Learning to subtract appears to be more challenging for most students than learning to add. Once students recognize that subtraction is the inverse operation from addition, they are more likely to be able to subtract more efficiently. For this reason, this week the two open number line strategies that the students are practising are both counting back and counting on.
Remember that a strategy is a plan of action to reach an outcome. We ask students to use a strategy that works best for them. It should be efficient (not take a long time, so counting by 10's in quicker than counting by 1's) and it should make sense to the person using it and of course, it should result in a proper solution.
In the counting back strategy, the largest number (the minuend) is placed on the far right side of the open number line. The student then 'jumps back the value of the second number (the one you are subtracting is called the subtrahend). The jumps must equal that number. Once the jumps are complete, the final landing spot is the solution to the equation, or the difference. We avoid using the word answer so that students don't see their solution as right or wrong. We, instead, talk about whether it makes sense. This goes back to the idea of algebra, and recognizing that the equal sign actually means that the two sides balance. Think of it this way: 10=3+7 but 10=4+6 as well.
In the counting on strategy, the students who like to add might be more comfortable. The smallest number (the subtrahend) is placed on the farthest lest side of the open number line. The student then jumps UP to the value of the largest number (the minuend) to find the difference. The student must add the jumps that they did to find that difference. Think of it this way: 3+ ___=10. What number makes this equation true?
In our first attempt of practising these two different strategies, I had the students write which strategy they were trying. This one is trying the counting back strategy. Do the solutions work?
Surprise! The solutions using the counting on strategy should be the same? Did this kiddo, match the solutions of the first page? I can see where more teaching is needed as well as a great deal more practise!