In the following examples, we began to learn compensation by using only manipulators to represent numbers. I also used a Number Talk in which I showed pattern numbers similar to the following and asked the students how many there were. Students shared various strategies, including counting, creating a ten, grouping dozens and ones, and more. This method of adding more than we need, and then deducting the difference at the end, is called an additional compensation strategy. We used boards to practice this at least 5 times before I could see that the majority could apply this strategy independently. From there, it was time to move on to the symbolic level and practice mathematical consumables. Now that we understand how to apply the clearing method with our bonds numbered at ten, we will expand the strategy to add larger numbers. What are some of the strategies you teach your students or children to add two- and three-digit numbers? Do you use compensation? Or do you start teaching with the standard algorithm? Teaching students to be flexible in their strategies makes them more likely to persevere and find a solution. Compensation in mathematics is the process of reformulating a problem of addition, subtraction, multiplication, or division into a problem that is mentally easier to calculate. With practice, the compensation method can be used as a mental addition strategy to quickly add 2-digit numbers. One of the many strategies I`ve taught my students is to create a ten. The next step is the remuneration of teachers, which uses a number close to ten (10, 20, 30, 40, 50, etc.). With divisional compensation, you can divide or multiply the divisor and dividend by the same number.
The equal addition method is a compensation used for subtractions. In my district, we happen to use the Go Math textbook. The district encourages teachers NOT to use it as intended. Instead, the district encourages teachers to focus on norms, conversations about numbers, math conversations, and strategies. However, I still use math to practice (students have consumables). In Go Math, this process of adjusting numbers is called compensation. But wait! Some series of mathematics textbooks call it transformation! So what`s the difference? Research indicates that compensation adjusts only one number at a time, while transformation adjusts both numbers at once. While it sounds like semantics, teaching this strategy to second-graders makes a difference! If you want to make your own carpets to communicate the compensation strategy, subscribe to my newsletter to receive your copy! 42 x 5 can be found with multiplicative compensation as follows Students would physically move students to one side to complete a ten. Note that we didn`t exchange the ten new ones for a rod (which comes later when we focus on bundling).
14 add 1 equals 15, so 24 remove 9 leaves 15 meebs still in the race. . I gave the students two numbers that they had to represent on either side of the zigzag line. For this part, I asked the students to work together as partners who shared a mat, as I was limited in the number of manipulators I had for this lesson. Removing 9 can be a bit tricky, but 9 is only 1 of 10, so we take 10 instead. 22 was divided by 2 and 25 by multiplication by 2. 5 times 11 is easy to do. It`s 55 Then all we have to do is put the 0 next to 55 to get 550 Many years ago I trained in Math Their Way®.
Thanks to this training, I teach a concept or strategy at a concrete level. At the concrete level, students use only means of manipulation. The next level is the connection level. The connection layer connects numbers and symbols to manipulators or patterns that students have created. Then we move on to the symbolic level where students use paper and pencil. To simplify this addition calculation, we can add 2 to 18 to get our next multiple of ten, which is 20. Now that the students understood the concept of adjusting or compensating numbers, it was time to put aside the manipulators and draw models for the number, as well as add numbers and symbols for addition. In our first example of addition below, we are asked to add 6 + 7: we will look at the examples of addition in which we first add numbers in the tenfold array.
We start by using our 33 – 27 can be considered 40 – 34 by adding 7 to 33 and 27 everyone finds some numbers easier to work with than others. Adding or removing 10 may be easier than 9 or 11. Then we have to put back 1 because we removed 10, but we only wanted to take 9. Compensation is a way to add or remove numbers that you find easier. As rewriting the problem as 97 + 3 + 61 can help us get an answer quickly We will subtract 3 out of 16 to get our final answer. You add or remove a little too much or a little too little, so you`ll have to add or remove that too. Do you want a copy of the carpets? Then subscribe to my newsletter to receive your copy! To do subtraction 58 – 40, we added 1 in 57 and 39 so we still have the same subtraction problem. It may not be easy to add 97 and 64 mentally. However, a small adjustment, we have to remove another 1 because we wanted to remove 11, not just 10. Here is a video of one of my students applying this strategy independently. You drive time trials with your race meebs.
NARRATOR: Oh look, 2 more meebs just gave up, which means 11 of the 24 that started gave up. Before I started teaching strategy, I made work mats that were double-sided and would help give some structure to the lesson. For example, in the additional example below, we have 15 +18. 84/14 is the same as 42/7 and if you know your multiplication table, you know that 42/7 = 6 you removed 1 too much (10 is 1 more than 9) Fin and Snoot add up some of their favorite snacks: space larvae and astro insects. Note that 42 has been multiplied by 2 and 5 by 2 Since we added 2 at the beginning, we now need to subtract 2 from our answer to compensate for this. It is not easy to do one of these supplements mentally. You can find out by removing 10 again, as 11 is only 1 in 10. 25 + 25 + 20 and it`s mentally very easy to do like 25 + 25 = 50 and 50 + 20 = 70 It was an easier addition because the units remain at six, we just add ten more in front.
However, if we take 2 out of 27 and add that to 18, the problem becomes compensation is defined as adjusting a number when adding. .