At that point, they are ready to use the standard algorithm. Students can solve problems using both methods side-by-side until they are comfortable with the standard algorithm and can explain the place value concepts behind regrouping. Notice how it really sets them up for success with the standard algorithm.įinally, after students have had plenty of practice using this expanded form procedure, we can come in and put the standard algorithm right alongside it. So now they can record it as shown below. They also know that 5 tens and 7 ones have the same value as 4 tens and 17 ones. They realize they can’t subtract 8 ones from 7 ones. When regrouping is required, students use their experiences with direct modeling. We write the numbers in expanded form, subtract the ones and the tens, and then write the expanded form answer using standard form. Using the same idea, subtraction without regrouping is pictured below. This strategy involves using expanded form to work with the value of the digits. We often use a strategy called partial sums for addition, and we can use the same process for subtraction. A word of caution-don’t begin this process until students have a very strong understanding of regrouping using direct modeling. It’s finally time to introduce the standard algorithm. The purpose of invented strategies is to allow students to use the strategy that makes sense to them! The Standard Algorithm It’s not necessary that every student understand every strategy. If I take away 5 ones, that gets me to 30 and taking away 3 more ones makes 27. I can start by subtracting 10 from 45 and that’s 35.But then I have to take 3 away because that’s what I added to 45 to make 48. I can pretend that 45 is 48, because 48 – 18 is easy to solve.Forty-five minus 20 is 25, and then I have to add back 2, since I’m really only subtracting 18.Here are several ways students might solve 45 – 18 using mental math invented strategies: These strategies do not replace the standard algorithm, but they do build a better understanding of the procedure. It also highlights the fact that math should make sense and that multiple strategies for solving math problems are encouraged and celebrated. Using number talk routines as an ongoing part of math instruction helps students develop flexible strategies and number sense.
Invented strategies are any strategies other than direct modeling or the standard algorithm. Then they practice with additional problems requiring regrouping. All I really need is for at least one pair of students to realize that they can trade a ten for ten ones and my lesson is gold! All of the students get the opportunity to grapple with the problem, the students who solve it can share out what they did, and then I can come in behind and reinforce the concept-if there are not enough ones to subtract, I can trade, or regroup, a ten for ten ones.
Right away they will likely realize that the process they have been using doesn’t work with this problem-they only have 5 ones, so they can’t subtract 8.
Pair up students and ask them to use their base-10 blocks to solve 45 – 18. You can get even more bang for your buck by introducing this next phase using problem-solving. Next up, you want to introduce a problem that will require regrouping. Stacking the numbers in a vertical format will come later. Notice that the problem is written horizontally. You want students to develop the understanding that we subtract ones from ones and tens from tens. Give students plenty of practice using base-10 blocks for problems that don’t require regrouping before moving on to the next step. Be sure to stress place value language during this phase of instruction-subtracting with regrouping is all about place value! So, for example, to solve 45 – 14, students would build 45 and remove 1 ten and 4 ones. Begin with problems that don’t require regrouping. Base-10 blocks are a great tool for modeling the process. Not surprisingly, we build understanding for the standard algorithm by starting with hands-on, concrete learning. There is no additional cost to you, and I only link to books and products that I personally use and recommend. This post contains affiliate links, which simply means that when you use my link and purchase a product, I receive a small commission. This post focuses on the progression for teaching subtraction with regrouping. This is a good thing! There are several developmental steps that students should move through before being introduced to the algorithm. More and more curriculum maps are delaying the teaching of the standard algorithm for addition and subtraction until later in the year.
0 kommentar(er)
