This will help you to develop a more learner-focused teaching environment. When you are ready, use the activities with your students and reflect again on the way the activity went and the learning that happened. Trying for yourself will mean you get insights into a learner’s experiences that can in turn influence your teaching and your experiences as a teacher. It would be even better if you could try them out with a colleague as that will help you when you reflect on the experience. Make sure that your students understand the ‘count all together’ method of counting before doing the next activity, which is designed to help them understand that if the units ‘make a ten’ then you add that ten onto the other tens.īefore attempting to use the activities in this unit with your students, it would be a good idea to complete all, or at least part, of the activities yourself. These can be easily ripped into singles in order to show decomposition. Two of the activities in this unit use strips of paper with 10 dots on them to represent tens. Once students have a secure understanding of how numbers are composed then decomposition makes much more sense!įigure 6 Bringing real money into the classroom. One way to be sure that they do understand is to check that they are able to articulate the way that numbers are composed. The students need to clearly understand that numbers are made up in this way before they start to add or subtract them. Note that there are no ‘tens’ recorded, which might confuse the students with the number 97. It is important not to forget to use examples of numbers containing a zero so that the students understand that sometimes there are no tens and/or no units.įor example, the number 907 is made up (or composed) of 9 hundreds and 7 units. The number 35.7 is made up (or composed) of three tens, five ones and seven tenths:ģ × 10 + 5 × 1 + 7 × 0.1 = 30 + 5 + 0.7 = 35.7 The decimal system is used world-wide and students will need to understand that numbers in differing positions have different values, and that a whole number is composed of those values.įor example, the number 357 is made up (or composed) of three hundreds, five tens and seven ones:ģ × 100 + 5 × 10 + 7 × 1 = 300 + 50 + 7 = 357 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. TI-AIE: Using manipulatives: decomposition and regrouping What this unit is about
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