![]() These activities are about helping students understand the underlying concepts behind manipulatives as effective teaching and learning tools. The manipulatives in this unit have been designed to enable students to actually compose and decompose numbers, feeling and thinking about what they are doing and in the process, building a fundamental understanding of what to do. They offer a concrete representation of abstract mathematical ideas. Manipulatives are objects that students can handle for themselves. However, if students do not understand the meaning behind the algorithms before they start, they may forget what to do and make unnecessary mistakes. The ultimate goal is that students will be able to use addition and subtraction algorithms fluently for all types of numbers. ![]() Number is a very abstract concept, even though it is used extensively in society. Your students will take time to develop number concepts. Allowing students to first fully understand the concept of composition – that is, how the number system works in groups of tens, hundreds, tenths and so on – will help when they learn how to subtract. Written addition and subtraction algorithms depend on composition and decomposition, and on re-grouping, especially when the numbers are more than single digits. They may notice that larger numbers can be decomposed into more groups or sets, while smaller numbers might only be decomposed once or twice.TI-AIE: Using manipulatives: decomposition and regrouping What this unit is about It would be helpful if you wrote down the various numbers that you can take apart so learners can see what numerals make up the numbers. Let them help you split them up in different ways. Demonstrate to your young learner that this group of pencils can be split up into several different arrangements. Get a group of twelve pencils and separate them into two piles. It’s important to stress that no matter what “position” the number is in, the result is the same.ĭecomposing numbers with kids can be just as fun. Place them together and recount the pencils. Now, switch around the pencils so that you’re holding the amount they had and they are holding the amount you had. They will get extra practice with their counting skills too! You can count the bunch of pencils as you put them in a pile together. Now, explain that you’re going to compose them by putting them together. You could let your young learner select a few pencils to hold in their hand, then you can put a few in your hand. ![]() You could use pencils to illustrate your point and make a little game out of it. Since kids will learn best when using their hands and objects, get a few objects to show them how this concept of composing and decomposing numbers works. Composing and Decomposing Numbers in Everyday Life Larger numbers can be decomposed into more sets. For example, the number six can be split up into the numbers three and two or five and one. Help your students see that there is often more than one way to decompose a number. Teaching young learners about decomposing numbers involves breaking a larger number into smaller numbers. For now, you might want to stick with no more than three numbers when working with young ones. They can compose two, three, or even four numbers. The other great thing you can teach your young learners is that there is no limit on how many numbers they put together. You can compose a number in more than one way!
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