![]() In a 1st-grade class, a student uses their knowledge of number combinations to solve 8 = ? + 3, modeling the problem with counters. And trust me, the time it takes a child to do this is a lot less than the time it takes me to explain it! They can now solve it by decomposing the 5 into 2 and 3, adding the 2 to the 8 to make 10, and then adding the remaining 3 to get 13. They know that a combination for 5 is 2 and 3. Say the student is now presented larger numbers, like 8 + 5. This is actually the foundation for learning basic facts, but it goes beyond that. Consider the following examples:Ī Kindergarten student uses number bracelets to find all the combinations for a given number. Ĭomposing and decomposing numbers became part of our instructional vocabulary after the Common Core State Standards for Mathematics (CCSSM) were adopted in 2010. It’s a skill that starts in Kindergarten and follows students throughout their mathematical career, and it’s something that should be present in your classroom on a daily basis. One of the key factors in reaching that goal is helping our students learn to compose and decompose numbers. Think about the ultimate goal of math instruction-students with strong skills and flexibility with numbers. So what does that have to do with math you might ask. Every four years, I’m blown away by the strength and flexibility of these athletes. Anybody else? I have to admit that I was not very flexible-I couldn’t do a smooth backward roll to save my life! That said, one of my favorite Olympic events is the gymnastics competition. 47 on 100, or 47 hundredths, 4 tenths, plus seven hundredths.As a young girl, I briefly took gymnastics lessons. Plus these one, two, three, four, five, six, seven Which is the same thing as 40 hundredths, shaded in blue. So you see, 47 hundredths, which is all the stuff shaded, that's the same thing as the four tenths. ![]() The star right over here, I could write that as seven hundredths. So the star right over here, this is going to, let me actually, let me erase this. So 40 hundredths plus seven hundredths is the same thing as four But what's left over? Well, we still have the So hopefully you're convinced that 40 hundredths is the same So 40 divided by 10 is four, 100 divided by 10 is 10. And you'd also divide the numerator by 10, going from hundredths to tenths. The denominator by 10, when you go from hundredths to tenths. Another way you could think about it, when you go from hundredths to tenths, each 10 hundredths, each 10 hundredths, is are equal to one tenth. And so you see, these 40 hundredths that are in blue right over there, that's the same thing as one tenth, two tenths, three tenths, and four tenths. Into a hundred equal sections, but into ten equal sections. Notice, if you look at the orange lines, I've divided my square not So this would be four tenths, (mumbles) doing five tenths, six tenths, six tenths, seven tenths, eight tenths, and nine tenths, and then 10 tenths. If I'm taking the larger, if I'm taking the larger square, instead of dividing it into hundredths, I divide it into tenths. And all I'm doing here, is I'm dividing the larger thing into tents, into tenths, I should say. One is, you could think about dividing this larger, larger square into tenths, so this would be a tenth right over here, that would be a tenth, this would be another tenth, that's two tenths. Now, 40 hundredths is the same thing as four tenths. Here, we’ll only consider trend and seasonal decompositions. More extensive decompositions might also include long-run cycles, holiday effects, day of week effects and so on. This is 10, 20, 30, 40 hundredths, plus, one, two, three, four,įive, six, seven hundredths. Decomposition procedures are used in time series to describe the trend and seasonal factors in a time series. You see that over here,ġ0, 20, 30, 40 hundredths. Alright, so let's, let'sĬould say immediately, is we could say that 47 over 100 is equal to 40 hundredths, 40 hundredths. And my question to you is, what is the star going to be equal to? The star is equal to what? And pause the video to I wanna write it as four over 10, plus, plus something over 100. I wanna write it as 40 over, actually lemme write it this way. Now what I'm curious about is, I wanna break up this fraction. Hundredths of the entire, of the entire whole. ![]() Or you could say that this, what's shaded in in blueĪnd green right over here, this represents 47 hundredths. So over here, we have colored in 47 out of 100 equal, smaller squares. So this, this picture right over here, we've taken this square, we've divided it into 100Įqual, smaller squares, and then we've colored in, let's see how many we've colored in.
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