Teaching Decimal Operations This resource is principally concerned with student's understanding of decimal notation, not with their ability to compute with decimals. This is because understanding the meaning of the numbers is fundamental to both interpreting answers to computation and remembering algorithms. Inadequate understanding underlies many of the difficulties that students have with computation and "simple" procedures such as rounding and understanding significant figures and scientific notation. Here is a summary of some key points. The CD-ROM resource "Foundations for Teaching Arithmetic" explains these ideas fully. Key Ideas for Addition and Subtraction: Only quantities of the same magnitude can be added or subtracted, so tenths must be added to or subtracted from tenths, hundredths with hundredths, etc. In the base ten system, "trading" bundles of ten for one in the next column on the left is needed so that no column holds more than nine. Concrete models, such as LAB, MAB or an abacus, demonstrate this well. The similarity of the algorithms for addition and subtraction for whole numbers and decimals means that students have few problems. The main difficulty is dealing with "ragged decimals" (e.g. 0.38 + 0.4), which requires understanding of decimal notation. Key Ideas for Multiplication and Division: A range of meanings of multiplication must be understood. If multiplication is only understood as repeated addition, multiplication by a decimal does not make sense. For example, if 3 x 0.98 is only understood as 0.98+0.98 +0.98, then 0.29 x 0.98 is meaningless. One approach using an area model. A range of meanings of division must be understood. If division is only understood as sharing then division by a decimal does not make sense. For example, if 0.45 divided by 3 is only understood as "share 0.45 into 3 equal parts", then 0.45 divided by 0.15 does not make any sense. Teach operations in the following order: Phase 1: Multiplying and dividing by ten (it fits the decimal system!) Multiplying and dividing by powers of ten (e.g. 1000)( Lesson plan) Phase 2: Multiplying/dividing decimals by small whole numbers (e.g. 3) Multiplying/dividing by multiples of ten (e.g. 20) Multiplying/dividing by any whole number (e.g. 23) Phase 3: Multiplying/dividing by decimals less than one. (This requires special activities to develop meanings). Note that concrete models cannot adequately explain all of the ideas involved. Students need to understand and generalize the mathematical principles.