Book Blogging Buddies: What’s Your Math Problem Chapter 5

book blogging buddiesAs we get into Chapter 5- Visualizing Strategies, I started to think of all the many different ways that we visualize things in our lives. We depend on the use of sight for so much that many times we take it for granted but for many people when we add that visualization with the use of movement, manipulating, or drawing it makes it stick with us so much more. We all know about our kinesthetic learners in our classroom. Yep, I’m one of those.

Gojak breaks down the four Visualizing Strategies as:

-Make a Model

-Draw a Picture/Diagram

-Act it Out

-Make or Use a Graph

Make A Model: This strategy is honestly one of my favorite for my more concrete learning objectives. This is when you are able to incorporate manipulatives of all types in your class to help focus on the building of a solid foundation.

I think that it is important for us as teachers to show our students how to use different manipulatives to support various forms of problem solving. Not only do we need to teach them, we need to let them use them. This was a hard one for me because I wanted to know where things were at all times but I had to let go of the control and let them be used instead of just a pretty box on the shelf.

Manipulative Storage

Tip: Take time to sort and label your manipulatives clearly in your classroom. This will not only save you time but also your students will know where they belong.

Draw a Picture/Diagram: Taking time to think things out in pictures is great for students who are able to visualize what they know. When a student “sees” what is happening they can then relate that to something from their own lives and therefore that abstract picture gains purpose to help them reach their solution.

Super Hero Problem Solving

When teaching students to Draw a Picture/Diagram, it is important to teach them to Get Rid of the Trash. Yep, all the fluff that is there to embellish the problem needs to go so it doesn’t distract us! When I am teaching Technical Reading Strategies for Problem Solving to my students, I try to get them to limit their info to 5-7 important words.

Act It Out: I will admit that “Acting Out” problems is something that doesn’t just come naturally to me. Well, it didn’t before I started creating most of the problems I use in my classroom. By doing this I am able to prepare ahead of time (back to Planning Problem Solving from Chapter 2).

I have however used the form of videos and songs to help my students act out and remember various concepts. Check out one of my favorite on Exponents.

Make/Use a Graph: Organizing data in the form of a graph is one strategy that is often overlooked, from what I have experienced, because it takes TIME! Yes, we know our students get to the point that they just want to get things done so taking time to work through, what I think is one of the most efficient strategy, is just not their idea of fun.


Over the past few years of teaching Middle School students, I learned that taking time to show various graph styles in class (mostly humorous) really started to get my students under the realization that they were beneficial and easy to read. The best part is when they start using them for an open-ended response and you weren’t expecting it. Those are some proud teacher moments!

So after reading about Visualizing Strategies, Gojak asks questions for us to reflect upon. Feel free to answer in the comments in and come back to continue on with the discussion with others.

1. Which strategy was most difficult for you? Why? How can you become more comfortable using this strategy

2. Were any of these strategies new to you? If so, how did hey help you think about solving problems in a different way?

3. Which strategy do you think you will use with your students first? Why?

6 thoughts on “Book Blogging Buddies: What’s Your Math Problem Chapter 5”

  1. I am a visual learner, so this chapter resonated with me most so far. I usually draw diagrams or pictures when solving problems, in addition to using graphs and solving simpler problems (more on that coming up in Chapter 6!).

    If your classroom is stocked with manipulatives to use for model-making, then use them! I find that plastic/paper play money is great for money word problems, and rods/base-10 manipulatives are great for fractions problems. Don’t have manipulatives? Make them! It is amazing what you can create with a few sheets of paper and a pair of scissors.

    The best take-away from this chapter? The reminder that organizing information, reading/creating graphs, and analyzing data are critical skills to have in this world. Of all 3 visualizing strategies examined in this chapter, I believe making/using graphs is the most critical one to develop from an early age. Jennifer – I love your idea of showing various graphs to your MS students. I’ve seen graphs in magazine articles, advertisements, and even comic strips….let’s make sure our students also see these to know their relevance to media and the world around us.

    • I loved this chapter, too! After solving the penny model I was pumped! The garden problem…blah! I like to see things, hold them, and manipulate manipulatives! So the draw a picture or diagram was probably my least favorite! I will need to hone this approach/skill.
      I am familiar with each strategy but I appreciated “seeing” each applied grade k-2, 3-5, and 6-8. What I gained was insight into how I might “steer” my students dependent on their learning styles/strengths.
      Use a model is a favorite and I can foresee me starting the year with this strategy. I believe what I take away from this chapter is the need to learn to organize work, draw conclusions, use a strategy/ies to solve, and be able to understand the process and apply it to various problems.

  2. Chapter 5 was only 15 pages long but it was “meaty” for me. It clarified information that I didn’t know I needed clarified. I’m still processing the difference between draw a picture and draw a diagram on page 110. Now I know how my students feel. The problem solving for the primary grades were on my level (heehee). I spent 12 years in 1st grade. I struggled with the 6-8 grade problems but I forced myself to break through (At times, with my freshman son’s help). It was not the strategies that challenged me, but my own grade level problems 6-8. This chapter was correct in stating that its the beginning step where we get stuck.

    I will definitely be using the make a graph more at the beginning of the year. Our sixth grade texts seems to jump to use a graph. I didn’t realize I had students that didn’t know the problem solving connection in using a graph until I stumbled. I predict it is because they lack experience in making a graph with a connection to problem solving. In first grade, I created lots of graphs, but I did it superficially because I was focused on the basic operations practice the graph making activity provided. I did not “dig” into problem solving.


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