Week Five: Chapter 4A Getting Started: Anticipating Students’ Responses and Monitoring their work

06 Feb 2014 4:28 AM | Anonymous member (Administrator)

Week Five:  Chapter 4A  Getting Started:  Anticipating Students’ Responses and Monitoring their work


Read pp 31-42


Do the “try this” on page 42 and share your guide

Select a high-level task that has the potential to help students achieve a learning goal you have identified.  


Individually, or in collaboration with one or more colleagues, do the following:

       

Anticipate all the ways in which students are likely to solve the task and the errors they might make.

       

Consider questions that you could ask about these approaches that could help students in making progress on the task.

       

Create a monitoring sheet you can use to record data during the lesson.


Share this by next week

You can ask for feedback.

Comments

  • 10 Feb 2014 6:46 PM | Anonymous member (Administrator)
    So I haven't been completely faithful in this book study, but I have picked a task with a colleague and we have tried to create a guide.
    We picked a task that has students multiply fractions by a whole number. The difficulty is that there are two problems within one scenario. Following a reading of Full House by Dayle Ann Dodds, each guest staying in the inn ate 2/3 lb of potato and 6/8 lb of chicken. Students are to find out how much potato and chicken Miss Bloom cooked. Students need to determine how many people are being included in the count, including Miss Bloom. Students have also learned how to add fractions with uncommon denominators, and may assume they are adding the two fractions together, instead of seeing that they are separate problems.
    Some of the expected misconceptions include:
    only counting 5 guests- and forgetting the innkeeper,
    trying to add 2/3 + 6/8 correctly by using 24ths,instead of finding 2/3 X 6 and 6/8 X 6 individually,
    adding 2/3 + 6/8 incorrectly by adding numerators and adding denominators,
    finding equivalent fractions instead of multiplying fractions (because they are accustomed to that with finding a common denominator)
    Students are required to write an equation, use a visual model, and write an explanation. Hopefully, at that point students reflect and question some of those common misconceptions.
    Models could include: pictures, number lines, bar models, area models or circle models.
    Strategies to solve the problem could be to create a table, use repeated addition, scale up (with each fraction) and use multiplication.
    Writing a clear explanation of their process and justifying their answer may also prove to be a challenge for several students.
    We plan to teach one day, when students will solve with a rough draft and then make a final copy to present to the class the following day. That gives us the evening to look at their work, and decide how to order the discussion through a conversation together. That way we can support each other through deciding on the best practice with the misconceptions we see. We are planning to teach this lesson on Tuesday Feb. 25th, and hold the discussion the following day.
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    • 10 Feb 2014 7:02 PM | Anonymous member (Administrator)
      I couldn't figure out how to add the link to the monitoring sheet we created.
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    • 12 Feb 2014 2:40 PM | Deleted user
      Holly,

      Nice lesson tied to ELA!!! Students could also add the 2 fractions and then multiply by 6 which could cause some of the misconceptions you presented as well. Some students may also recognize that 6/8 is the same as 3/4 to make the problem simpler to add before multiplying. Good luck with the lesson & I am looking forward to reading your remarks afterwards!!
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      • 27 Feb 2014 9:03 PM | Anonymous member (Administrator)
        Donna, I thought about your comment also when I read Holly's task. I wondered if kids new about distributive property and if they'd add the two fractions and then multiply by six.
        I also agree Holly, students often leave out the inn keeper in these types of problems. When a question says, "Jim and his three friends..." Jim often gets left out.
        I know we are working on having students explain their work and thinking about the solution of a problem through writing. This is hard for students. We work to provide students with opportunities to talk about their work before they begin writing.
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  • 13 Feb 2014 1:49 PM | Deleted user
    The lesson was about using similar triangles to find side length.
    A single diagram that represents a ramp with several posts coming down was used. The goal was to see if students could use their understanding of similar triangles and of proportions to find the height of the uprights and the length of what would be the hypotenuse if it were a right triangle. Students alone first and then worked in pairs and trios.
    The first problems was understanding the sentences explaining the problem
    Setting up proportions in the correct order can be tricky
    Another problem is that it looks like is not the same as it is ( it looks like a right triangle)
    questions to be asked:
    Retread these 2 sentences - what is known and what is asked?
    Can you prove it is a right triangle?
    Even if the drawing looks like the line is halfway, , do you have a way of proving that?

    I did not set up a monitoring sheet but think this is worth my time next time to keep track of who is stuck where.
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    • 27 Feb 2014 9:05 PM | Anonymous member (Administrator)
      I love these kinds of problems Mary. I think students also have trouble with imbedded triangles and it sounds like this might be that type of problem. I also agree that setting up the proportion correctly is sometimes difficult for students. I often ask them to verbalize what each number in their proportion represents as a way to help them be sure that they've set the problem up correctly.
      I also think it's important for students to be able to prove their work.
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  • 27 Feb 2014 8:58 PM | Anonymous member (Administrator)
    Task:
    The problem that I chose for the task is from the CMP3 sixth grade Let’s Be Rational unit. Students are beginning to think about dividing fractions and start with thinking about a whole number divided by a fraction.
    "Naylah plans to make small cheese pizzas to sell at the school carnival. She has nine blocks of cheese. How many pizzas can she make if each pizza needs the given amount of cheese."
    a. 1/3 block b. 1/4 block
    c. 1/5 block d. 2/3 block
    e. 3/5 block f. 4/3 block

    I am going to focus on part d. I’m curious to see what the students will do with 2/3 of \ a block of cheese and how they will deal with the left over 1/3 from each block of cheese.

    Anticipated solutions and errors:
    I expect to see drawings that represent the blocks of cheese.
    The problem was launched with a number line, so I might see students using a number line but as it’s blocks of cheese they might also draw individual rectangles to represent the cheese.
    A possible error might be a response of 9 pizzas, with the student forgetting to deal with the 1/3 part left over from each block of cheese.
    Students might start by trying to write an equation for the situation.
    Students might not recognize this as a division problem.

    Questions to ask about the approaches used by students to help them make progress on the task:
    Can you represent the problem?
    Would using a number line be helpful?
    Would using a picture help you?
    What does your picture represent?
    Would it help to label your work?

    Monitoring sheet to record data during the lesson:
    Who Strategy Prompts from Teacher Notes
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