Here’s the mistake we started with:

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On twitter, I asked some elementary school colleagues what they made of this.

Here are some of the ideas we came up with:

I wasn’t able to turn all of the ideas into activities, but here are the follow-up activities I came up with. If I were addressing this error in class I think this could be a progression of activities that help address the thinking in this mistake.

Response to How Much Longer Mistake (8) Response to How Much Longer Mistake (7)

Response to How Much Longer Mistake (9)

What do you think?

Update: This post from Andrew seems relevant.

  • Howard Phillips

    1. Justin was probably in a rush.
    2. More to the point, if a problem is posed in some detail then the “answer” must be posed in the same or similar detail, so the subsequent question for Justin is “How much longer ……?”. To finish Justin has to answer this question. Therefore the given answer is not an answer at all, just a collection of symbols, and earns about 2 out of ten.

  • Jo

    How much/many more is a tough concept but if they’re not pretty familiar with that language until they’re adding and subtracting three digit numbers then they missed something in first grade. Common core is pretty specific about comparison problems being one of the types of subtraction problems.

    it’s hard for kids to understand that this is a part part whole problem where you are missing a part. Some things I have done to help them understand what we are trying to find:
    –make 2 equal stacks of books and then add a few more to one stack and show them that what you are trying to find is the more that were added to one stack.
    –had one student stand on one step and another stand a few steps above and asked how many more steps the first student had to climb to be on the same step
    –build towers out of unifix cubes and have them break off the extra of one of the towers and find out how many more the second tower had

    It’s hard because more tends to mean addition to them but in this case it’s how much has been added to the equal parts to make one part bigger. It’s a really tough concept and they need to see it, and then relate it to a part part whole model (like a vertical tape model). Once they get the concept they don’t stumble over it any more.

  • Julie

    Hi! Just wanted to say I really like the variety of options pointed out by contributors and your follow up activities. It’s interesting how many ways one problem can be addressed. How do you decide which is best? Is it from familiarity with the class/this individual student, talking to the student to find out more about their thinking, or is there something else that you would base this decision on?

  • Jeff Holcomb

    Something that might be worthwhile is to use “bet lines” as a protocol for pitching a problem like this to the class. Here is how I see it play out for this problem.

    1) Write up the first line of the problem on the board: “Justing is preparing for a violin performance this weekend.” Then ask the students what they bet will come next. Discuss, asking for reasoning behind their suggestions.
    2) Write the next line. Again ask what they bet will come next and discuss the reasoning.
    3) Repeat for the following lines. Being careful of pacing so you get to the ending sentence without creating the feeling of beating a dead horse.
    4) Have the kids solve the problem.

    There are lots of things I like about this protocol. One of the biggest is the opportunity to be developing my own understanding of how the kids are thinking about this problem, what they are picking up from the words, how they are creating the picture in their head of what’s going on, how they are making the decision for how they are going to go about finding a solution. As kids share out their thinking they are providing an opportunity for the teacher to represent their thinking using a good model (possibly like the one @joeshwartz10a suggested above).

    Also, credit where credit is due, I picked up this protocol via http://www.therecoveringtraditionalist.com/