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Allowing students time to play with the discs will help them grasp the concept of the different forms of a decimal. You can use and display this frame: "My number is ____. You can show this in the traditional way as well, but we want students to see that, as we get 12 tenths, another name for that is one and two tenths. Then we look at those tens.
Don't forget to check out the video in our video library – the Math Might Subtraction Showdown (scroll down for the decimal video)! But now, we're in trouble. Once students show an understanding of how to make numbers using the disks, move on to the representational level. All of these activities and resources provide opportunities for students to really develop a foundation of understanding for division. Let this be an inquiry-based exercise – pose the problem and leave it there. The 10-frames aren't labeled because, with non-proportional manipulatives there would be no need to label the place value. Once students are familiar with the value of numbers and can easily recognize and build the different forms of a number, we can move into solving different kinds of problems with the place value discs. Draw place value disks to show the numbers lesson 13. We usually first look at D. C. for decomposing and composing to make a friendly number, then Abracus to show compensation, and Value Pak for Partial Sums. Adding that 100 to three hundreds, it becomes four hundreds, leaving nothing in the tens place. For example, in Kindergarten and in first grade, we don't have any activities that use the non-proportional discs because, at that age developmentally, they're learning to count and they're learning to understand our number system. I think students do not get enough hands-on experience to really fluidly understand what they're learning with decimals before they're pushed into the traditional method of subtraction. We also want to help students see what happens when adding more flips to a different place value. You can definitely write in the labels at the top until students get used to using the mat and know where each place value goes. For example, you can use the mat and disks to help students with expanded notation when adding and subtracting.
End with the abstract. Have students cut out the disks. Explain place value disks. Or if I had 12, and I wanted to divide it into four equal groups, how many would be in each? So, again, we subtract 12 from 14 and we're left with the remainder, which will also be left with the discs. We DO NOT want to say "carry" because we're not actually carrying anything. In our second example, we have one and 37 hundredths (1. Connect: Link school to home. Before we get into the traditional method, it's really important to have students add 10 more to a number like 398, where they are going to be required to flip into the next place value with a regroup. Right away, students should be able to see that we have one and two tenths (1. Modeling with Number Disks (solutions, worksheets, lesson plans, videos. Students who learn and think differently may have trouble making a connection between our base 10 number system and the language we use for numbers. As students move on to start regrouping, it's really important to go slow and make sure students are attending to place value! What would be 10 less?
Invite students to explain what they placed in each column and say the standard number. After setting up the problem, let the students make groups. I certainly could never do this with a proportional tool like base-10 blocks because it would be too clunky and messy for students. Add 100 more by adding one orange hundreds disc to the mat, and simultaneously, change the value of the number with the place value strips. But that's not actually the case. Then, as they physically take one of the red tens discs away, they will also make the change in their place value strips. In the early elementary grades, students should have learned that the value of a digit depends on its place in a number. Draw place value disks to show the numbers 4. Many students will really benefit from acting out the process of adding one tenth more or even one hundredth more, you could even have them show one whole more. Students can choose a bottom or top regroup, either works well. In the pictures, you can see how we underline the 13 and draw an arrow so students can see that 13 actually equals 130 because we technically have 13 tens.
In a traditional addition problem, we'll start by building the first addend on the mat. Showing the change in value in a conceptual way will help the concept click so much faster. It's important here for students to see a decimal number in word form, then build it, then write it in numerical form. After mastering the representational level, move on to the abstract level. Draw place value disks to show the numbers. Model how to draw circles on the place value mat: Draw a circle in the appropriate column and write the corresponding number (1, 10, 100, or 1, 000) in the circle. Again, just like we do with multiplication, students can use counters or one-inch square tiles to physically see how division works with smaller quantities before you jump into using place value discs. You could use place value to show the groups in a linear way (see picture). Start with the concrete. Students who struggle with fine motor skills may find it difficult to cut out or handle paper disks. Then, you can move on to this strategy of using place value disks with larger numbers. It can be a challenge to wrap your mind around, but slowing it down and acting it out can really help students see what they're doing.
They can see it, they can manipulate the discs and then learn to visualize the idea as well. The mat and disks can help students with rounding to the nearest ten, hundred, or thousand. It is essential that we do a lot of this kind of work before we move into using the place value discs. Our fact flap cards are a really great tool for this! Students already find the idea of a number smaller than one slightly confusing, so we need to give them a chance to develop familiarity with this concept. Let's look at the "groups of" concept for decimals.
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