prior to listening to the song.

    Coming Up With Your Own:
    Students will now write two of their own multiple choice word problems, and see my examples first. They will receive a sheet with topics for their questions. We may then move on to problem-solving games in the five groups before completing the lesson. The games will be differentiated for the five groups.


    *Make sure when students work on their "Glue and Do" questions that they use words, numbers and pictures to solve their problems. You can make a page on Microsoft Word for this observation that has room for illustrating and writing beneath the word problem.

    Expand the Lesson

    The lesson can be expanded by students visiting Math Maven's Mysteries, where problems can be completed online as well as printed out. 

    Here is one last thing I would like to share with you:

    IMG_4625

    Think of everything you can in your classroom as a potential word problem. Let's say the parents in my class sliced 90 slices of turkey together for our recent Thanksgiving feast. If there are 23 students in the class and 10 parents attended, how many slices of turkey could each person receive at the most?

    IMG_4631
    One class mom baked three delicious fruit pies for our feast.

    • How many slices were there between the three pies if each pie was cut into eight slices?
    • If students ate X out of eight slices of one pie, what fraction of the pie was eaten? What is that fraction expressed as a decimal and percent?

    I thank every person who has asked me about problem-solving strategies this year, and I hope to share more with you as the year progresses.

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