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Chapter 4 – Option 3 (Action)

02/03/2019 10:57 PM | Anonymous

Representation is an important component of curriculum and standards (NCTM & Common Core) for all math grade levels.  Think of an example task from your grade level where the Connecting Representations routine would be applicable.  If you implemented it with your students, tell us how it went.


If you want to share a task with the group, send a document, photo, or link to atomicbookclub@gmail.com and I will set up a shared google drive folder for the materials.


Comments

  • 02/04/2019 1:09 PM | Alison Foley
    I think in grade three when students are developing an understanding of multiplication would be a good time to use the Connecting Representations routine. Students are learning many types of models (arrays, jumping on a number line, drawing equal groups etc.) to make sense of multiplication. It is important to make connections between the different types of representations and for students to realize how these models connect to tasks. An example of a task would be:
    Jill is making goodie bags for 4 of her friends. If she wants to have 9 items in his or her bag, how many items will she need to buy? Show your reasoning with a model.
    Although this task is fairly straightforward, I think the connections between different models for multiplication would be very powerful for students at the beginning of their understanding of multiplication (for example, drawing 4 bags and putting 9 items in each relates to using a number line and jumping 9 for a total of 4 times -the 4 jumps relates to the four bags and the distance of 9 relates to the 9 items in each bag). I have not done the Connecting Representations routine in full yet but look forward to trying it!
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  • 02/05/2019 2:04 PM | Cindy Noftle
    I think that connecting representations routine would be applicable in connecting algebraic expressions with geometric representations. Specifically, using algebra tiles to factor trinomials. I used part of this routine in my class but I neglected to use sentence frames and starters. I did use repeated phrases myself but I should have requested that the students do the same. They did very well with noticing specifics about the tiles and then connecting info to the given trinimial. I made sure that all students had a handout of problems and their own set of tiles. In addition they worked in pairs. When students were asked to create an area model of the trinomial they at first were hesitant and confused but after a problem or two they were solving them easily. They were able to summarize how to put them together and then they were able to just extend this by sketching the geo model without the tiles. By the end of the lesson the students had created an algebraic expression that modeled the factoring.
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    • 02/09/2019 8:55 AM | Marianne Springer
      Cindy,

      I should have read your comment before writing mine under prompt 1 for this chapter. I'd love to get more info from you about this factoring lesson and we could even practice the routine together during PD time. I know I need more practice keeping the "ask yourself" and sentence frames and starters in mind during any of the routines. My "ask yourself" questions have typically been tied to the task at hand but I'm trying to make them more general as is promoted in these routines.
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      • 02/09/2019 6:30 PM | Cindy Noftle
        Absolutely let’s plan a routine in out an upcoming cot.
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  • 02/07/2019 9:35 AM | Cortni Muir
    Again I am going back to using Exemplars (problem solving real world problems).

    One of the main components of Exemplars is trying to encourage students to use a variety of representations. When I am demonstrating in a classroom how you could use different representations, I think this specific routine could become a valuable tool for students to think structurally.

    More and more recently between this book and some other professional learning I am doing, I am realizing how important the idea of annotating work and color coding those annotations can be for a student. For this routine, providing students with a few different representations of the same work and allowing them to interpret and look at structures and relationships will help build deeper understanding. The idea that the annotation is like "visual residue" for student to be able to reference allows all different levels of students to make connections. It helps to keep student organized and keep track of different steps so students don't get lost in the process. Additionally it allows students to revisit and refine their thinking when they have written evidence to refer back to.
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  • 02/10/2019 12:06 PM | Allison Day
    I think identifying decimals would be a good lesson for connecting representations. There are always a lot of misconceptions around fraction and decimal equivalents. Getting students to visualize what the decimal means and connect it to a representation will help students think about the decimal structure when they compare, round, and operate with decimals in the future. For example, students sometimes think 0.05 has the same value as 0.5. Sometimes students think the numerator in the fraction is the number of squares shaded in on a hundredths grid, even though the denominator may not be in tenths or hundredths, such as 1/8. It is important for students to be flexible with their thinking and identify the decimal numbers on different grids (tenths, hundredths, thousandths grid etc.) This task relates well to the quote in the book on page 76, "to connect a numeric expression to a visual without completing any calculations-- was designed to encourage you think in that way." This connection and flow of the routine make it very low risk for students. It requires students to pause and attend to the representation, numeric expression, or language. Noticing what is the same and what is different highlights the structure. This task also supports the thinking of "chunk, change, and connect." Students may change the visual from hundredths to thousandths, they may connect money with decimals or times for sporting events. I love how there are many ways of thinking about this problem.
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  • 02/22/2019 7:00 AM | Walter Pohle
    I feel the Connecting Representations routine would be applicable in many areas of our 5th grade curriculum. Students are introduced to Volume in the 5th grade and although most learn and understand how to calculate the volume of a rectangular prism quite easily, it's when two or more rectangular prisms are combined to make a complex rectangular prism is when it becomes difficult for the students to calculate the total volume. I have many "Matthews" in my class as described in the opening vignette of the chapter. Students just aren't thinking critically enough and often make careless mistakes with their calculations. I can use this Connecting Representations routine as a view of volume before MCAS. I will show students the complex rectangular prisms on the board or have models made out of card stock. Depending on how the complex rectangular prisms are decomposed, the expressions used to calculate the volumes will vary. Giving them the expressions to match up with the physical model will help the students think structurally as they progress toward solving the problem.
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