|I borrowed this photo from Linda at Kinder Doodles! Be sure to check out this post for great ideas for building number sense!|
Comparison subtraction is such a hard concept for kiddos! Pose the following problem:
Susan has 8 marbles. Lisa has 3 marbles. How many more marbles does Susan have than Lisa?
If you asked this question to a classroom of 1st graders, what answer do you think you’d get most often? Did you say 11? Trust me, they would! They might also say 8, because that’s how many Susan has. Way too often take-away subtraction is the only type of subtraction students see in our classrooms. If you look at standardized tests, though, the type of subtraction most often tested is comparison subtraction. Why is that? In Planting the Seeds of Algebra, author Monica Neagoy quotes Bob Moses, founder of a movement called the Algebra Project, regarding subtraction:
“If students are only taught the take-away metaphor, they’ll have trouble in algebra. In algebraic expressions involving subtraction, such as x2 – x1 or y2 – y1, the take-away metaphor is of no help. The distance between two points, on the x-axis or y-axis, is the helpful metaphor.”
Now, if you don’t totally understand everything Mr. Moses said in this quote, don’t feel bad. The point is that when an expert on algebra says we need to teach other structures besides take-away, we should listen. And if if take-away is not the helpful subtraction structure for algebra readiness, then it’s not going to be tested on standardized tests.
I blogged before about a kinesthetic approach to teaching comparison subtraction, and today I want to suggest using a floor-sized number line as an additional representation. As pictured above, create a floor-sized number line in your classroom. I’ve seen teachers put them by the door where students line up to leave the classroom and use it as a classroom management technique. Have two students start at 0, and then have one student walk 8 steps and the other walk 3. The question becomes, “How many steps farther did Student 1 walk than Student 2?” Or “How many more steps did Student 1 walk than Student 2?” Or, and this one is important because it’s being used with great regularity on standardized tests, “What is the difference in the steps walked by Student 1 and Student 2?” Mix up your questions as you repeat the activity, so students become familiar with comparison subtraction in all of its forms!