What does the kid think the distributive property is?

It’s easy to say: “Well, I’d avoid this mistake in my class by teaching the distributive property correctly.” Well, what’s the wrong way to teach this thing, then? What’s the smartest possible way to teach this, and still end up with your kids making that mistake?

After you’re done writing an awesome comment to this post, go check out Josh Weisenfeld’s blog. He spotted and submitted this gem of a mistake.

  • Distribute the properties! I wonder what would happen if there were three terms in the group. Subtraction next, or division?

    Saying one is going to teach it correctly does not mean one is going to teach it in a way that will help the student. (teaching correctly != saying it louder with more enunciation).

  • I always focus on the area model and have them draw a lot of rectangles for multiplying (and distributing). It slows them down a bit but it does seem to help avoid these kinds of mistakes.

  • Write the front number, with a dot for multiply, in front, then give it to each other item on the next line. Colors help.

  • Distributed Arithmetic is an expression used to calculate Sum of Products. For three arbitrary real numbers-
    a∗(b+c)=a∗b+a∗c
    For example:-
    2 * 7 can be broken down into
    2∗ (5+2)
    = 2∗5+2∗2
    = 10+4
    = 14