· Addition and subtraction of decimals may be investigated using a variety of models (e.g., 10-by-10 grids, number lines, money). · Decimal computation uses similar procedures as those developed for whole number computation and applies them to decimal place values, giving careful attention to the placement of the decimal point in the solution. · Multiplication of decimals follows the same procedure as multiplication of whole numbers. The only difference is that a decimal point must be correctly placed in the product giving careful attention to the placement of the decimal point in the solution. · The product of decimals is dependent upon the two factors being multiplied. · In cases where an exact product is not required, the product of decimals can be estimated using strategies for multiplying whole numbers, such as front-end and compatible numbers, or rounding. In each case, the student needs to determine where to place the decimal point to ensure that the product is reasonable. · Division is the operation of making equal groups or shares. When the original amount and the number of shares are known, divide to find the size of each share. When the original amount and the size of each share are known, divide to find the number of shares. Both situations may be modeled with Base-10 manipulatives. · The fair-share concept of decimal division can be modeled, using manipulatives (e.g., Base-10 blocks). · Division with decimals is performed the same way as division of whole numbers. The only difference is theplacement of the decimal point in the quotient. · The quotient can be estimated, given a dividend expressed as a decimal through thousandths (and no adding of zeros to the dividend during the division process) and a single-digit divisor. · Estimation can be used to check the reasonableness of a quotient. · Terms used in division are *dividend, divisor*, and *quotient.* *dividend **¸** divisor = quotient* * quotient* * divisor )dividend*
· A multistep problem needs to incorporate no more than two operational steps (operations can be the same or different). | **All students should**
· Use similar procedures as those developed for whole number computation and apply them to decimal place values, giving careful attention to the placement of the decimal point in the solution. · Select appropriate methods and tools from among paper and pencil, estimation, mental computation, and calculators according to the context and nature of the computation in order to compute with decimal numbers. · Understand the various meanings of *division* and its effect on whole numbers. · Understand various representations of division, i.e., *dividend **¸** divisor = quotient* * quotient*
* divisor*
* ** = quotient.*
| **The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to**
· Determine an appropriate method of calculation to find the sum, difference, product, and quotient of two numbers expressed as decimals through thousandths, selecting from among paper and pencil, estimation, mental computation, and calculators. · Estimate to find the number that is closest to the sum, difference, and product of two numbers expressed as decimals through thousandths. · Find the sum, difference, and product of two numbers expressed as decimals through thousandths, using paper and pencil, estimation, mental computation, and calculators. · Determine the quotient, given a dividend expressed as a decimal through thousandths and a single-digit divisor. For example, 5.4 divided by 2 and 2.4 divided by 5. · Use estimation to check the reasonableness of a sum, difference, product, and quotient. · Create and solve single-step and multistep problems. · A multistep problem needs to incorporate two or more operational steps (operations can be the same or different). |